Some properties of positive one-peak posets and tables of
their Tits roots
Marcin Gąsiorek (Toruń) and Daniel Simson (Toruń)
∗
Faculty of Mathematics and Computer Science, Nicolaus Copernicus University
ul. Chopina 12/18, 87-100 Toruń, Poland
31 March 2012
Abstract
A complete list of positive Tits one-peak posets with at most 9 vertices is given. For
every such a poset I we list its Tits roots, number of Tits-sincere roots and the matrix
bI with its transpose. In the last
BI ∈ MI (Z) defining Z-congruency of the Tits matrix C
section we present sources of the algorithms used for the computations. See [1]-[3] for
details.
1
Introduction
We denote by N ⊆ Z ⊆ Q the set of non-negative integers, the ring of integers and the rational
number field. We denote by Mm (Z) the Z-algebra of all square m by m matrices, and by
E ∈ Mm (Z) the identity matrix. By a poset J ≡ (J, ) we mean a partially ordered set J with
respect to a partial order relation . Obviously, J is uniquely determined by its incidence
matrix CJ ∈ Mm (Z), that is, the integer square m × m matrix
(
1, for i j,
CJ = [cij ]i,j∈J ∈ Mm (Z) = MJ (Z), with cij =
0, for i 6 j,
where m = |J|. Throughout, we make the identifications Mm (Z) ≡ MJ (Z) and Zm ≡ ZJ .
A poset I is called a one-peak poset if I has a unique maximal element ∗. Throughout
we assume that I is a one-peak poset of the form I = {1, 2, . . . , n, ∗ = n + 1}, with a unique
maximal element ∗ = n + 1, and
tr
1.
C
−u
T
bI =
∈ Mn+1 (Z), with u = .. ,
C
0
1
1
is the Tits matrix of I, where CT ∈ MT (Z) = Mn (Z) is the incidence matrix of the poset
T = I \ {∗} = {1, 2, . . . , n}, see [7]–[8]. The Tits quadratic form qbI : ZI → Z of such a poset
I = {1, 2, . . . , n, ∗ = n + 1} is defined by the formula
X
bI · xtr .
(1.3)
qbI (x) = x21 + · · · + x2n + x2n+1 +
xi xj − (x1 + · · · + xn )xn+1 = x · C
i≺j≤n
I
n+1
We denote by qI , q I : Z ≡ Z
→ Z the incidence quadratic form and the Euler quadratic
form of I defined by the formulae
∗
e-mail: [email protected], [email protected]
1
qI (x) =
P
j∈I
x2j +
P
i≺j
xi xj = x · CI · xtr
q I (x) = x · C I · xtr ,
where C I = CI−1 ∈ Mn+1 (Z) is the Euler matrix of I, see we call I positive if each (or some) of
the forms qbI , qI , and q I is positive, that is, qbI (v) > 0, for any v = (v1 , . . . , vn , vn+1 ) ∈ ZI ≡ Zn+1 .
The poset I is defined to be Tits-sincere, if qbI has a sincere Tits root v ∈ ZI , that is, a
vector v ∈ ZI such that qbI (v) = 1 and each of its coordinates v1 , . . . , vn , vn+1 is non-zero, see
[2], [4], [6], [7]. Given a poset I, we denote by sI the number of sincere Tits roots of I, that is,
the sincere roots of the Tits form qbI of I.
In [1]-[2], we study the positive one-peak posets I in relation with the simply-laced Dynkin
diagrams
Simply-laced Dynkin diagrams
Am :
Dm :
E6 :
E7 :
E8 :
•1−−−−
•2−−−−
•3−−−− . . . −−−−
•−−−−
•m
(m vertices, m ≥ 1);
•2
|
•1−−−− •3 −−−−
•4−−−− . . . −−−−
•−−−−
•m
(m vertices, m ≥ 4);
•4
|
•1−−−−
•2−−−−
•3 −−−−
•5−−−−
•6 ;
•4
|
•1−−−−
•2−−−−
•3 −−−−
•5−−−−
•6−−−−
•7 ;
•4
|
•1−−−−
•2−−−−
•3 −−−−
•5−−−−
•6−−−−
•7−−−−
•8 ;
It is shown in [2] (see also [5] and [9]) that, given a positive one-peak poset I, there is a simplylaced Dynkin diagram ∆I ∈ {An+1 , Dn+1 , E6 , E7 , E8 } (uniquely determined by I and called the
Coxeter-Dynkin type of I) such that the Coxeter polynomial
bI · C
b−tr ) = det(t · E + C −1 · C tr ) ∈ Z[t]
coxI (t) := det(t · E + CI · CI−tr ) = det(t · E + C
I
I
I
of I (see [8]) coincides with the Coxeter polynomial F∆I (t) of the diagram ∆I , where
 m
for ∆ = Am , m ≥ 1,
 t + tm−1 + · · · + t2 + t + 1, c∆ = m + 1,


m
m−1

+ t + 1,
c∆ = 2(m − 1), for ∆ = Dm , m ≥ 4,
 t +t
6
5
3
t + t − t + t + 1,
c∆ = 12,
for ∆ = E6 ,
(1.6)
F∆ (t) :=

7
6
4
3

t
+
t
−
t
−
t
+
t
+
1,
c
=
18,
for ∆ = E7 ,

∆

 8
7
5
4
3
t + t − t − t − t + t + 1, c∆ = 30,
for ∆ = E8 ,
and c∆ is the Coxeter number of ∆.
2
List of positive posets
In this section we present a complete list of positive Tits one-peak posets with at most 9 vertices.
For every such a poset I we list its Tits roots, number of Tits-sincere roots and the matrix
bI with its transpose, that is matrix B
BI ∈ MI (Z) defining Z-congruency of the Tits matrix C
such that
bItr = B · C
bI · B tr , and B 2 = E.
C
2.1
2.1.1
Posets with 1 vertex
Posets of type A1
• I ≡ 0 A∗0 :
1
2
CI =
b I =
Cox
bI =
C
1
−1
1
BI =
1
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1 ],
2.2
2.2.1
[1]
Posets with 2 vertices
Posets of type A2
• I ≡ 0 A∗1 :
1
∗
CI =
1
0
0
−1
b I=
Cox
1
1
1
−1
−1
1
1
0
bI =
C
BI =
1
−1
0
−1
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1 ],
2.3
2.3.1
[ 1,1 ],
[ −1,0 ],
[ 0,−1 ],
[ 0,1 ],
[ 1,0 ]
Posets with 3 vertices
Posets of type A3
• I ≡ 0 A∗2 :
1
2
∗

1
CI = 0
0

b I =
Cox
0
0
−1

1
1 
1
1
1
0
1
0
0

1
1 
−1
3

bI =
C
1
1
0

0
1
0
0
BI = 0
1

−1
−1 
1
1
1
−1

1
0 
0
Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,0,−1 ],
[ −1,0,0 ],
• I ≡ 1 A∗2 :
[ −1,1,0 ],
[ 0,−1,−1 ],
[ 0,−1,0 ],
[ 0,0,−1 ],
[ 0,0,1 ],
[ 0,1,0 ],
[ 0,1,1 ],
[ 1,−1,0 ],
[ 1,0,0 ],
[ 1,0,1 ]
∗
1
2

1
CI = 0
0

0
1
−1
b I =
Cox
0
1
0
1
0
−1

1
1 
1

bI =
C

1
1 
−1
1
0
0
0
1
0

1
0
−1
BI =

−1
−1 
1
0
1
−1

0
0 
−1
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−1 ],
2.4
2.4.1
[ −1,0,−1 ],
[ 1,1,1 ],
[ −1,0,0 ],
[ 0,−1,−1 ],
[ 0,−1,0 ],
[ 0,0,−1 ],
[ 0,0,1 ],
[ 0,1,0 ],
[ 0,1,1 ],
Posets with 4 vertices
Posets of type A4
• I ≡ 0 A∗3 :
1
2
∗
3

1

CI = 00
0

b I =
Cox

0
0
0
−1
1
1
0
0
1
1
1
0

1
1 

1 
1
1
0
0
0
0
1
0
0

1
1 

1 
−1

1
bI = 1
C
 1
0
0
1
1
0
0
0
1
0

−1
−1 

−1 
1

−1
0
0
0
0
0
0
1
1
1
1
−1

BI =

0
1 

0 
0
Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,0, 0,−1 ],
[ 0,0,−1,−1 ],
[ 0,1, 0, 0 ],
[ −1,0, 0,0 ],
[ 0,0,−1,0 ],
[ 0,1, 0,1 ],
[ −1, 0,1, 0 ],
[ 0, 0,0,−1 ],
[ 1,−1,0, 0 ],
[ −1,1, 0,0 ],
[ 0,0, 0,1 ],
[ 1,0,−1,0 ],
4
[ 0,−1,0,−1 ],
[ 0, 0,1, 0 ],
[ 1, 0,0, 0 ],
[ 0,−1,0,0 ],
[ 0, 0,1,1 ],
[ 1, 0,0,1 ]
[ 0,−1, 1,0 ],
[ 0, 1,−1,0 ],
[ 1,0,0 ],
[ 1,0,1 ]
1
• I ≡ 2 A∗3 :
∗
2
3


1
1 

1 
1
1

CI = 00
0
1
1
0
0
0
0
1
0

1
0
0
0
1
1
0
−1
0
b I = 0
Cox
 1
−1

1
bI = 1
C
 0
0

1
1 

1 
−1
0
1
0
0

0

BI = 01
0
0
0
1
0

−1
−1 

−1 
1
1
1
0
−1
1
0
0
0

1
0 

1 
−1
Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,0,−1,−1 ],
[ 0,0,−1,−1 ],
[ 0,1, 0, 1 ],
2.4.2
[ −1,0, 0,−1 ],
[ 0,0,−1, 0 ],
[ 0,1, 1, 1 ],
[ −1, 0,0, 0 ],
[ 0, 0,0,−1 ],
[ 1,−1,0, 0 ],
[ −1,1,0,0 ],
[ 0,0,0,1 ],
[ 1,0,0,0 ],
[ 0,−1,−1,−1 ],
[ 0, 0, 1, 0 ],
[ 1, 0, 0, 1 ],
[ 0,−1,0,−1 ],
[ 0, 0,1, 1 ],
[ 1, 0,1, 1 ]
[ 0,−1,0,0 ],
[ 0, 1,0,0 ],
Posets of type D4
• I ≡ D∗3 :
2
∗
3
1

1
 0

CI = 0
0
0
1
0
0

1
1 

1 
1
1
1
1
0

b I =
Cox

0
1
0
−1

1
 0
b

CI = 1
0
1
0
0
−1
0
0
0
1
0
1
1
0
0
0
1
0

−1
−1 

−1 
1

1
1 

1 
−1
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,1,−1 ],
[ 0, −1,0, −1 ],
[ 0, 0,1, 0 ],
[ 1, 0,0, 1 ],
[ −1,−1, 0,−1 ],
[ 0,−1, 1, 0 ],
[ 0, 1,−1, 0 ],
[ 1, 1, 0, 1 ]
[ 1, 1,−1,1 ],
[ 0,−1, 0,0 ],
[ 0, 0, 1,1 ],
[ 1, 1, −1,0 ],
b ∗ A1 :
• I≡D
2
1
[ −1,−1, 1, 0 ],
[ 0, 0,−1,−1 ],
[ 0, 1, 0, 0 ],
2
3
∗
5
[ −1,0, 0,−1 ],
[ 0,0,−1, 0 ],
[ 0,1, 0, 1 ],
[ −1,0, 0, 0 ],
[ 0,0, 0,−1 ],
[ 1,0,−1, 0 ],
[ −1,0,1,0 ],
[ 0,0,0,1 ],
[ 1,0,0,0 ],

1

CI = 00
0
1
1
0
0
1
0
1
0

1
1 

1 
1

0
b I = 0
Cox
 0
−1

1
bI = 1
C
 1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0

−1
−1 

−1 
1

1
1 

1 
−1
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 1, 1, 1 ],
[ 0,−1,−1,−1 ],
[ 0, 0, 1, 0 ],
[ 1, 0,−1, 0 ],
[ −1, 0,0,−1 ],
[ 0,−1,0, 0 ],
[ 0, 1,0, 0 ],
[ 1, 0,0, 1 ]
[ 1,−1,−1,−1 ],
[ 0, −1, 0, −1 ],
[ 0, 0, 1, 1 ],
[ 1, 0, 0, 0 ],
[ −1,0, 0, 0 ],
[ 0,0,−1,−1 ],
[ 0,1, 0, 1 ],
[ −1,0, 1,0 ],
[ 0,0,−1,0 ],
[ 0,1, 1,1 ],
[ −1, 1, 0, 0 ],
[ 0, 0, 0,−1 ],
[ 1,−1,−1, 0 ],
[ −1, 1,1,0 ],
[ 0, 0,0,1 ],
[ 1,−1,0,0 ],
1
• I≡
∗
0 D2
A1 :
∗
2
3

1

CI = 00
0
0
1
0
0
0
0
1
0

1
1 

1 
1

0
b I = 1
Cox
 1
−1

1
bI = 0
C
 0
0
1
0
1
−1
1
1
0
−1
0
1
0
0
0
0
1
0

−1
−1 

−1 
1

1
1 

1 
−1
Number of sincere Tits roots of poset I sI = 4.
Table of roots of qbI
[ −1,−1,−1,−2 ],
[ −1, 0, 0, 0 ],
[ 0, 0, 0, 1 ],
[ 1, 0, 0, 1 ],
2.5
2.5.1
[ −1,−1,−1,−1 ],
[ 0, −1, −1, −1 ],
[ 0, 0, 1, 0 ],
[ 1, 0, 1, 1 ],
[ 1, 1,1, 1 ],
[ 0,−1,0,−1 ],
[ 0, 0,1, 1 ],
[ 1, 1,0, 1 ]
[ 1, 1,1,2 ],
[ 0,−1,0,0 ],
[ 0, 1,0,0 ],
Posets with 5 vertices
Posets of type A5
• I ≡ 0 A∗4 :
1
2
3
4
∗
6
[ −1,−1, 0,−1 ],
[ 0, 0,−1,−1 ],
[ 0, 1, 0, 1 ],
[ −1,0,−1,−1 ],
[ 0,0,−1, 0 ],
[ 0,1, 1, 1 ],
[ −1,0,0,−1 ],
[ 0,0,0,−1 ],
[ 1,0,0, 0 ],
1
 0
CI = 0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
−1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
−1



b I =
Cox

1
 1
bI = 1
C
 1
0

0
1
1
1
0











BI =
0
−1
0
0
0

0
0
1
1
0
−1
−1
−1
−1
1
0
0
0
1
0
−1
0
0
0
0
0
0
0
0
1





1
1
1
1
−1
0
0
1
0
0





Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0,0,−1 ],
[ 0,−1, 0,0,−1 ],
[ 0, 0,−1,0, 0 ],
[ 0, 0, 0,0, 1 ],
[ 0, 0, 1,0, 1 ],
[ 1,−1, 0,0, 0 ],
• I ≡ 3 A∗4 :
1
[ −1, 0, 0,0,0 ],
[ 0,−1, 0,0,0 ],
[ 0, 0,−1,1,0 ],
[ 0, 0, 0,1,0 ],
[ 0, 1,−1,0,0 ],
[ 1, 0,−1,0,0 ],
2
[ −1, 0,0, 1, 0 ],
[ 0,−1,0, 1, 0 ],
[ 0, 0,0,−1,−1 ],
[ 0, 0,0, 1, 1 ],
[ 0, 1,0,−1, 0 ],
[ 1, 0,0,−1, 0 ],
[ −1, 0,1, 0,0 ],
[ 0,−1,1, 0,0 ],
[ 0, 0,0,−1,0 ],
[ 0, 0,1,−1,0 ],
[ 0, 1,0, 0,0 ],
[ 1, 0,0, 0,0 ],
[ −1,1, 0,0, 0 ],
[ 0,0,−1,0,−1 ],
[ 0,0, 0,0,−1 ],
[ 0,0, 1,0, 0 ],
[ 0,1, 0,0, 1 ],
[ 1,0, 0,0, 1 ]
∗
3
4
1
 0

CI = 0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
−1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
−1



b I =
Cox

1
1
1
1
1
1
 1

bI = 1
C
 0
0






1
1
1
1
−1





0
1
1
0
0
0
 0

BI = 0
−1
1

0
0
1
0
0
−1
−1
−1
−1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
−1





0
1
0
0
0
1
1
0
0
0





Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0,−1,−1 ],
[ 0,−1, 0,−1,−1 ],
[ 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1 ],
[ 1,−1, 0, 0, 0 ],
• I ≡ 2 A∗4 :
1
[ −1, 0, 0,0,−1 ],
[ 0,−1, 0,0,−1 ],
[ 0, 0,−1,0, 0 ],
[ 0, 0, 0,1, 0 ],
[ 0, 1,−1,0, 0 ],
[ 1, 0,−1,0, 0 ],
∗
2
3
[ −1, 0,0, 0, 0 ],
[ 0,−1,0, 0, 0 ],
[ 0, 0,0,−1,−1 ],
[ 0, 0,0, 1, 1 ],
[ 0, 1,0, 0, 0 ],
[ 1, 0,0, 0, 0 ],
4
7
[ −1, 0,1, 0,0 ],
[ 0,−1,1, 0,0 ],
[ 0, 0,0,−1,0 ],
[ 0, 0,1, 0,0 ],
[ 0, 1,0, 0,1 ],
[ 1, 0,0, 0,1 ],
[ −1,1, 0, 0, 0 ],
[ 0,0,−1,−1,−1 ],
[ 0,0, 0, 0,−1 ],
[ 0,0, 1, 0, 1 ],
[ 0,1, 0, 1, 1 ],
[ 1,0, 0, 1, 1 ]
1
 0
CI = 0
0
0
1
1
0
0
0



b I =
Cox

0
0
1
1
−1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
−1
0
0
1
0
0
1
1
1
1
−1
1
 1
bI = 0
C
 0
0

0
1
0
0
0











BI =

0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
−1
−1
−1
−1
1
1
1
0
0
−1
1
0
0
0
0
0
0
1
1
−1





1
0
1
0
−1





Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0,−1,0,−1 ],
[ 0,−1,−1,0,−1 ],
[ 0, 0,−1,0, 0 ],
[ 0, 0, 0,0, 1 ],
[ 0, 0, 1,0, 1 ],
[ 1,−1, 0,0, 0 ],
2.5.2
[ −1, 0, 0,−1,−1 ],
[ 0,−1, 0,−1,−1 ],
[ 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 1, 0 ],
[ 0, 1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0 ],
[ −1, 0,0, 0,−1 ],
[ 0,−1,0, 0,−1 ],
[ 0, 0,0,−1,−1 ],
[ 0, 0,0, 1, 1 ],
[ 0, 1,0, 0, 1 ],
[ 1, 0,0, 0, 1 ],
[ −1, 0,0, 0,0 ],
[ 0,−1,0, 0,0 ],
[ 0, 0,0,−1,0 ],
[ 0, 0,1,−1,0 ],
[ 0, 1,0, 1,1 ],
[ 1, 0,0, 1,1 ],
[ −1,1, 0,0, 0 ],
[ 0,0,−1,0,−1 ],
[ 0,0, 0,0,−1 ],
[ 0,0, 1,0, 0 ],
[ 0,1, 1,0, 1 ],
[ 1,0, 1,0, 1 ]
Posets of type D5
• I ≡ D∗4 :
2
3
∗
4
1
1
 0
CI = 0
0
0



b I =
Cox

0
1
1
0
−1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
−1
0
1
0
0
0
0
−1
0
0
1
1
 0
bI = 0
C
 1
0






1
1
1
1
−1






BI =

0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
−1
−1
−1
−1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
−1





0
0
0
−1
0





Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−1, 1,−1 ],
[ −1, 0, −1, 0, −1 ],
[ −1, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, −1 ],
[ 0, 0, 1, 0, 0 ],
[ 0, 1, 0, 0, 1 ],
[ 1, 0, 1,−1, 1 ],
[ 1, 1, 1,−1, 1 ],
[ −1, 0,−1, 1,−1 ],
[ 0,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1 ],
[ 1, 0, 0, −1, 0 ],
[ 1, 0, 1, 0, 1 ],
[ −1,−1, 0, 0,−1 ],
[ −1, 0,−1, 1, 0 ],
[ 0,−1, 0, 0, 0 ],
[ 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 1, 0 ],
[ 0, 1,−1, 0, 0 ],
[ 1, 0, 0, 0, 0 ],
[ 1, 1, 0,−1, 0 ],
8
[ −1,−1,0, 1,−1 ],
[ −1, 0,0, 0,−1 ],
[ 0,−1,0, 1, 0 ],
[ 0, 0,0,−1,−1 ],
[ 0, 0,0, 1, 1 ],
[ 0, 1,0,−1, 0 ],
[ 1, 0,0, 0, 1 ],
[ 1, 1,0,−1, 1 ],
[ −1,−1,0, 1,0 ],
[ −1, 0,0, 0,0 ],
[ 0,−1,1, 0,0 ],
[ 0, 0,0,−1,0 ],
[ 0, 0,1,−1,0 ],
[ 0, 1,0, 0,0 ],
[ 1, 0,1,−1,0 ],
[ 1, 1,0, 0,1 ]
1
• I ≡ 0 D∗4 A0 :
2
3
1
 0

CI = 0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
−1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
−1



b I =
Cox

∗
4
0
1
0
0
−1
1
 0

bI = 1
C
 1
0
0
1
1
1
0







BI =
−1
0
0
0
0






0
0
1
1
0
−1
−1
−1
−1
1
0
0
0
1
0
0
−1
0
0
0
0
0
0
0
1





1
1
1
1
−1
0
0
1
0
0





Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0,0,−1 ],
[ −1,−1, 1,1, 0 ],
[ 0,−1, 0,0,−1 ],
[ 0, 0,−1,0, 0 ],
[ 0, 0, 0,0, 1 ],
[ 0, 0, 1,0, 1 ],
[ 1, 0,−1,0, 0 ],
[ 1, 1,−1,0, 0 ],
[ −1,−1, 0, 1,−1 ],
[ −1, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0 ],
[ 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 1, 0 ],
[ 0, 1,−1, 0, 0 ],
[ 1, 0, 0,−1, 0 ],
[ 1, 1,−1, 0, 1 ],
[ −1,−1,0, 1, 0 ],
[ −1, 0,0, 0, 0 ],
[ 0,−1,0, 1, 0 ],
[ 0, 0,0,−1,−1 ],
[ 0, 0,0, 1, 1 ],
[ 0, 1,0,−1, 0 ],
[ 1, 0,0, 0, 0 ],
[ 1, 1,0,−1, 0 ],
[ −1,−1,1, 0,−1 ],
[ −1, 0,0, 1, 0 ],
[ 0,−1,1, 0, 0 ],
[ 0, 0,0,−1, 0 ],
[ 0, 0,1,−1, 0 ],
[ 0, 1,0, 0, 0 ],
[ 1, 0,0, 0, 1 ],
[ 1, 1,0,−1, 1 ],
[ −1,−1, 1, 0, 0 ],
[ −1, 0, 1, 0, 0 ],
[ 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0,−1 ],
[ 0, 0, 1, 0, 0 ],
[ 0, 1, 0, 0, 1 ],
[ 1, 1,−1,−1, 0 ],
[ 1, 1, 0, 0, 1 ]
1
• I≡
∗
0 D3
A1 :
2
∗
3
4


CI =


b I =
Cox

0
1
0
1
−1
1
0
0
0
0
1
0
0
1
−1
0
1
0
0
0
1
1
1
0
0
0
0
0
−1
1
0
0
0
1
0
1
1
1
0
−1
1
1
1
1
1






bI =
C

1
1
1
1
−1






1
0
1
0
0
0
1
1
0
0
0
 −1

BI = 0
0
1

0
0
1
0
0
0
0
0
1
0
−1
0
0
0
1
−1
−1
−1
−1
1
1
1
1
0
−1





0
0
0
−1
1
0
0
0
0
1





Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1, 1,−1,−1 ],
[ −1, −1, 1, 0, −1 ],
[ −1, 0, 1, 0, 0 ],
[ 1, 1,−1, 1, 1 ],
[ −1,−1, 1, 0, 0 ],
[ 0,−1, 0,−1,−1 ],
[ −1,−1, 0,−1,−2 ],
[ −1, 0, 0,−1,−1 ],
[ 0,−1, 0, 0,−1 ],
9
[ −1,−1,0,−1,−1 ],
[ −1, 0,0, 0,−1 ],
[ 0,−1,0, 0, 0 ],
[ −1,−1,0, 0,−1 ],
[ −1, 0,0, 0, 0 ],
[ 0,−1,1, 0, 0 ],
[
[
[
[
[
0,
0,
0,
0,
1,
0,−1, −1, −1 ],
0, 0, 0, −1 ],
0, 1, 0, 1 ],
1, 0, 1, 1 ],
1,−1, 0, 0 ],
[
[
[
[
[
0,
0,
0,
1,
1,
0, −1,
0, 0,
0, 1,
0, −1,
1, −1,
0,−1 ],
0, 1 ],
1, 1 ],
0, 0 ],
0, 1 ],
[
[
[
[
[
0,
0,
0,
1,
1,
0,−1,
0, 0,
1,−1,
0, 0,
1, 0,
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1

1
1
0
0
−1
0
0
1
0
0
1
1
1
1
−1
0,
1,
0,
0,
0,
0 ],
0 ],
0 ],
0 ],
1 ],
[
[
[
[
[
0,
0,
0,
1,
1,
1
 0

bI = 0
C
 0
0
0
1
0
0
0
0,0,−1,−1 ],
0,0, 1, 1 ],
1,0, 0, 0 ],
0,0, 0, 1 ],
1,0, 1, 1 ],
[
[
[
[
[
−1
−1
−1
−1
1

0,
0,
0,
1,
1,
0,0,−1,
0,1, 0,
1,0, 0,
0,0, 1,
1,0, 1,
0 ],
0 ],
1 ],
1 ],
2]
1
• I≡
∗
0 D2
A2 :
∗
2
3
4
1
 0

CI = 0
0
0



b I =
Cox

0
1
1
1
−1
0
1
0
0
0
1
0
1
1
−1












BI =
1
0
1
0
−1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
−1
1
1
0
0
−1




0
0
1
1
−1
1
1
1
0
−2





Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−1,−1,−2 ],
[ −1, −1, 0, −1, −1 ],
[ −1, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, −1 ],
[ 0, 0, 1, 0, 0 ],
[ 0, 1, 1, 0, 1 ],
[ 1, 1, 0, 0, 1 ],
• I ≡ 1 D∗4 A0 :
[ −1,−1,−1, 0,−2 ],
[ −1, 0,−1, 0,−1 ],
[ 0,−1, 0,−1,−1 ],
[ 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 1, 0 ],
[ 0, 1, 0, 0, 0 ],
[ 1, 0, 0, 0, 1 ],
[ 1, 1, 0, 1, 2 ],
[ 1, 1, 1,1, 2 ],
[ −1,−1, 0,0,−1 ],
[ 0,−1,−1,0,−1 ],
[ 0, 0,−1,0, 0 ],
[ 0, 0, 0,0, 1 ],
[ 0, 0, 1,0, 1 ],
[ 1, 0, 0,0, 0 ],
[ 1, 1, 0,1, 1 ],
1
[ −1,−1,−1, 0,−1 ],
[ −1, 0, 0,−1,−1 ],
[ 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 1 ],
[ 1, 0, 0, 1, 1 ],
[ 1, 1, 1, 0, 1 ],
[ −1,−1,0,−1,−2 ],
[ −1, 0,0, 0,−1 ],
[ 0,−1,0, 0, 0 ],
[ 0, 0,0,−1, 0 ],
[ 0, 0,1,−1, 0 ],
[ 0, 1,0, 1, 1 ],
[ 1, 0,1, 0, 1 ],
[ 1, 1,1, 0, 2 ]
2
3
∗
4


CI =


b I =
Cox

0
0
0
0
−1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
−1
0
0
0
0
1
1
1
1
0
1
1
1
1
1






bI =
C

1
1
1
1
−1






BI =

Number of sincere Tits roots of poset I sI = 0.
10

1
1
1
1
0
0
0
0
0
−1
0
1
0
1
0
0
0
1
1
0
−1
0
−1
0
1
0
0
0
1
0
−1
−1
0
0
1
−1
−1
−1
−1
1





1
1
1
1
−1
−1
0
0
0
0





Table of roots of qbI
[ −1, 0, 0, 0,−1 ],
[ −1, 1, 1,−1, 0 ],
[ 0,−1,−1, 1, 0 ],
[ 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1 ],
[ 0, 1, 1,−1, 1 ],
[ 1,−1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0 ],
[ 0,−1, 0, 0,−1 ],
[ 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 1, 0 ],
[ 0, 1, 0,−1, 0 ],
[ 0, 1, 1, 0, 1 ],
[ 1, 0,−1, 0, 0 ],
1
• I≡
∗
1 D3
[ −1, 0, 0, 1, 0 ],
[ −1, 1, 1, 0, 1 ],
[ 0,−1, 0, 0, 0 ],
[ 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 0 ],
[ 1,−1,−1, 0,−1 ],
[ 1, 0, 0,−1, 0 ],
[ −1, 0, 1, 0, 0 ],
[ 0,−1,−1, 0,−1 ],
[ 0,−1, 0, 1, 0 ],
[ 0, 0, 0,−1, 0 ],
[ 0, 0, 1,−1, 0 ],
[ 0, 1, 0, 0, 1 ],
[ 1,−1,−1, 0, 0 ],
[ 1, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0 ],
[ 0,−1,−1, 1,−1 ],
[ 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0,−1 ],
[ 0, 0, 1, 0, 0 ],
[ 0, 1, 1,−1, 0 ],
[ 1,−1,−1, 1, 0 ],
[ 1, 0, 0, 0, 1 ]
2
A1 :
∗
3
4


CI =


b I =
Cox

1
0
0
0
0
0
0
0
1
−1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
−1
1
1
1
1
1






bI =
C

1
1
1
1
−1






BI =


1
1
1
0
0
0
1
0
0
0
1
1
1
0
−1
0
0
1
0
0
0
−1
0
0
0
−1
−1
−1
−1
1
0
0
0
1
0
0
0
−1
0
0





0
0
0
1
−1
0
0
0
0
−1





Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 0 ],
[ 0,−1,−1,−1,−1 ],
[ 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0,−1 ],
[ 0, 0, 1, 0, 1 ],
[ 0, 1, 1, 0, 1 ],
[ 1,−1, 0, 0, 0 ],
b ∗ A2 :
• I≡D
2
[ 1,−1,−1,−1,−1 ],
[ −1, 1, 0, 0, 0 ],
[ 0, −1, −1, 0, −1 ],
[ 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1 ],
[ 0, 1, 1, 1, 1 ],
[ 1, 0, −1, 0, 0 ],
1
[ −1, 0, 0,−1,−1 ],
[ −1, 1, 1, 0, 0 ],
[ 0,−1, 0,−1,−1 ],
[ 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0 ],
[ 0, 1, 0, 0, 0 ],
[ 0, 1, 1, 1, 2 ],
[ 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 0,−1 ],
[ −1, 1, 1, 0, 1 ],
[ 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 1 ],
[ 1,−1,−1, 0,−1 ],
[ 1, 0, 0, 0, 1 ],
[ −1, 0, 0, 0, 0 ],
[ 0,−1,−1,−1,−2 ],
[ 0,−1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0 ],
[ 0, 0, 1, 0, 0 ],
[ 0, 1, 0, 1, 1 ],
[ 1,−1,−1, 0, 0 ],
[ 1, 0, 0, 1, 1 ]
∗
2
3
4
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
−1
1
0
0
1
0
1
1
0
0
−1


CI =


b I =
Cox

1
0
1
1
0
1
1
1
1
1
0
0
0
0
1






bI =
C

1
1
1
1
−1
11






1
1
0
1
0
0
1
0
0
0
0
 0

BI = 0
0
1

0
0
1
1
0
1
1
0
0
−1
−1
−1
−1
−1
1
0
0
0
1
0
1
0
0
1
0





0
0
1
0
−1
1
0
0
0
0





Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0,−1, 0,−1 ],
[ −1, 0, 0, 1, 0 ],
[ 0,−1,−1, 0,−1 ],
[ 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1 ],
[ 1,−1, 0,−1,−1 ],
[ 1, 0, 0, 0, 0 ],
b ∗ A1 :
• I≡D
3
[ −1, 0,−1, 1,−1 ],
[ −1, 1,−1, 1, 0 ],
[ 0,−1, 0,−1,−1 ],
[ 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 1, 0 ],
[ 0, 1, 0, 0, 0 ],
[ 1,−1, 0,−1, 0 ],
[ 1, 0, 0, 0, 1 ],
1
2
[ −1, 0,−1, 1, 0 ],
[ −1, 1, 0, 0, 0 ],
[ 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 1 ],
[ 1,−1, 0, 0, 0 ],
[ 1, 0, 1,−1, 0 ],
[ −1, 0,0, 0,−1 ],
[ −1, 1,0, 1, 0 ],
[ 0,−1,0, 0, 0 ],
[ 0, 0,0,−1, 0 ],
[ 0, 0,1,−1, 0 ],
[ 0, 1,0, 1, 1 ],
[ 1,−1,1,−1, 0 ],
[ 1, 0,1,−1, 1 ],
[ −1,0, 0, 0, 0 ],
[ −1,1, 0, 1, 1 ],
[ 0,0,−1, 0,−1 ],
[ 0,0, 0, 0,−1 ],
[ 0,0, 1, 0, 0 ],
[ 0,1, 1, 0, 1 ],
[ 1,0, 0,−1, 0 ],
[ 1,0, 1, 0, 1 ]
∗
3
4
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
−1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
−1


CI =


b I =
Cox







bI =
C


1
1
1
1
0






BI =

0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
−1
0
0
−1
1
1
0
0
1
0
1
1
1
0
−1
−1
−1
−1
−1
1





1
1
0
1
−1
1
1
0
0
0





Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,1, 1, 1, 1 ],
[ −1,0, 1, 0, 0 ],
[ −1,1, 0, 1, 1 ],
[ 0,0,−1,−1,−1 ],
[ 0,0, 0, 0,−1 ],
[ 0,0, 1, 0, 1 ],
[ 0,1, 0, 1, 1 ],
[ 1,0,−1,−1, 0 ],
2.6
2.6.1
[ 1,−1,−1,−1,−1 ],
[ −1, 0, 1, 1, 0 ],
[ 0, −1, 0, −1, −1 ],
[ 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1 ],
[ 1, −1, 0, −1, −1 ],
[ 1, 0, −1, 0, 0 ],
[ −1, 0, 0, 0,−1 ],
[ −1, 0, 1, 1, 1 ],
[ 0,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0 ],
[ 0, 1,−1, 0, 0 ],
[ 1,−1, 0,−1, 0 ],
[ 1, 0, 0,−1, 0 ],
Posets with 6 vertices
Posets of type A6
• I ≡ 0 A∗5 :
1
2
3
4
5
∗
12
[ −1, 0,0, 0, 0 ],
[ −1, 1,0, 0, 0 ],
[ 0,−1,0, 0, 0 ],
[ 0, 0,0,−1,−1 ],
[ 0, 0,0, 1, 1 ],
[ 0, 1,0, 0, 0 ],
[ 1,−1,0, 0, 0 ],
[ 1, 0,0, 0, 0 ],
[ −1, 0, 0, 1, 0 ],
[ −1, 1, 0, 1, 0 ],
[ 0,−1, 1, 0, 0 ],
[ 0, 0, 0,−1, 0 ],
[ 0, 0, 1, 0, 0 ],
[ 0, 1, 0, 0, 1 ],
[ 1, 0,−1,−1,−1 ],
[ 1, 0, 0, 0, 1 ]
1
0
0
0
0
0



CI =




b I =
Cox


0
0
0
0
0
−1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1










b
CI =

1
1
1
1
1
−1








BI =



1
1
1
1
1
0
0
1
1
1
1
0
0
0
−1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
−1
0
0
0
0
0
0
−1
0
0
0
0
−1
−1
−1
−1
−1
1
0
0
0
0
1
0
0
0
0
0
0
1







1
1
1
1
1
−1
0
0
0
1
0
0







Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0, 0,−1 ],
[ −1, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 1, 0,−1, 0 ],
[ 0, 1, 0,−1, 0, 0 ],
[ 1,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0 ],
• I ≡ 4 A∗5 :
1
[ −1, 0, 0, 0, 0,0 ],
[ −1, 1, 0, 0, 0,0 ],
[ 0,−1, 0, 1, 0,0 ],
[ 0, 0,−1, 0, 1,0 ],
[ 0, 0, 0,−1, 1,0 ],
[ 0, 0, 0, 0, 0,1 ],
[ 0, 0, 0, 1, 0,0 ],
[ 0, 0, 1, 0, 0,0 ],
[ 0, 1, 0, 0,−1,0 ],
[ 1, 0,−1, 0, 0,0 ],
[ 1, 0, 0, 0, 0,1 ]
2
3
[ −1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 1, 0, 0, 0 ],
[ 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0 ],
[ −1, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1,−1, 0, 0 ],
[ 0, 1,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 0, 0,−1, 0 ],
∗
4
5
1
0
0
0
0
0



CI =




b
CoxI =

0
0
0
0
1
−1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
−1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0










BI =

−1
0
0
0
0
0








bI =
C

1
1
1
1
1
−1



0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
−1
1
0
0
0
0
1
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1
1
1
1
1
0
−1







0
0
1
0
0
0
0
1
1
0
0
0







Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0,
[ −1, 0, 1,
[ 0,−1, 0,
[ 0, 0,−1,
0,−1,−1 ],
0, 0, 0 ],
0, 0, 0 ],
0, 0,−1 ],
[ −1, 0, 0,
[ −1, 1, 0,
[ 0,−1, 0,
[ 0, 0,−1,
0,0,−1 ],
0,0, 0 ],
1,0, 0 ],
0,0, 0 ],
[ −1, 0, 0,
[ 0,−1, 0,
[ 0,−1, 1,
[ 0, 0,−1,
13
0, 0, 0 ],
0,−1,−1 ],
0, 0, 0 ],
1, 0, 0 ],
[ −1, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0,−1,−1,−1 ],
[
[
[
[
[
[
[
0, 0,
0, 0,
0, 0,
0, 0,
0, 1,
1,−1,
1, 0,
0,−1,
0, 0,
0, 1,
1, 0,
0,−1,
0, 0,
0, 0,
0,−1 ],
0,−1 ],
0, 0 ],
0, 0 ],
0, 0 ],
0, 0 ],
0, 1 ],
1
• I ≡ 3 A∗5 :
[
[
[
[
[
[
[
2
0,
0,
0,
0,
0,
1,
1,
0, 0,−1,0,
0, 0, 0,0,
0, 0, 1,0,
0, 1, 0,0,
1, 0, 0,0,
0,−1, 0,0,
0, 0, 0,1,
0,
0,
0,
0,
0,
1,
0,
0,
0,
0,
1,
0,
0, 0,−1,−1 ],
0, 0, 1, 0 ],
0, 1, 1, 1 ],
1, 0, 1, 1 ],
0, 0, 0, 1 ],
0,−1, 0, 0 ],
1
1
1
1
1
1








bI =
C

[
[
[
[
[
[
0,
0,
0,
0,
0,
1,
0, 0, 0,−1,
0, 0, 0, 1,
0, 1,−1, 0,
1,−1, 0, 0,
1, 0, 0, 1,
0, 0, 0, 0,
0 ],
1 ],
0 ],
0 ],
1 ],
0 ],
5
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
−1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
−1



CI =



b
CoxI =

[
[
[
[
[
[
∗
3
4

0 ],
1 ],
1 ],
1 ],
0 ],
0 ],
1]
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0










BI =

0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
−1



1
1
1
1
1
−1
−1
−1
−1
−1
−1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0







1
1
0
1
1
−1







Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0,−1, 0,−1 ],
[ −1, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 1,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 1 ],
2.6.2
[ −1, 0, 0, 0,−1,−1 ],
[ −1, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 1, 1 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 1, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 1 ]
[ −1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 0,−1 ],
[ 0,−1, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, 1, 1 ],
[ 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0,−1,−1 ],
[ 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1,−1, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 0, 1 ],
Posets of type D6
• I ≡ D∗5 :
2
3
4
∗
5
1



CI =

1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1










b
CI =

14
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1







0
1
1
1
0
−1



b
CoxI =

1
0
0
0
0
−1
0
1
0
0
0
0
0
0
1
0
0
0
0
−1
−1
0
0
1
1
1
1
1
1
−1







Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1,−1, 0, 1,−1 ],
[ −1,−1, 0, 0, 1, 0 ],
[ −1, 0,−1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1,−1, 0, 0 ],
[ 0, 1,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 0, 1,−1, 0 ],
[ 1, 0, 1, 0,−1, 1 ],
[ 1, 1, 0, 0,−1, 1 ],
• I ≡ 0 D∗5 A0 :
[ −1,−1, 0,−1, 1,−1 ],
[ −1, 0,−1,−1, 1,−1 ],
[ −1, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 1, 0,−1, 0 ],
[ 0, 1, 0,−1, 0, 0 ],
[ 1, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 1,−1, 1 ],
[ 1, 0, 1, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, 1 ],
[ −1,−1, 0, 0, 0,−1 ],
[ −1, 0,−1, 0, 0,−1 ],
[ −1, 0, 0,−1, 1,−1 ],
[ −1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, 1,−1, 1 ],
[ 1, 1, 0, 1,−1, 1 ],
[ −1,−1, 0, 0, 1,−1 ],
[ −1, 0,−1, 0, 1,−1 ],
[ −1, 0, 0,−1, 1, 0 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 1, 0, 0, 0 ],
[ 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0,−1, 0 ],
[ 1, 1, 0, 0,−1, 0 ],
[ 1, 1, 1, 0,−1, 1 ]
1
2
3



CI =

4
1
0
0
0
0
0
0
1
0
0
0
0
∗
5
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0



b
CoxI =

1
1
1
1
1
1
0
1
0
0
0
−1








bI =
C

1
0
0
0
0
−1
0
0
0
0
0
1



0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
−1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1














Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 0, 0,−1 ],
[ −1,−1, 0, 1, 0, 0 ],
[ −1,−1, 1, 0, 1, 0 ],
[ −1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ −1,−1, 0, 0, 1,−1 ],
[ −1,−1, 0, 1, 1, 0 ],
[ −1,−1, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1,−1, 0 ],
[ −1,−1, 0, 0,
[ −1,−1, 1, 0,
[ −1, 0, 0, 0,
[ −1, 0, 1, 0,
[ 0,−1, 0, 1,
[ 0, 0,−1, 0,
[ 0, 0, 0,−1,
[ 0, 0, 0, 0,
[ 0, 0, 0, 1,
15
1, 0 ],
0,−1 ],
0,−1 ],
0, 0 ],
0, 0 ],
1, 0 ],
1, 0 ],
0, 1 ],
0, 0 ],
[ −1,−1, 0,
[ −1,−1, 1,
[ −1, 0, 0,
[ 0,−1, 0,
[ 0,−1, 1,
[ 0, 0,−1,
[ 0, 0, 0,
[ 0, 0, 0,
[ 0, 0, 0,
1, 0,−1 ],
0, 0, 0 ],
0, 0, 0 ],
0, 0,−1 ],
0, 0, 0 ],
1, 0, 0 ],
0,−1,−1 ],
0, 1, 0 ],
1, 0, 1 ],
[
[
[
[
[
[
0,
0,
0,
1,
1,
1,
0, 1,−1,
1,−1, 0,
1, 0, 0,
0, 0, 0,
1,−1, 0,
1, 0,−1,
0,
0,
0,
0,
0,
0,
0 ],
0 ],
1 ],
0 ],
0 ],
1 ],
[
[
[
[
[
[
0,
0,
1,
1,
1,
1,
0, 1, 0,−1,
1, 0,−1, 0,
0,−1, 0, 0,
0, 0, 0, 0,
1,−1, 0, 0,
1, 0, 0,−1,
0 ],
0 ],
0 ],
1 ],
1 ],
0 ],
[
[
[
[
[
[
0,
0,
1,
1,
1,
1,
0, 1, 0, 0,
1, 0, 0,−1,
0, 0,−1, 0,
1,−1,−1, 0,
1, 0,−1,−1,
1, 0, 0,−1,
0 ],
0 ],
0 ],
0 ],
0 ],
1 ],
[
[
[
[
[
[
0,
0,
1,
1,
1,
1,
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
−1

0, 1, 0, 0,
1, 0, 0, 0,
0, 0, 0,−1,
1,−1, 0,−1,
1, 0,−1, 0,
1, 0, 0, 0,
1 ],
0 ],
0 ],
0 ],
0 ],
1]
1
• I ≡ 0 D∗4 A1 :
2
3
∗
4
5
1
0
0
0
0
0



CI =

0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0

0
1
0
0
1
−1


b
CoxI =

1
1
1
1
1
1








bI =
C




1
0
0
0
1
−1
0
0
0
0
−1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
−1
−1
−1
−1
−1
−1
1













Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 0,−1,−2 ],
[ −1,−1, 0, 1, 0,−1 ],
[ −1,−1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1,−1, 0, 0 ],
[ 0, 1,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 1 ],
[ 1, 0, 0, 0, 0, 1 ],
[ 1, 1,−1, 0, 0, 1 ],
[ 1, 1, 0,−1, 1, 1 ],
[ −1,−1, 0, 0,−1,−1 ],
[ −1,−1, 0, 1, 0, 0 ],
[ −1,−1, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0 ],
[ 1, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 1 ],
[ 1, 1,−1, 0, 1, 1 ],
[ 1, 1, 0, 0, 0, 1 ],
[ −1,−1, 0, 0, 0,−1 ],
[ −1,−1, 1, 0,−1,−1 ],
[ −1, 0, 0, 0,−1,−1 ],
[ −1, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0 ],
[ 1, 1,−1,−1, 0, 0 ],
[ 1, 1, 0,−1, 0, 0 ],
[ 1, 1, 0, 0, 1, 1 ],
[ −1,−1, 0, 1,−1,−1 ],
[ −1,−1, 1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0,−1,−1 ],
[ 0,−1, 1, 0, 0, 0 ],
[ 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 0, 1, 1 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1, 1,−1, 0, 0, 0 ],
[ 1, 1, 0,−1, 0, 1 ],
[ 1, 1, 0, 0, 1, 2 ]
1
• I≡
∗
0 D3
A2 :
2
∗
3
4
5



CI =

1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1








bI =
C

16



1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1










b
CoxI =

0
1
0
1
1
−1
1
0
0
1
1
−1
0
0
0
−1
−1
1
1
1
1
0
0
−1
0
0
0
1
0
0
1
1
1
1
1
−1







Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0,−1,−1,−2 ],
[ −1,−1, 0, 0,−1,−1 ],
[ −1,−1, 1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0,−1,−1 ],
[ 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1,−1, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 1, 1 ],
[ 1, 1,−1, 0, 1, 1 ],
[ 1, 1, 0, 0, 1, 2 ],
[ −1,−1, 0,−1, 0,−2 ],
[ −1,−1, 0, 0, 0,−1 ],
[ −1,−1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 1, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 1 ],
[ 1, 1,−1, 1, 0, 1 ],
[ 1, 1, 0, 1, 0, 1 ],
[ −1,−1, 0,−1,0,−1 ],
[ −1,−1, 1,−1,0,−1 ],
[ −1, 0, 0,−1,0,−1 ],
[ −1, 0, 1, 0,0, 0 ],
[ 0,−1, 0, 0,0, 0 ],
[ 0, 0,−1, 0,0,−1 ],
[ 0, 0, 0,−1,1, 0 ],
[ 0, 0, 0, 0,0, 1 ],
[ 0, 0, 0, 1,0, 0 ],
[ 0, 0, 1, 0,1, 1 ],
[ 0, 1, 0, 0,0, 1 ],
[ 1, 0, 0, 0,0, 0 ],
[ 1, 1,−1, 0,0, 0 ],
[ 1, 1, 0, 0,0, 1 ],
[ 1, 1, 0, 1,0, 2 ],
[ −1,−1, 0, 0,−1,−2 ],
[ −1,−1, 1, 0,−1,−1 ],
[ −1, 0, 0, 0,−1,−1 ],
[ 0,−1, 0,−1, 0,−1 ],
[ 0,−1, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, 1, 1 ],
[ 1, 0, 0, 0, 0, 1 ],
[ 1, 1,−1, 0, 0, 1 ],
[ 1, 1, 0, 0, 1, 1 ],
[ 1, 1, 0, 1, 1, 2 ]
1
• I≡
∗
0 D2
A3 :
∗
2
3
4



CI =

5
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0



b
CoxI =

0
0
1
1
1
0
0
1
1
1
1
−1
1
1
1
1
1
1








bI =
C

1
0
1
1
1
−1



1
1
0
0
0
−1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
−1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1














Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1,−1,−1, 0,−2 ],
[ −1,−1, 0,−1,−1,−2 ],
[ −1,−1, 0, 0,−1,−1 ],
[ −1, 0, 0, 0,−1,−1 ],
[ 0,−1, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ −1,−1,−1, 0,−1,−2 ],
[ −1,−1, 0,−1, 0,−2 ],
[ −1,−1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1 ],
17
[ −1,−1,−1, 0,0,−2 ],
[ −1,−1, 0,−1,0,−1 ],
[ −1, 0,−1, 0,0,−1 ],
[ −1, 0, 0, 0,0, 0 ],
[ 0,−1, 0, 0,0,−1 ],
[ 0, 0,−1, 0,1, 0 ],
[ 0, 0, 0,−1,1, 0 ],
[ 0, 0, 0, 0,0, 1 ],
[ −1,−1,−1, 0, 0,−1 ],
[ −1,−1, 0, 0,−1,−2 ],
[ −1, 0, 0,−1, 0,−1 ],
[ 0,−1,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[
[
[
[
[
[
[
0,
0,
0,
0,
1,
1,
1,
0,
0,
1,
1,
0,
1,
1,
0, 0,
1,−1,
0, 0,
1, 0,
0, 1,
0, 0,
1, 0,
• I ≡ 1 D∗5 A0 :
1,
0,
0,
0,
0,
1,
0,
1 ],
0 ],
0 ],
1 ],
1 ],
2 ],
1 ],
[
[
[
[
[
[
[
1
0,
0,
0,
1,
1,
1,
1,
0,
0,
1,
0,
0,
1,
1,
0,
1,
0,
0,
1,
0,
1,
1,−1,
0,−1,
0, 0,
0, 0,
0, 0,
1, 0,
0, 0,
0 ],
0 ],
1 ],
0 ],
1 ],
1 ],
2 ],
[
[
[
[
[
[
[
0,
0,
0,
1,
1,
1,
1,
0,
0,
1,
0,
1,
1,
1,
0,
1,
0,
0,
0,
0,
1,
1,0,
0,0,
0,1,
0,0,
0,0,
1,0,
0,1,








bI =
C

1
1
1
1
1
0
0 ],
0 ],
1 ],
1 ],
1 ],
2 ],
2 ],
[
[
[
[
[
[
[
0,
0,
0,
1,
1,
1,
1,
0,
0,
1,
0,
1,
1,
1,
0,
1,
0,
0,
0,
0,
1,
1,
0,
1,
0,
0,
1,
1,
0,
0,
0,
1,
1,
1,
0,
1 ],
1 ],
1 ],
1 ],
1 ],
2 ],
2]
2
3
4
1
0
0
0
0
0



CI =

∗
5
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0



b
CoxI =

1
1
1
1
1
1
0
0
0
0
0
−1
1
0
1
0
0
0



1
1
0
0
0
0
−1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
−1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1














Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0, 0,−1 ],
[ −1, 0, 1, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0 ],
[ 0,−1,−1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1,−1, 0, 0 ],
[ 0, 1, 0,−1, 0, 0 ],
[ 0, 1, 1,−1,−1, 0 ],
[ 0, 1, 1, 0,−1, 1 ],
[ 1,−1,−1, 0, 1, 0 ],
[ 1, 0, 0,−1, 0, 0 ],
1
• I≡
∗
1 D4
A1 :
[ −1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 1 ],
[ 0,−1,−1, 1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 1, 0,−1, 0 ],
[ 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 1,−1, 0, 0 ],
[ 0, 1, 1, 0, 0, 1 ],
[ 1,−1,−1, 1, 0, 0 ],
[ 1, 0, 0, 0,−1, 0 ],
[ −1, 0, 0, 0,1, 0 ],
[ −1, 1, 1,−1,0, 0 ],
[ 0,−1,−1, 0,0,−1 ],
[ 0,−1,−1, 1,0, 0 ],
[ 0,−1, 0, 0,1, 0 ],
[ 0, 0,−1, 0,1, 0 ],
[ 0, 0, 0,−1,1, 0 ],
[ 0, 0, 0, 0,0, 1 ],
[ 0, 0, 0, 1,0, 0 ],
[ 0, 0, 1, 0,0, 0 ],
[ 0, 1, 0, 0,0, 0 ],
[ 0, 1, 1,−1,0, 1 ],
[ 1,−1,−1, 0,0,−1 ],
[ 1,−1, 0, 0,0, 0 ],
[ 1, 0, 0, 0,0, 0 ],
[ −1, 0, 0,1, 0, 0 ],
[ −1, 1, 1,0,−1, 0 ],
[ 0,−1,−1,0, 1,−1 ],
[ 0,−1,−1,1, 1, 0 ],
[ 0,−1, 0,1, 0, 0 ],
[ 0, 0,−1,1, 0, 0 ],
[ 0, 0, 0,0,−1,−1 ],
[ 0, 0, 0,0, 1, 0 ],
[ 0, 0, 0,1, 0, 1 ],
[ 0, 0, 1,0, 0, 1 ],
[ 0, 1, 0,0, 0, 1 ],
[ 0, 1, 1,0,−1, 0 ],
[ 1,−1,−1,0, 0, 0 ],
[ 1, 0,−1,0, 0, 0 ],
[ 1, 0, 0,0, 0, 1 ]
2
3
∗
4
5



CI =

1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1








bI =
C

18



1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1










b
CoxI =

0
0
0
0
1
−1
1
0
1
0
0
0
1
1
0
0
0
0
−1
0
0
0
0
0
1
1
1
1
0
−1
1
1
1
1
1
−1







Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0,−1,−1 ],
[ −1, 0, 1, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 1 ],
[ 0,−1,−1, 0, 0,−1 ],
[ 0,−1, 0, 0,−1,−1 ],
[ 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1,−1, 0, 0 ],
[ 0, 1, 0,−1, 0, 0 ],
[ 0, 1, 1,−1, 0, 0 ],
[ 0, 1, 1, 0, 1, 1 ],
[ 1,−1,−1, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0 ],
[ −1, 0, 0, 0, 0,−1 ],
[ −1, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 1, 1 ],
[ 0,−1,−1, 1,−1,−1 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 1,−1, 0, 1 ],
[ 0, 1, 1, 0, 1, 2 ],
[ 1,−1,−1, 1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0 ],
1
• I≡
∗
1 D3
A2 :
[ −1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1,−1, 0, 0 ],
[ 0,−1,−1, 0,−1,−2 ],
[ 0,−1,−1, 1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 1,−1, 1, 1 ],
[ 1,−1,−1, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1 ],
[ −1, 0, 0,1, 0, 0 ],
[ −1, 1, 1,0, 0, 0 ],
[ 0,−1,−1,0,−1,−1 ],
[ 0,−1,−1,1, 0, 0 ],
[ 0,−1, 0,1, 0, 0 ],
[ 0, 0,−1,1, 0, 0 ],
[ 0, 0, 0,0,−1,−1 ],
[ 0, 0, 0,0, 1, 0 ],
[ 0, 0, 0,1, 1, 1 ],
[ 0, 0, 1,0, 1, 1 ],
[ 0, 1, 0,0, 1, 1 ],
[ 0, 1, 1,0, 0, 1 ],
[ 1,−1,−1,0, 0,−1 ],
[ 1, 0,−1,0, 0, 0 ],
[ 1, 0, 0,0, 1, 1 ]
2
∗
3
4
5



CI =

1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0



b
CoxI =

1
1
1
1
1
1
0
0
0
1
1
−1








bI =
C




1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
−1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
−1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1














Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0,−1, 0,−1 ],
[ −1, 0, 1, 0, 0, 0 ],
[ −1, 1, 1, 0, 1, 1 ],
[ 0,−1,−1,−1, 0,−1 ],
[ 0,−1, 0,−1, 0,−1 ],
[ 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ −1, 0, 0, 0,−1,−1 ],
[ −1, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 1, 0, 1 ],
[ 0,−1,−1, 0,−1,−2 ],
[ 0,−1, 0, 0,−1,−1 ],
[ 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1 ],
[ −1, 1, 1, 0, 0, 0 ],
[ 0,−1,−1,−1,−1,−2 ],
[ 0,−1,−1, 0,−1,−1 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
19
[ −1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 1 ],
[ 0,−1,−1,−1, 0,−2 ],
[ 0,−1,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[
[
[
[
[
[
[
0, 0, 0,
0, 0, 1,
0, 1, 0,
0, 1, 1,
0, 1, 1,
1,−1,−1,
1, 0, 0,
• I ≡ 2 D∗5 A0 :
0,
0,
0,
0,
1,
0,
0,
1, 1 ],
0, 0 ],
0, 0 ],
0, 1 ],
0, 2 ],
0,−1 ],
0, 0 ],
[
[
[
[
[
[
[
1
0, 0, 0,
0, 0, 1,
0, 1, 0,
0, 1, 1,
0, 1, 1,
1,−1,−1,
1, 0, 0,
2
1
0
0
0
0
0


CI =

0 ],
1 ],
1 ],
1 ],
2 ],
0 ],
1 ],
[
[
[
[
[
[
[
0, 0, 0, 1,
0, 0, 1, 0,
0, 1, 0, 0,
0, 1, 1, 0,
1,−1,−1,−1,
1,−1, 0, 0,
1, 0, 0, 0,
0, 0 ],
1, 1 ],
1, 1 ],
1, 2 ],
0,−1 ],
0, 0 ],
1, 1 ],
[
[
[
[
[
[
[
0, 0, 0,
0, 0, 1,
0, 1, 0,
0, 1, 1,
1,−1,−1,
1, 0,−1,
1, 0, 0,
1, 0, 1 ],
1, 0, 1 ],
1, 0, 1 ],
1, 0, 1 ],
0,−1,−1 ],
0, 0, 0 ],
1, 0, 1 ]
3
4

1,−1,
0, 0,
0, 0,
0, 1,
1, 1,
0, 0,
0, 0,
∗
5
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0



b
CoxI =

1
1
1
1
1
1
0
0
0
0
0
−1








bI =
C




1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
−1
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
−1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1














Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 1, 0, 1 ],
[ 0,−1, 0, 0, 1, 0 ],
[ 0,−1, 1, 1, 0, 0 ],
[ 0, 0,−1,−1, 1, 0 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 1,−1, 1 ],
[ 0, 1,−1,−1, 1, 0 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 1, 0,−1,−1, 0, 0 ],
[ 1, 0, 0, 0,−1, 0 ],
[ −1, 0, 0, 0, 0,−1 ],
[ −1, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 0, 0 ],
[ 0,−1, 1, 1, 0, 1 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 1 ],
[ 0, 1,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 1, 0,−1,−1, 1, 0 ],
[ 1, 0, 0, 0, 0, 0 ],
1
• I≡
∗
2 D4
2
[ −1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 1,−1, 0 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 1, 0, 0, 0 ],
[ 0, 0,−1,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1,−1,−1, 0,−1 ],
[ 0, 1, 0,−1, 0, 0 ],
[ 1,−1, 0, 0, 0, 0 ],
[ 1, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1 ],
[ −1, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0,−1, 1, 1,−1, 0 ],
[ 0, 0,−1,−1, 1,−1 ],
[ 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 1,−1, 0 ],
[ 0, 1,−1,−1, 0, 0 ],
[ 0, 1, 0, 0,−1, 0 ],
[ 1, 0,−1,−1, 0,−1 ],
[ 1, 0, 0,−1, 0, 0 ],
[ 1, 1,−1,−1, 0, 0 ]
3
A1 :
∗
4
5



CI =

1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1








bI =
C

20



1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1







0
0
0
0
1
−1



b
CoxI =

1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
−1
1
1
1
1
1
−1







Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 1, 1, 1 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 1 ],
[ 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 1, 1, 1 ],
[ 0, 1,−1,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 1, 0,−1,−1, 0,−1 ],
[ 1, 0, 0, 0, 0, 0 ],
• I ≡ 3 D∗5 A0 :
[ −1, 0, 0, 0,−1,−1 ],
[ −1, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 0, 0 ],
[ 0,−1, 1, 1, 1, 1 ],
[ 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 2 ],
[ 0, 1,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 1 ],
[ 1, 0,−1,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 1 ],
1
2
3


CI =

1
0
0
0
0
0
1
1
0
0
0
0
[ −1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 1 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 1, 1, 0, 0 ],
[ 0, 0,−1,−1,−1,−1 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 1 ],
[ 0, 1,−1,−1, 0,−1 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 1, 0,−1,−1,−1,−1 ],
[ 1, 0, 0,−1, 0, 0 ],
[ 1, 1,−1,−1, 0, 0 ]
4
∗
5

[ −1, 0, 0, 0, 0,−1 ],
[ −1, 0, 1, 1, 0, 0 ],
[ 0,−1, 0, 0,−1,−1 ],
[ 0,−1, 1, 0, 0, 0 ],
[ 0, 0,−1,−1,−1,−2 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 1, 1 ],
[ 0, 1,−1,−1,−1,−1 ],
[ 0, 1, 0,−1, 0, 0 ],
[ 1,−1, 0, 0, 0, 0 ],
[ 1, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 1 ],
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1

0
0
0
0
0
−1


b
CoxI =









bI =
C




1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
−1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1














Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 1 ],
[ 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ −1, 0,−1, 1,
[ −1, 0, 0, 1,
[ −1, 1, 0, 0,
[ 0,−1, 0, 0,
[ 0,−1, 1, 0,
[ 0, 0,−1, 1,
[ 0, 0, 0,−1,
[ 0, 0, 0, 0,
[ 0, 0, 0, 1,
1, 0 ],
0, 0 ],
0, 0 ],
1, 0 ],
0, 0 ],
0, 0 ],
0,−1 ],
0,−1 ],
0, 0 ],
[ −1, 0, 0, 0,
[ −1, 0, 0, 1,
[ 0,−1,−1, 1,
[ 0,−1, 0, 1,
[ 0, 0,−1, 0,
[ 0, 0,−1, 1,
[ 0, 0, 0,−1,
[ 0, 0, 0, 0,
[ 0, 0, 0, 1,
21
0,−1 ],
1, 0 ],
1, 0 ],
0, 0 ],
0,−1 ],
1, 0 ],
0, 0 ],
0, 1 ],
0, 1 ],
[ −1, 0, 0,
[ −1, 0, 0,
[ 0,−1, 0,
[ 0,−1, 0,
[ 0, 0,−1,
[ 0, 0,−1,
[ 0, 0, 0,
[ 0, 0, 0,
[ 0, 0, 0,
0, 0, 0 ],
1, 1, 1 ],
0, 0,−1 ],
1, 1, 0 ],
0, 0, 0 ],
1, 1, 1 ],
0,−1,−1 ],
0, 1, 0 ],
1, 1, 1 ],
[
[
[
[
[
[
0,
0,
0,
0,
1,
1,
0,
0,
1,
1,
0,
0,
1,−1,−1,−1 ],
1, 0, 0, 0 ],
0,−1,−1, 0 ],
0, 0, 0, 1 ],
0,−1,−1,−1 ],
0, 0, 0, 0 ],
b ∗ A3 :
• I≡D
2
[
[
[
[
[
[
0,
0,
0,
0,
1,
1,
1
3
0,
0,
1,
1,
0,
0,
1,−1,−1,
1, 0, 0,
0,−1, 0,
1,−1,−1,
0,−1,−1,
0, 0, 0,
4


CI =

[
[
[
[
[
[
0, 0, 1,−1, 0,
0, 1,−1, 0, 0,
0, 1, 0, 0,−1,
1,−1, 0, 0, 0,
1, 0, 0,−1, 0,
1, 0, 1,−1,−1,
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
[
[
[
[
[
[
0,
0,
0,
1,
1,
1,
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0, 1, 0,−1, 0 ],
1, 0,−1,−1,−1 ],
1, 0, 0, 0, 0 ],
0,−1, 0, 0, 0 ],
0, 0, 0,−1, 0 ],
1, 0,−1,−1, 0 ]
∗
2

0 ],
1 ],
0 ],
0 ],
0 ],
1 ],
5
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0



b I =
Cox


1
1
1
1
1
1
0
0
1
1
0
−1










b
CI =

1
0
0
0
1
0
1
1
0
0
0
−1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
−1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
−1
−1
−1
−1
−1
−1
1














Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0,−1,−1, 1,−1 ],
[ −1, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0 ],
[ 0,−1, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 0, 1 ],
[ 1,−1, 0, 1,−1, 0 ],
[ 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0,−1, 0 ],
b ∗ A2 :
• I≡D
3
1
[ −1, 0,−1, 0, 0,−1 ],
[ −1, 0, 0,−1, 1,−1 ],
[ −1, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 1, 0 ],
[ 0,−1, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 1, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 1,−1, 0, 0,−1,−1 ],
[ 1,−1, 1, 0,−1, 0 ],
[ 1, 0, 0, 1,−1, 0 ],
[ 1, 0, 1, 0,−1, 1 ],
2


CI =

1
0
0
0
0
0
[ −1, 0,−1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0,−1 ],
[ −1, 1, 0,−1, 1, 0 ],
[ 0,−1,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 1 ],
[ 1,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, 1,−1, 1 ]
∗
3
4

[ −1, 0,−1, 0, 1,−1 ],
[ −1, 0, 0,−1, 1, 0 ],
[ −1, 1,−1, 0, 1, 0 ],
[ −1, 1, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 1 ],
[ 1,−1, 0, 0,−1, 0 ],
[ 1, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 1,−1, 1 ],
[ 1, 0, 1, 0, 0, 1 ],
5
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1








bI =
C

22



1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1







0
0
0
1
0
−1



b
CoxI =

1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
−1
0
0
0
0
0
1
1
1
1
1
1
−1







Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 0 ],
[ −1, 1, 0, 0, 1, 0 ],
[ 0,−1, 0, 0,−1,−1 ],
[ 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1,−1, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 1 ],
[ 1,−1, 0, 0, 0, 0 ],
[ 1, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1 ],
b ∗ A1 :
• I≡D
4
1
[ −1, 0, 0,−1, 1,−1 ],
[ −1, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 1, 1 ],
[ −1, 1, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 1,−1,−1, 0,−1,−1 ],
[ 1,−1, 0, 1,−1, 0 ],
[ 1, 0,−1, 1,−1, 0 ],
[ 1, 0, 0, 1,−1, 0 ],
2
3
[ −1, 0, 0,−1, 1, 0 ],
[ −1, 0, 1,−1, 1, 0 ],
[ −1, 1, 0,−1, 1, 0 ],
[ −1, 1, 1, 0, 1, 1 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 1, 1 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 1,−1, 0, 0,−1,−1 ],
[ 1, 0,−1, 0,−1,−1 ],
[ 1, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 1,−1, 1 ],
[ −1, 0, 0, 0, 0,−1 ],
[ −1, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0 ],
[ 0,−1, 0,−1, 0,−1 ],
[ 0,−1, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, 1, 1 ],
[ 1,−1, 0, 0,−1, 0 ],
[ 1, 0,−1, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 1 ]
∗
4
5



CI =

1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
1
1
1
1

0
0
0
0
0
−1


b
CoxI =









bI =
C




1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
−1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1














Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 1, 0 ],
[ −1, 0, 1, 0, 1, 1 ],
[ −1, 1, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ −1, 0, 0, 0,
[ −1, 0, 0, 1,
[ −1, 0, 1, 1,
[ −1, 1, 0, 1,
[ 0,−1, 0, 0,
[ 0, 0,−1, 0,
[ 0, 0, 0,−1,
[ 0, 0, 0, 0,
[ 0, 0, 0, 1,
0, 0 ],
1, 1 ],
1, 1 ],
1, 1 ],
0, 0 ],
0,−1 ],
0,−1 ],
0,−1 ],
0, 0 ],
[ −1, 0, 0, 0,
[ −1, 0, 1, 0,
[ −1, 1, 0, 0,
[ −1, 1, 1, 0,
[ 0,−1, 0, 1,
[ 0, 0,−1, 0,
[ 0, 0, 0,−1,
[ 0, 0, 0, 0,
[ 0, 0, 0, 1,
23
1,
0,
0,
1,
0,
0,
0,
0,
0,
0 ],
0 ],
0 ],
1 ],
0 ],
0 ],
0 ],
1 ],
1 ],
[ −1, 0, 0,
[ −1, 0, 1,
[ −1, 1, 0,
[ 0,−1, 0,
[ 0,−1, 1,
[ 0, 0,−1,
[ 0, 0, 0,
[ 0, 0, 0,
[ 0, 0, 0,
1, 0, 0 ],
0, 1, 0 ],
0, 1, 0 ],
0,−1,−1 ],
0, 0, 0 ],
1, 0, 0 ],
0,−1,−1 ],
0, 1, 0 ],
1, 1, 1 ],
[
[
[
[
[
[
2.6.3
0, 0, 1,−1, 0,
0, 1,−1, 0, 0,
0, 1, 0, 0, 1,
1,−1, 0, 0,−1,
1, 0,−1, 0,−1,
1, 0, 0,−1, 0,
0 ],
0 ],
1 ],
0 ],
0 ],
0 ],
[
[
[
[
[
[
0, 0, 1, 0, 0, 0 ],
0, 1, 0,−1, 0, 0 ],
1,−1,−1, 0,−1,−1 ],
1,−1, 0, 0, 0, 0 ],
1, 0,−1, 0, 0, 0 ],
1, 0, 0, 0,−1, 0 ],
[
[
[
[
[
[
0, 0, 1, 0, 0, 1 ],
0, 1, 0, 0, 0, 0 ],
1,−1, 0,−1,−1,−1 ],
1, 0,−1,−1,−1,−1 ],
1, 0, 0,−1,−1,−1 ],
1, 0, 0, 0, 0, 0 ],
[
[
[
[
[
[
0, 0, 1, 0, 1, 1 ],
0, 1, 0, 0, 0, 1 ],
1,−1, 0, 0,−1,−1 ],
1, 0,−1, 0,−1,−1 ],
1, 0, 0,−1,−1, 0 ],
1, 0, 0, 0, 0, 1 ]
Posets of type E6
∗
5
• I ≡ P1 :
4
1
3
2



CI =




b I =
Cox


0
1
1
0
0
−1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
−1
0
1
0
0
0
0
0
−1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0










b
CI =

1
1
1
1
1
−1
1
0
0
1
1
0








BI =



0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
−1
−1
−1
−1
−1
−1
1







0
−1
−1
−1
−1
0
0
0
1
0
0
0







Number of sincere Tits roots of poset I sI = 4.
Table of roots of qbI
[ −2,−1,−1, 1, 1,−1 ],
[ −1, −1, −1, 0, 1, −1 ],
[ −1, −1, 0, 0, 1, −1 ],
[ −1, −1, 0, 1, 1, 0 ],
[ −1, 0, −1, 1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0,−1, 0, −1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1,−1, 0, 0 ],
[ 0, 1, −1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0,−1, 0 ],
[ 1, 1, 0,−1, 0, 0 ],
[ 1, 1, 0, 0, 0, 1 ],
[ −1,−1,−1, 1, 1,−1 ],
[ −1, −1, −1, 1, 0, −1 ],
[ −1, −1, 0, 0, 1, 0 ],
[ −1, 0, −1, 0, 0, −1 ],
[ −1, 0, −1, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 1, 0,−1, 0 ],
[ 0, 1, 0,−1, 0, 0 ],
[ 1, 0, 0,−1, 0, 0 ],
[ 1, 0, 1,−1,−1, 0 ],
[ 1, 0, 1, 0,−1, 1 ],
[ 1, 1, 0,−1, 0, 1 ],
[ 1, 1, 1,−1,−1, 0 ],
24
[ 1, 1, 1,−1,−1, 1 ],
[ −1,−1,−1, 1, 1, 0 ],
[ −1,−1, 0, 1, 0,−1 ],
[ −1, 0,−1, 0, 1,−1 ],
[ −1, 0,−1, 1, 1, 0 ],
[ −1, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1, 0, 0, −1, 0 ],
[ 1, 0, 0, 0, −1, 0 ],
[ 1, 0, 1, −1, 0, 0 ],
[ 1, 0, 1, 0, 0, 1 ],
[ 1, 1, 0, 0, −1, 0 ],
[ 1, 1, 1, −1, 0, 1 ],
[ 2, 1, 1,−1,−1, 1 ],
[ −1,−1, 0, 0, 0,−1 ],
[ −1,−1, 0, 1, 0, 0 ],
[ −1, 0,−1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 1, 0, 0, 0 ],
[ 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, −1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, −1, 0, 1 ],
[ 1, 1, 0, −1, −1, 0 ],
[ 1, 1, 0, 0, −1, 1 ],
[ 1, 1, 1, 0, −1, 1 ]
∗
5
• I ≡ P2 :
2
1
4
3



CI =




b I =
Cox


0
1
1
1
1
−1
1
0
0
0
0
0
1
0
1
1
0
−1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
−1
0
0
1
1
0
0
0
1
1
1
1
0
−1
0
−1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1










b
CI =

1
1
1
1
1
−1
1
0
0
0
0
0








BI =



0
1
0
0
1
0
1
0
0
0
0
−1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
−1
0
0
0
0
1
0
0
1
0
0
0
−1
−1
−1
−1
−1
−1
1
0
−1
0
0
−1
0







0
0
−1
−1
0
1
0
0
0
0
0
−1







Number of sincere Tits roots of poset I sI = 6.
Table of roots of qbI
[ −1,−2,−1,−1, 1,−2 ],
[ 1, 1, 1, 1,−1, 2 ],
[ −1, −1, −1, 0, 0, −1 ],
[ −1, −1, 0, −1, 1, −1 ],
[ −1, 0, 0, 0, −1, −1 ],
[ 0, −1, −1, 0, 0, −1 ],
[ 0, −1, 0, −1, 1, −1 ],
[ 0, −1, 0, 0, 1, 0 ],
[ 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 1, −1, 0 ],
[ 0, 1, 1, 0, −1, 1 ],
[ 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, 1 ],
[ 1, 1, 1, 0, −1, 1 ],
[ −1,−1,−1,−1, 1,−2 ],
[ 1, 2, 1, 1,−1, 2 ],
[ −1, −1, −1, 0, 1, −1 ],
[ −1, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, −1 ],
[ 0, −1, −1, 0, 1, −1 ],
[ 0, −1, 0, −1, 1, 0 ],
[ 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, −1, 0, 0 ],
[ 0, 1, 0, 0, −1, 0 ],
[ 0, 1, 0, 1, −1, 1 ],
[ 0, 1, 1, 0, 0, 1 ],
[ 1, 0, 0, 0, 1, 1 ],
[ 1, 1, 0, 1, −1, 1 ],
[ 1, 1, 1, 0, 0, 1 ],
[ −1,−1,−1,−1, 1,−1 ],
[ −1, −1, −1, −1, 0, −2 ],
[ −1, −1, 0, −1, 0, −2 ],
[ −1, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 1, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 1, 1,−1, 1 ],
[ 1, 0, 0, 1, 0, 1 ],
[ 1, 1, 0, 1, 0, 1 ],
[ 1, 1, 1, 0, 0, 2 ],
[ 1, 1, 1, 1,−1, 1 ],
[ −1,−1,−1, 0, 0,−2 ],
[ −1,−1, 0,−1, 0,−1 ],
[ −1, 0, 0,−1, 0,−1 ],
[ 0,−1,−1,−1, 1,−1 ],
[ 0,−1, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, −1, 0 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 0, 1 ],
[ 1, 1, 0, 1, 0, 2 ],
[ 1, 1, 1, 1, 0, 2 ]
∗
• I ≡ P3 :
1
3
5
2
4



CI =

1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1








bI =
C

25



1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1










b
CoxI =

0
1
1
1
1
−1
1
0
0
1
1
−1
0
1
0
0
0
0
1
1
1
0
0
−1
0
0
0
1
0
0
1
1
1
1
1
−1










BI =

0
1
0
1
0
−1
1
0
0
1
0
−1
0
1
1
0
0
−1
1
1
0
0
0
−1
0
0
0
1
1
−1
1
1
0
1
0
−2







Number of sincere Tits roots of poset I sI = 6.
Table of roots of qbI
[ −2,−1,−1,−1,−1,−3 ],
[ 1, 1, 1, 1, 1, 3 ],
[ −1, −1, 0, −1, −1, −2 ],
[ −1, −1, 0, 0, −1, −1 ],
[ −1, 0, −1, −1, 0, −1 ],
[ −1, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, −1, 0, −1 ],
[ 0, −1, 1, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, 1, 1 ],
[ 1, 0, 0, 0, 1, 1 ],
[ 1, 0, 1, 0, 1, 2 ],
[ 1, 1, 0, 0, 0, 1 ],
[ 1, 1, 0, 1, 0, 2 ],
[ −1,−1,−1,−1,−1,−3 ],
[ 2, 1, 1, 1, 1, 3 ],
[ −1, −1, 0, −1, 0, −2 ],
[ −1, −1, 0, 0, 0, −1 ],
[ −1, 0, −1, 0, −1, −2 ],
[ −1, 0, 0, 0, −1, −1 ],
[ 0, −1, 0, 0, −1, −1 ],
[ 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1, −1, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 1 ],
[ 1, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, 1, 0, 1 ],
[ 1, 1, 0, 0, 1, 1 ],
[ 1, 1, 0, 1, 1, 2 ],
[ −1,−1,−1,−1,−1,−2 ],
[ −1, −1, −1, −1, 0, −2 ],
[ −1, −1, 0, −1, 0, −1 ],
[ −1, 0, −1, −1, −1, −2 ],
[ −1, 0, −1, 0, −1, −1 ],
[ −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, −1 ],
[ 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 1, 0, 2 ],
[ 1, 1, 0, 0, 1, 2 ],
[ 1, 1, 1, 0, 1, 2 ],
[ 1, 1, 1, 1, 1, 2 ],
[ −1,−1,−1, 0,−1,−2 ],
[ −1,−1, 0, 0,−1,−2 ],
[ −1, 0,−1,−1, 0,−2 ],
[ −1, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 1, 1 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 1, 1 ],
[ 1, 0, 1, 1, 1, 2 ],
[ 1, 1, 0, 1, 0, 1 ],
[ 1, 1, 1, 1, 0, 2 ]
∗
5
• I ≡ P4 :
4
2
3
1



CI =




b
CoxI =

0
0
1
1
0
−1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
−1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
−1
0
−1
0
0
1
1
1
1
1
1
1








bI =
C

1
1
1
1
1
−1



1
1
0
0
1
0










BI =

0
1
0
0
1
0
1
1
0
0
0
−1
0
0
1
1
1
0
0
−1
0
0
−1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
−1
−1
−1
−1
−1
−1
1
0
0
0
−1
−1
0







0
0
0
0
1
0
0
0
0
0
−1
−1







Number of sincere Tits roots of poset I sI = 6.
Table of roots of qbI
[ −1,−1,−1,−1, 1,−2 ],
[ −1,−1,−1,−1, 1,−1 ],
26
[ −1,−1,−1,−1, 2,−1 ],
[ 1, 1, 1, 1,−2, 1 ],
[ 1, 1, 1, 1,−1, 1 ],
[ −1, 0, −1, −1, 1, −1 ],
[ −1, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, 0, 0, −1 ],
[ 0, −1, 0, −1, 1, −1 ],
[ 0, −1, 0, 0, 1, 0 ],
[ 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 1, −1, 0 ],
[ 0, 1, 1, 0, −1, 1 ],
[ 1, 0, 0, 0, −1, 0 ],
[ 1, 0, 0, 1, −1, 1 ],
[ 1, 0, 1, 0, 0, 1 ],
[ 1, 1, 1, 1,−1, 2 ],
[ −1, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, −1, 1, −1 ],
[ −1, 0, 0, 0, 1, 0 ],
[ 0, −1, −1, 0, 1, −1 ],
[ 0, −1, 0, −1, 1, 0 ],
[ 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, −1, 0, 0 ],
[ 0, 1, 0, 0, −1, 0 ],
[ 0, 1, 0, 1, −1, 1 ],
[ 0, 1, 1, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, 1, −1, 1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, −1, −1, 0, 1, −1 ],
−1, 0, −1, 0, 1, −1 ],
−1, 0, 0, −1, 1, 0 ],
−1, 1, 0, 0, 0, 0 ],
0, −1, −1, 0, 1, 0 ],
0, −1, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 0 ],
0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, −1 ],
0, 0, 0, 1,−1, 0 ],
0, 0, 1, 0,−1, 0 ],
0, 1, 0, 0, 0, 0 ],
0, 1, 0, 1, 0, 1 ],
0, 1, 1, 1,−1, 1 ],
1, 0, 0, 0, 0, 1 ],
1, 0, 1, 0,−1, 0 ],
1, 1, 0, 1,−1, 1 ],
[ −1,−1, 0,−1, 1,−1 ],
[ −1, 0,−1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0,−1 ],
[ 0,−1,−1,−1, 1,−1 ],
[ 0,−1, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, −1, 0 ],
[ 1,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, −1, 0 ],
[ 1, 0, 1, 0, −1, 1 ],
[ 1, 1, 1, 0, −1, 1 ]
∗
• I ≡ P5 :
4
5
2
3
1



CI =




b I =
Cox


0
0
0
0
0
−1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1










b
CI =

1
1
1
1
1
−1








BI =



1
1
1
1
1
0
0
1
0
1
0
0
−1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1
1
1
0
1
0
−1
1
0
1
0
1
−1







1
1
1
0
0
−1







Number of sincere Tits roots of poset I sI = 6.
Table of roots of qbI
[ −2, 1, 1, 1, 1, 1 ],
[ 1,−1,−1,−1,−1,−1 ],
[ −1, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0 ],
[ 0, −1, −1, 0, 0, −1 ],
[ 0, −1, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, 1, 1 ],
[ 1, −1, −1, 0, 0, −1 ],
[ 1, −1, 0, 0, −1, 0 ],
[ 1, 0, −1, −1, 0, 0 ],
[ 1, 0, 0, −1, 0, 0 ],
[ −1, 1, 1, 1, 1, 1 ],
[ 2,−1,−1,−1,−1,−1 ],
[ −1, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 1, 0, 0 ],
[ −1, 1, 0, 0, 1, 0 ],
[ −1, 1, 1, 0, 0, 1 ],
[ 0, −1, 0, 0, −1, −1 ],
[ 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, −1, 0 ],
[ 0, 1, 0, −1, 0, 0 ],
[ 0, 1, 1, 0, 0, 1 ],
[ 1, −1, −1, 0, 0, 0 ],
[ 1, −1, 0, 0, 0, 0 ],
[ 1, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, −1, 0 ],
27
[ −1, 1, 1, 1, 1, 2 ],
[ −1, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 1, 0 ],
[ −1, 0, 1, 1, 0, 1 ],
[ −1, 1, 0, 0, 1, 1 ],
[ −1, 1, 1, 0, 1, 1 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 1,−1,−1,−1, 0,−1 ],
[ 1,−1, 0,−1,−1,−1 ],
[ 1, 0,−1,−1,−1,−1 ],
[ 1, 0, 0,−1,−1,−1 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1,−1,−1,−1,−1,−2 ],
[ −1, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 1 ],
[ −1, 0, 1, 1, 1, 1 ],
[ −1, 1, 0, 1, 1, 1 ],
[ −1, 1, 1, 1, 0, 1 ],
[ 0, −1, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 1, −1, −1, 0, −1, −1 ],
[ 1, −1, 0, 0, −1, −1 ],
[ 1, 0, −1, −1, 0, −1 ],
[ 1, 0, 0, −1, −1, 0 ],
[ 1, 0, 0, 0, 0, 1 ]
∗
3
• I ≡ P6 :
5
4
2
1



CI =




b I =
Cox


0
0
1
0
0
−1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
−1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1










b
CI =

1
1
1
1
1
−1








BI =



1
1
0
1
1
0
1
1
0
1
1
−1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
−1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
−1
−1
−1
−1
−1
−1
1
0
0
0
−1
0
0







0
−1
0
0
0
0
0
0
0
0
0
−1







Number of sincere Tits roots of poset I sI = 6.
Table of roots of qbI
[ −1, 1, 1, 1, 1, 1 ],
[ 1,−1,−1,−1,−1,−2 ],
[ −1, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 1 ],
[ −1, 1, 0, 1, 0, 1 ],
[ 0, −1, −1, −1, 0, −2 ],
[ 0, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, −1, −1, −1 ],
[ 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 1, 1, 0, 1 ],
[ 1, −1, 0, −1, −1, −1 ],
[ 1, 0, −1, −1, −1, −1 ],
[ 1, 0, 0, 0, −1, 0 ],
[ −1, 1, 1, 1, 1, 2 ],
[ 1,−1,−1,−1,−1,−1 ],
[ −1, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 1, 1, 1 ],
[ −1, 1, 0, 1, 1, 1 ],
[ 0, −1, −1, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 1, 1, 1 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 0, 2 ],
[ 1, −1, 0, −1, 0, −1 ],
[ 1, 0, 0, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, 0 ],
∗
5
• I ≡ P7 :
4
2
3
1
28
[ −1, 1, 1, 2, 1, 2 ],
[ −1, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 1, 0, 1 ],
[ 0,−1,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 0 ],
[ 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 2 ],
[ 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 1, 1, 1, 2 ],
[ 1,−1, 0,−1, 0, 0 ],
[ 1, 0, 0,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 1 ],
[ 1,−1,−1,−2,−1,−2 ],
[ −1, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 1, 1, 0 ],
[ −1, 1, 0, 1, 0, 0 ],
[ 0, −1, −1, −1, −1, −2 ],
[ 0, −1, 0, −1, 0, −1 ],
[ 0, 0, −1, −1, −1, −2 ],
[ 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 1, 1 ],
[ 0, 1, 0, 0, −1, 0 ],
[ 0, 1, 1, 0, 0, 1 ],
[ 1, −1, −1, −1, 0, −1 ],
[ 1, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, −1, 0, 0 ],
[ 1, 0, 1, 0, 0, 1 ]



CI =




b I =
Cox


1
0
0
0
0
0
0
0
0
0
0
−1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
−1
0
−1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1










b
CI =

1
1
1
1
1
−1
1
1
1
1
1
0








BI =



0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
−1
0
0
0
1
1
0
−1
−1
−1
−1
−1
1
0
0
0
0
1
0
0
0
0
0
−1
0
1
0
1
0
0
0







0
0
−1
0
0
0
1
0
1
1
0
−1







Number of sincere Tits roots of poset I sI = 4.
Table of roots of qbI
[ −1, 1, 1, 1,−1, 1 ],
[ −1, 0, 0, 0, 0,−1 ],
[ −1, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 1 ],
[ −1, 1, 1, 1, −1, 0 ],
[ 0,−1,−1, 0, 1,−1 ],
[ 0,−1, 0,−1, 1, 0 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1,−1, 0, 0 ],
[ 0, 1, 0, 0, −1, 0 ],
[ 0, 1, 0, 1, −1, 1 ],
[ 0, 1, 1, 0, 0, 1 ],
[ 1,−1,−1, 0, 0,−1 ],
[ 1,−1, 0,−1, 0, 0 ],
[ 1, 0, 0,−1, 0, 0 ],
[ −1, 2, 1, 1,−1, 1 ],
[ −1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, −1, 0 ],
[ −1, 1, 1, 1, 0, 1 ],
[ 0,−1,−1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 1, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 1, 1, −1, 1 ],
[ 1,−1,−1, 0, 0, 0 ],
[ 1,−1, 0,−1, 1, 0 ],
[ 1, 0, 0, 0, −1, 0 ],
[ 1,−2,−1,−1, 1,−1 ],
[ −1, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 1,−1, 0 ],
[ −1, 1, 1, 0, 0, 0 ],
[ 0, −1, −1, −1, 1, −1 ],
[ 0, −1, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0,−1, 0 ],
[ 1, −1, −1, −1, 0, −1 ],
[ 1, −1, −1, 0, 1, 0 ],
[ 1, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1,−1,−1,−1, 1,−1 ],
[ −1, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 1, 0, 0 ],
[ −1, 1, 1, 0, 0, 1 ],
[ 0, −1, −1, 0, 0, −1 ],
[ 0, −1, 0, −1, 1, −1 ],
[ 0, −1, 0, 0, 1, 0 ],
[ 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, −1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 1,−1, 0 ],
[ 0, 1, 1, 0,−1, 1 ],
[ 1, −1, −1, −1, 1, 0 ],
[ 1, −1, 0, −1, 0, −1 ],
[ 1, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1 ]
∗
5
• I ≡ P8 :
4
3
2
1



CI =




b
CoxI =

0
0
0
0
0
−1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1








bI =
C

1
1
1
1
1
−1







29



1
1
1
1
1
0
0
 −1

BI = 00
 0
0

0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1
−1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
−1







1
1
1
1
0
−1







Number of sincere Tits roots of poset I sI = 4.
Table of roots of qbI
[ −1,−1, 1, 1, 1, 1 ],
[ −1, −1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 1 ],
[ −1, 0, 1, 1, 1, 1 ],
[ 0, −1, 0, 0, 1, 0 ],
[ 0, −1, 1, 0, 0, 0 ],
[ 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 0,−1, 0 ],
[ 0, 1,−1,−1,−1,−1 ],
[ 0, 1, 0,−1,−1,−1 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 1, 0,−1,−1, 0,−1 ],
[ 1, 0, 0,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 1 ],
[ −1,−1, 1, 2, 1, 1 ],
[ −1, −1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0 ],
[ 0, −1, 0, 1, 0, 0 ],
[ 0, −1, 1, 1, 0, 0 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1,−1,−1, 0,−1 ],
[ 0, 1, 0,−1,−1, 0 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 1, 0,−1,−1, 0, 0 ],
[ 1, 0, 0,−1, 0, 0 ],
[ 1, 1,−1,−1,−1, 0 ],
[ 1, 1,−1,−2,−1,−1 ],
[ −1,−1, 1, 1, 1, 0 ],
[ −1, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, −1 ],
[ 0,−1, 0, 1, 1, 0 ],
[ 0,−1, 1, 1, 0, 1 ],
[ 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, −1, −1, 0, 0 ],
[ 0, 1, 0, −1, 0, 0 ],
[ 1,−1, 0, 0, 0, 0 ],
[ 1, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, −1, 0 ],
[ 1, 1, −1, −1, 0, 0 ],
[ 1, 1,−1,−1,−1,−1 ],
[ −1, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 1, 1, 0 ],
[ −1, 0, 1, 1, 0, 1 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 1 ],
[ 0,−1, 1, 1, 1, 1 ],
[ 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 1 ],
[ 0, 1, −1, 0, 0, 0 ],
[ 0, 1, 0, 0, −1, 0 ],
[ 1, 0, −1, −1, −1, −1 ],
[ 1, 0, 0, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, −1, −1, 0 ]
∗
4
• I ≡ P9 :
1
5
3
2



CI =




b
CoxI =

0
1
1
0
1
−1
1
0
0
0
0
0
1
0
0
0
0
−1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
−1
0
0
−1
1
0
1
1
1
0
0
1
1
1
1
1
−1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0










BI =

1
1
1
1
0
−1
0
0
1
0
0
0
0
1
0
0
0
0
0
−1
−1
−1
0
0








bI =
C




−1
−1
−1
−1
−1
1







0
1
0
0
1
−1
0
1
1
0
0
−1







Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1,−1,
[ −1,−1, 0,
[ −1, 0,−1,
[ −1, 0, 0,
[ 0,−1, 0,
[ 0,−1, 0,
[ 0,−1, 1,
1, 0,−1 ],
1, 1, 0 ],
1,−1,−1 ],
0, 0,−1 ],
0, 0,−1 ],
1, 1, 0 ],
0, 1, 1 ],
[ −1,−1, 0,
[ −1, 0,−1,
[ −1, 0,−1,
[ −1, 0, 0,
[ 0,−1, 0,
[ 0,−1, 0,
[ 0,−1, 1,
0, 0,−1 ],
0,−1,−2 ],
1, 0,−1 ],
0, 0, 0 ],
0, 0, 0 ],
1, 1, 1 ],
1, 1, 1 ],
[ −1,−1, 0,
[ −1, 0,−1,
[ −1, 0,−1,
[ −1, 0, 0,
[ 0,−1, 0,
[ 0,−1, 1,
[ 0, 0,−1,
30
1, 0,−1 ],
0,−1,−1 ],
1, 0, 0 ],
1, 0, 0 ],
0, 1, 0 ],
0, 0, 0 ],
0,−1,−1 ],
[ −1,−1, 0,
[ −1, 0,−1,
[ −1, 0, 0,
[ −1, 1,−1,
[ 0,−1, 0,
[ 0,−1, 1,
[ 0, 0,−1,
1, 0, 0 ],
0, 0,−1 ],
0,−1,−1 ],
0,−1,−1 ],
1, 0, 0 ],
0, 1, 0 ],
0, 0,−1 ],
[
[
[
[
[
[
[
[
[
[
[
0, 0,−1, 0, 0,
0, 0, 0,−1, 0,
0, 0, 0, 0, 0,
0, 0, 0, 1, 0,
0, 0, 1, 0, 0,
0, 1,−1, 0,−1,
0, 1, 0,−1, 0,
1,−1, 1, 0, 1,
1, 0, 0, 0, 1,
1, 0, 1, 0, 0,
1, 1, 0,−1, 0,
0 ],
0 ],
1 ],
1 ],
1 ],
0 ],
0 ],
1 ],
1 ],
1 ],
0 ],
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
0,−1, 1, 0, 0 ],
0, 0, 0,−1,−1 ],
0, 0, 0, 1, 0 ],
0, 0, 1, 1, 1 ],
0, 1, 0, 1, 1 ],
1,−1, 0, 0, 0 ],
1, 0, 0,−1, 0 ],
0, 0,−1, 0, 0 ],
0, 1,−1, 0, 0 ],
0, 1, 0, 1, 1 ],
1, 0,−1, 0, 1 ],
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
0, 0,−1,−1,−1 ],
0, 0, 0,−1, 0 ],
0, 0, 0, 1, 1 ],
0, 1,−1, 0, 0 ],
1,−1,−1,−1,−1 ],
1, 0,−1,−1,−1 ],
1, 0, 0, 0, 0 ],
0, 0, 0, 0, 0 ],
0, 1,−1, 0, 1 ],
0, 1, 0, 1, 2 ],
1, 0, 0, 0, 1 ],
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0, 0,−1, 0,−1 ],
0, 0, 0, 0,−1 ],
0, 0, 1, 0, 0 ],
0, 1, 0, 0, 0 ],
1,−1, 0,−1,−1 ],
1, 0,−1,−1, 0 ],
1, 0, 0, 0, 1 ],
0, 0, 0, 0, 1 ],
0, 1,−1, 1, 1 ],
1, 0,−1,−1, 0 ],
1, 1,−1, 0, 1 ]
∗
• I ≡ P10 :
3
5
1
2
4



CI =




b I =
Cox


0
1
0
1
0
−1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
0
0
−1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
−1










b
CI =









BI =



0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
−1
0
1
0
1
0
−1
−1
−1
−1
−1
−1
1







0
0
0
0
−1
0
1
1
0
0
1
−1







Number of sincere Tits roots of poset I sI = 4.
Table of roots of qbI
[ −1,−1, 1, 1, 1, 1 ],
[ −1, −1, 0, 0, 0,−1 ],
[ −1, −1, 1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 1 ],
[ 0, −1, 0, 0, 0, 0 ],
[ 0, −1, 0, 1, 1, 1 ],
[ 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 1, 1, 1 ],
[ 0, 1, 0,−1,−1, 0 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 1, 0,−1, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 0,−1,−1, 0 ],
[ −1,−1, 1, 1, 2, 1 ],
[ −1, −1, 0, 0, 1,−1 ],
[ −1, −1, 1, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 1, 1, 1 ],
[ 0, −1, 0, 0, 1, 0 ],
[ 0, −1, 1, 1, 1, 1 ],
[ 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 2 ],
[ 0, 1, 0,−1, 0, 0 ],
[ 0, 1, 1, 0, 0, 1 ],
[ 1, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 1 ],
[ 1, 1, 0, 0,−1, 0 ],
[ 1, 1,−1,−1,−2,−1 ],
[ −1,−1, 0, 0, 1, 0 ],
[ −1, 0, 0, −1, 0, −1 ],
[ −1, 0, 1, 0, 0, 0 ],
[ 0,−1, −1, 0, 0, −1 ],
[ 0,−1, 0, 1, 0, 0 ],
[ 0, 0, −1, −1, −1, −2 ],
[ 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 1, 1 ],
[ 0, 1, −1, −1, −1, −1 ],
[ 0, 1, 0, 0, −1, 0 ],
[ 1, 0, −1, −1, −1, −1 ],
[ 1, 0, 0, 0, −1, 0 ],
[ 1, 1, −1, −1, −1, 0 ],
[ 1, 1, 0, 0, −1, 1 ],
31
[ 1, 1,−1,−1,−1,−1 ],
[ −1,−1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, −1 ],
[ −1, 0, 1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, −1 ],
[ 0,−1, 0, 1, 1, 0 ],
[ 0, 0, −1, −1, −1, −1 ],
[ 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 1 ],
[ 0, 1, 0, −1, −1, −1 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 1, 0, −1, 0, −1, −1 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1, 1, −1, 0, −1, 0 ],
[ 1, 1, 0, 0, 0, 1 ]
∗
• I ≡ P11 :
1
3
5
2
4



CI =




b
CoxI =

0
1
0
1
1
−1
1
0
0
0
0
0
1
0
0
1
0
−1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
−1
0
1
0
0
0
1
0
0
1
1
1
0
0
−1
0
1
0
1
1
0
1
1
1
1
1
1
−1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0










BI =

1
1
1
0
0
−1








bI =
C

1
1
1
1
1
−1



0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
−1
−1
0
0
0
−1
−1
−1
−1
−1
1
0
1
0
1
1
−1







0
−1
0
0
−1
0
0
1
0
0
0
−1







Number of sincere Tits roots of poset I sI = 4.
Table of roots of qbI
[ −1,−2, 1,−1, 1,−1 ],
[ −1, −1, 0, −1, 0, −2 ],
[ −1, −1, 1, −1, 0, −1 ],
[ −1, −1, 1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, −1, 1, 0 ],
[ 0, −1, 1, −1, 1, 0 ],
[ 0, 0,−1, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1,−1, 0,−1, −1 ],
[ 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0, 1,−1, 1 ],
[ 1, 0, 0, 0, 0, 1 ],
[ 1, 1,−1, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 1 ],
[ −1,−1, 1,−1, 1,−1 ],
[ −1, −1, 0, −1, 0, −1 ],
[ −1, −1, 1, −1, 1, 0 ],
[ −1, 0, 0, −1, 0, −1 ],
[ −1, 0, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 1, 0, 0, 0 ],
[ 0, 0,−1, 0,−1, −1 ],
[ 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1,−1, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 1, 1 ],
[ 1, 1,−1, 0, 0, 1 ],
[ 1, 1, 0, 1,−1, 1 ],
[ 1, 1,−1, 1,−1, 1 ],
[ −1,−1, 0,−1, 1,−1 ],
[ −1,−1, 1, 0, 0,−1 ],
[ −1, 0, 0, 0, −1,−1 ],
[ 0,−1, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 1, 0 ],
[ 0, 0, −1, 0, 0,−1 ],
[ 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 1, 1 ],
[ 0, 1, −1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 1, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 1 ],
[ 1, 1, −1, 1, −1, 0 ],
[ 1, 1, 0, 1, 0, 1 ],
[ 1, 2,−1, 1,−1, 1 ],
[ −1,−1, 0, 0, 0,−1 ],
[ −1,−1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 1,−1 ],
[ 0,−1, 0, 0, 1, 0 ],
[ 0,−1, 1, 0, 1, 1 ],
[ 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 0, 1 ],
[ 0, 1, −1, 1, −1, 0 ],
[ 0, 1, 0, 1, −1, 0 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1, 1, −1, 0, −1, 0 ],
[ 1, 1, −1, 1, 0, 1 ],
[ 1, 1, 0, 1, 0, 2 ]
∗
• I ≡ P12 :
4
5
2
3
1



CI =

1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1








bI =
C

32



1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1










b
CoxI =

0
0
1
0
0
−1
1
0
0
0
0
0
1
1
0
1
0
−1
−1
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
−1










BI =

0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
−1
0
−1
0
0
−1
0
−1
−1
0
−1
−1
0
1
1
0
1
0
−1







Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−1, 1, 1,−1 ],
[ −1, −1, −1, 1, 2, 0 ],
[ −1, 0, −1, 0, 1, 0 ],
[ −1, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0 ],
[ 0, −1, −1, 1, 1, 0 ],
[ 0, −1, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0,−1, 0, −1 ],
[ 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1, 0,−1,−1, 0 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 1 ],
[ 1, 0, 0,−1, 0, 0 ],
[ 1, 0, 1,−1,−1, 0 ],
[ 1, 1, 0,−1,−1, 0 ],
[ −1,−1,−1, 0, 1,−1 ],
[ −1, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 1, 0 ],
[ 0,−1,−1, 0, 1,−1 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 1 ],
[ 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 1 ],
[ 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 1, 0,−1, 0 ],
[ 1, 0, 0,−1,−1,−1 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0,−1, 1 ],
[ 1, 1, 1,−1,−1, 0 ],
[ 1, 1, 1,−1,−1, 1 ],
[ −1,−1, 0, 1, 1, 0 ],
[ −1, 0,−1, 1, 1, 0 ],
[ −1, 0, 0, 1, 0, 0 ],
[ 0,−1,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 0, 1, 1, 0 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, −1, 0, 0 ],
[ 0, 1, 1, −1, −1, 0 ],
[ 1,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, −1, 0 ],
[ 1, 0, 1, 0, −1, 0 ],
[ 1, 1, 1, −1, −2, 0 ],
[ −1,−1,−1, 1, 1, 0 ],
[ −1, 0,−1, 0, 1,−1 ],
[ −1, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 1 ],
[ 0,−1,−1, 0, 1, 0 ],
[ 0,−1, 0, 0, 1, 0 ],
[ 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 0,−1, 0 ],
[ 0, 1, 0,−1,−1,−1 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 1, 0,−1, 1 ],
[ 1, 0, 0,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 1 ],
[ 1, 1, 1, 0,−1, 1 ]
∗
5
• I ≡ P13 :
4
2
3
1



CI =




b
CoxI =

0
0
1
0
0
−1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
−1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
−1








bI =
C




1
1
0
1
1
0










BI =

0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
−1
1
0
0
1
1
0
0
0
0
0
−1
0
−1
−1
−1
−1
−1
1







0
0
0
−1
0
0
1
0
1
1
1
−1







Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 1,−1, 1, 1, 1 ],
[ 1,−1, 1,−1,−1,−1 ],
33
[ −2, 1,−1, 1, 1, 0 ],
[ −1, 0,−1, 0, 0,−1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, −1, 0, 1,−1 ],
−1, 0, −1, 1, 1, 0 ],
−1, 0, 0, 1, 0, 0 ],
−1, 1, 0, 0, 0, 0 ],
−1, 1, 0, 1, 0, 1 ],
0,−1, 0, 0,−1,−1 ],
0, 0, −1, 0, 0, 0 ],
0, 0, 0,−1, 0, 0 ],
0, 0, 0, 0, 0,−1 ],
0, 0, 0, 1,−1, 0 ],
0, 0, 1, 0,−1, 0 ],
0, 1, 0, 0, 0, 1 ],
1,−1, 0,−1,−1,−1 ],
1,−1, 0, 0,−1, 0 ],
1,−1, 1, 0,−1, 0 ],
1, 0, 0, 0, 0, 1 ],
1, 0, 1, 0,−1, 0 ],
[ −1, 0,−1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, −1 ],
[ −1, 1,−1, 0, 1, 0 ],
[ −1, 1, 0, 0, 1, 0 ],
[ −1, 1, 0, 1, 1, 1 ],
[ 0, −1, 0, 0, 0, −1 ],
[ 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 1 ],
[ 1, −1, 0, −1, 0, −1 ],
[ 1, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, −1, 0, 0 ],
[ 1, 0, 1, −1, −1, 0 ],
[ 1, 0, 1, 0, −1, 1 ],
[ −1, 0,−1, 1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0 ],
[ −1, 1,−1, 1, 0, 0 ],
[ −1, 1, 0, 0, 1, 1 ],
[ 0,−1,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 1 ],
[ 1,−1, 0,−1, 0, 0 ],
[ 1,−1, 1,−1,−1, 0 ],
[ 1, 0, 0, 0,−1, 0 ],
[ 1, 0, 1,−1, 0, 0 ],
[ 1, 0, 1, 0, 0, 1 ],
[ −1, 0,−1, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0 ],
[ −1, 1,−1, 1, 1, 0 ],
[ −1, 1, 0, 1, 0, 0 ],
[ 0,−1, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 0, 1 ],
[ 1,−1, 0, 0,−1,−1 ],
[ 1,−1, 1,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1, 0, 1,−1, 0, 1 ],
[ 2,−1, 1,−1,−1, 0 ]
∗
• I ≡ P14 :
1
3
5
2
4
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
−1
0
1
0
0
1
0
1
1
1
0
0
−1



CI =




b
CoxI =

0
1
1
1
1
−1
0
0
0
1
0
0
0
1
0
1
1
0
−1
0
0
0
0
1
1
1
1
1
1
1








bI =
C

1
1
1
1
1
−1



1
0
0
0
0
0










BI =

0
1
1
0
1
0
1
0
0
0
0
−1
0
0
1
0
0
0
0
1
0
1
1
−1
0
0
0
1
1
0
0
0
0
0
1
0
0
−1
0
0
−1
0
−1
−1
−1
−1
−1
1
0
1
1
0
0
−1







0
−1
−1
−1
−1
1
0
0
0
0
0
−1







Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1,−1,−1, 0,−2 ],
[ −1,−1, 0, 0, 0,−1 ],
[ −1, 0,−1, 0,−1,−2 ],
[ −1, 0, 0, 0,−1,−1 ],
[ 0,−1, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 1, 0 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 1, 1 ],
[ 0, 1,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 1,−1, 1, 0, 1, 1 ],
[ 1, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, 1, 0, 1 ],
[ 1, 1, 0, 1,−1, 1 ],
[ −1,−1, 0,−1, 0,−2 ],
[ −1, 0,−1,−1,−1,−2 ],
[ −1, 0,−1, 0,−1,−1 ],
[ −1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 1,−1 ],
[ 0,−1, 0, 0, 1, 0 ],
[ 0,−1, 1, 0, 1, 1 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 0, 1 ],
[ 0, 1,−1, 1,−1, 0 ],
[ 0, 1, 0, 1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 1, 0, 2 ],
[ 1, 1, 0, 1, 0, 1 ],
[ −1,−1, 0,−1, 0,−1 ],
[ −1, 0,−1,−1, 0,−2 ],
[ −1, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0,−1, 1, 0 ],
[ 0,−1, 1,−1, 1, 0 ],
[ 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1,−1, 0,−1,−1 ],
[ 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0, 1,−1, 1 ],
[ 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 1, 1 ],
[ 1, 0, 1, 1, 1, 2 ],
[ 1, 1, 0, 1, 0, 2 ],
34
[ −1,−1, 0,−1, 1,−1 ],
[ −1, 0,−1,−1, 0,−1 ],
[ −1, 0, 0,−1, 0,−1 ],
[ −1, 1,−1, 0,−1,−1 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 1, 0, 0, 0 ],
[ 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1,−1, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 1, 1 ],
[ 1, 0, 1, 0, 1, 2 ],
[ 1, 1, 0, 0, 0, 1 ],
[ 1, 1, 1, 1, 0, 2 ]
∗
• I ≡ P15 :
4
5
2
3
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
−1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
−1
0
0
0
0
0



CI =




b I =
Cox


1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
1








BI =
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
−1
1
0
0
0
0
0










b
CI =

1
1
1
1
1
−1










1
1
1
0
1
−1







Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 1, 1, 0 ],
[ −1, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 1, 0, 0 ],
[ −1, 1, 1, 0,−1, 0 ],
[ 0,−1,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 0, 1, 1, 0 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0,−1, 0, 0 ],
[ 0, 1, 1,−1,−1, 0 ],
[ 1,−1,−1,−1, 0,−1 ],
[ 1,−1, 0, 0, 0, 0 ],
[ 1, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0 ],
[ −1, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 1, 0 ],
[ −1, 0, 1, 1, 0, 1 ],
[ −1, 1, 1, 0, 0, 0 ],
[ 0,−1,−1, 0, 1,−1 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 1 ],
[ 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 1 ],
[ 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 1, 0,−1, 0 ],
[ 1,−1,−1, 0, 0,−1 ],
[ 1, 0,−1,−1,−1,−1 ],
[ 1, 0, 0,−1,−1,−1 ],
[ 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 1 ],
[ −1, 0, 1, 1, 1, 1 ],
[ −1, 1, 1, 0, 0, 1 ],
[ 0,−1,−1, 0, 1, 0 ],
[ 0,−1, 0, 0, 1, 0 ],
[ 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 0,−1, 0 ],
[ 0, 1, 0,−1,−1,−1 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 1, 0,−1, 1 ],
[ 1,−1,−1, 0, 0, 0 ],
[ 1, 0,−1,−1, 0,−1 ],
[ 1, 0, 0,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 1 ],
∗
5
• I ≡ P16 :
4
2
3
1
35
[ −1, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 1, 0, 1 ],
[ 0,−1,−1, 1, 1, 0 ],
[ 0,−1, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1, 0,−1,−1, 0 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 1 ],
[ 1,−1,−1, 0, 1, 0 ],
[ 1, 0,−1,−1, 0, 0 ],
[ 1, 0, 0,−1, 0, 0 ],
[ 1, 1, 0,−1,−1, 0 ]



CI =




b I =
Cox


1
0
0
0
0
0
0
0
1
0
0
−1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
0
0
−1
0
0
0
0
0
1
−1
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0








BI =
0
0
−1
0
0
1










b
CI =

1
1
1
1
1
−1



0
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
−1
0
0
0
0
1
0
0
0
0
1
0
0
−1
−1
−1
−1
−1
1
0
0
1
0
0
0







0
0
−1
−1
−1
0
1
0
0
1
0
0







Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1,−1, 0, 1,−1 ],
[ −1, 0,−1, 1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0 ],
[ 0,−1,−1,−1, 1,−1 ],
[ 0,−1, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0,−1, 0 ],
[ 1,−1, 0,−1, 0,−1 ],
[ 1,−1, 1,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0,−1, 0 ],
2.7
2.7.1
[ −1, 0,−1, 0, 0,−1 ],
[ −1, 0,−1, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 1,−1, 0 ],
[ 0,−1,−1, 0, 0,−1 ],
[ 0,−1, 0,−1, 1,−1 ],
[ 0,−1, 0, 0, 1, 0 ],
[ 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 1,−1, 0 ],
[ 0, 1, 1, 0,−1, 1 ],
[ 1,−1, 0,−1, 0, 0 ],
[ 1, 0, 0,−1, 0, 0 ],
[ 1, 0, 1,−1,−1, 0 ],
[ 1, 0, 1, 0,−1, 1 ],
[ −1, 0,−1, 0, 1,−1 ],
[ −1, 0,−1, 1, 1, 0 ],
[ −1, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 1, 0, 0 ],
[ 0,−1,−1, 0, 1,−1 ],
[ 0,−1, 0,−1, 1, 0 ],
[ 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 1,−1, 0, 0 ],
[ 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0, 1,−1, 1 ],
[ 0, 1, 1, 0, 0, 1 ],
[ 1,−1, 0,−1, 1, 0 ],
[ 1, 0, 0, 0,−1, 0 ],
[ 1, 0, 1,−1, 0, 0 ],
[ 1, 0, 1, 0, 0, 1 ],
[ −1, 0,−1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0,−1 ],
[ −1, 1,−1, 1, 0, 0 ],
[ −1, 1, 0, 1, 0, 1 ],
[ 0,−1,−1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 1, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 1, 1,−1, 1 ],
[ 1,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1, 0, 1,−1, 0, 1 ],
[ 1, 1, 1, 0,−1, 1 ]
Posets with 7 vertices
Posets of type A7
• I ≡ 5 A∗6 :
1
2
3
4
∗
5
6




CI =






b
CoxI =


0
0
0
0
0
1
−1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
−1
1
1
1
1
1
1
1













bI =
C



1
1
1
1
1
1
−1









36
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
 −1

 0
BI = 0
 0
 0
0

0
0
1
1
1
0
0
−1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
−1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1
1
1
1
1
1
0
−1









0
0
0
1
0
0
0
0
0
1
1
0
0
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
• I ≡ 4 A∗6 :
1
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
2
3




b
CoxI =


6
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
−1



CI =


[ −1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 1 ]
∗
4
5

[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0













BI =


0
0
0
0
−1
−1
1













b
CI =


1
1
1
1
1
1
−1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
1
0
0
0
0









0
1
0
0
0
0
0
1
1
1
0
0
0
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
37
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ]
1
• I ≡ 3 A∗6 :
2
4
5




CI =






b
CoxI =


∗
3
6
1
0
0
0
0
0
0
0
0
0
1
1
1
−1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
−1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
−1













b
CI =


1
1
1
0
0
0
0













BI =


0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1
1
1
1
0
0
0
−1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
−1









1
1
0
1
1
0
−1









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0,−1, 0,0,−1 ],
[ −1, 0, 0, 0, 0,0, 0 ],
[ 0,−1, 0, 0,−1,0,−1 ],
[ 0,−1, 1, 0, 0,0, 0 ],
[ 0, 0,−1, 0, 0,0,−1 ],
[ 0, 0, 0,−1, 0,1, 0 ],
[ 0, 0, 0, 0,−1,1, 0 ],
[ 0, 0, 0, 0, 0,0, 1 ],
[ 0, 0, 0, 0, 1,0, 0 ],
[ 0, 0, 0, 1, 0,0, 0 ],
[ 0, 0, 1, 0, 0,1, 1 ],
[ 0, 1, 0, 0, 0,0, 0 ],
[ 0, 1, 0, 1, 0,0, 1 ],
[ 1, 0, 0, 0, 0,0, 1 ],
2.7.2
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ −1, 0, 0, 0, 0,−1,−1 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ]
Posets of type D7
• I ≡ D∗6 :
2
3
4
5
∗
6
1




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1













bI =
C



38
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
1
1
1
0
−1
1
0
0
0
0
0
−1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
−1
−1
−1
0
0
1
1
1
1
1
1
1
−1













BI =


1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
−1
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1,−1, 0, 0, 1,−1 ],
[ −1,−1, 0, 0, 0, 1,−1 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0,−1, 1,−1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 0, 1, 1,−1, 1 ],
[ 1, 0, 1, 0, 1,−1, 1 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
• I ≡ 0 D∗6 A0 :
[ −1,−1, 0,−1, 0, 1,−1 ],
[ −1,−1, 0, 0, 0, 1, 0 ],
[ −1, 0,−1, 0, 0, 1,−1 ],
[ −1, 0, 0,−1, 0, 1,−1 ],
[ −1, 0, 0, 0,−1, 1, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 1, 0,−1, 0 ],
[ 1, 0, 1, 0, 0,−1, 0 ],
[ 1, 0, 1, 1, 0,−1, 1 ],
[ 1, 1, 0, 0, 1,−1, 1 ],
[ −1,−1, 0, 0,−1, 1,−1 ],
[ −1, 0,−1,−1, 0, 1,−1 ],
[ −1, 0,−1, 0, 0, 1, 0 ],
[ −1, 0, 0,−1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 1,−1, 0 ],
[ 1, 0, 0, 1, 0,−1, 1 ],
[ 1, 0, 1, 0, 0,−1, 1 ],
[ 1, 1, 0, 0, 0,−1, 0 ],
[ 1, 1, 0, 1, 0,−1, 1 ],
[ −1,−1, 0, 0, 0, 0,−1 ],
[ −1, 0,−1, 0,−1, 1,−1 ],
[ −1, 0, 0,−1,−1, 1,−1 ],
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 1,−1, 1 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 1, 0, 0, 0,−1, 1 ],
[ 1, 1, 1, 0, 0,−1, 1 ]
1
2
3




CI =






b
CoxI =


0
1
0
0
0
0
−1
1
0
0
0
0
0
0
4
5
∗
6
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
−1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
−1













b
CI =











1
0
1
1
1
1
0
0
1
1
1
1
1
0
−1
 0

 −1
BI = −1
 0
 0
0

0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
−1
−1
−1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
−1
−1
−1
−1
−1
−1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1









1
1
1
1
1
1
−1
0
0
0
0
1
0
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 0, 0, 0,−1 ],
[ −1,−1, 0, 0, 0, 1,−1 ],
[ −1,−1, 0, 0, 0, 1, 0 ],
39
[ −1,−1, 0, 0, 1, 0,−1 ],
[ −1,−1, 0, 0, 1, 0, 0 ],
[ −1,−1, 0, 1, 0, 1, 0 ],
[ −1,−1, 1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1,−1, 0, 0, 0, 0 ],
[ 1, 1, 0,−1, 0, 0, 0 ],
[ 1, 1, 0, 0,−1, 0, 1 ],
[ −1,−1, 0, 0, 1, 1, 0 ],
[ −1,−1, 0, 1, 1, 0, 0 ],
[ −1,−1, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 1,−1,−1, 0, 0, 0 ],
[ 1, 1,−1, 0, 0, 0, 1 ],
[ 1, 1, 0,−1, 0, 0, 1 ],
[ 1, 1, 0, 0, 0,−1, 0 ],
[ −1,−1, 0, 1, 0, 0,−1 ],
[ −1,−1, 1, 0, 0, 0,−1 ],
[ −1,−1, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 1,−1, 0,−1, 0, 0 ],
[ 1, 1, 0,−1,−1, 0, 0 ],
[ 1, 1, 0, 0,−1,−1, 0 ],
[ 1, 1, 0, 0, 0,−1, 1 ],
[ −1,−1, 0, 1, 0, 0, 0 ],
[ −1,−1, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1,−1, 0, 0,−1, 0 ],
[ 1, 1, 0,−1, 0,−1, 0 ],
[ 1, 1, 0, 0,−1, 0, 0 ],
[ 1, 1, 0, 0, 0, 0, 1 ]
1
• I≡
∗
0 D5
A1 :
2
3
4
∗
5
6




CI =






b I =
Cox



0
1
0
0
0
1
−1
1
0
0
0
0
0
0
1
0
0
0
0
1
−1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
−1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
−1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0













BI =


−1
0
0
0
0
0
0













bI =
C



1
1
1
1
1
1
−1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
−1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
−1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1
1
1
1
1
1
0
−1









0
0
0
1
0
0
0
0
0
1
1
0
0
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 0, 0,−1,−2 ],
[ −1,−1, 0, 0, 1, 0,−1 ],
[ −1,−1, 0, 1, 0, 0, 0 ],
[ −1,−1, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ −1,−1, 0, 0, 0,−1,−1 ],
[ −1,−1, 0, 0, 1, 0, 0 ],
[ −1,−1, 0, 1, 1, 0, 0 ],
[ −1,−1, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ −1,−1, 0, 0, 0, 0,−1 ],
[ −1,−1, 0, 1, 0,−1,−1 ],
[ −1,−1, 1, 0, 0,−1,−1 ],
[ −1,−1, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
40
[ −1,−1, 0, 0, 1,−1,−1 ],
[ −1,−1, 0, 1, 0, 0,−1 ],
[ −1,−1, 1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[
[
[
[
[
1,
1,
1,
1,
1,
0, 0,−1, 0,
0, 0, 0, 0,
1,−1, 0, 0,
1, 0,−1, 0,
1, 0, 0,−1,
0,
1,
0,
0,
1,
0 ],
1 ],
1 ],
1 ],
1 ],
[
[
[
[
[
1,
1,
1,
1,
1,
0, 0, 0,−1,
1,−1,−1, 0,
1,−1, 0, 0,
1, 0,−1, 0,
1, 0, 0, 0,
0,
0,
1,
1,
0,
0 ],
0 ],
1 ],
1 ],
1 ],
[
[
[
[
[
1,
1,
1,
1,
1,
0, 0, 0, 0,
1,−1, 0,−1,
1, 0,−1,−1,
1, 0, 0,−1,
1, 0, 0, 0,
0,
0,
0,
0,
1,
0 ],
0 ],
0 ],
0 ],
1 ],
0
0
1
1
0
0
0
0
0
0
1
0
0
0
[
[
[
[
[
1,
1,
1,
1,
1,
0, 0, 0, 0,
1,−1, 0, 0,
1, 0,−1, 0,
1, 0, 0,−1,
1, 0, 0, 0,
0,
0,
0,
0,
1,
1 ],
0 ],
0 ],
1 ],
2]
1
• I≡
∗
0 D4
A2 :
2
3
∗
4
5



CI =


1
0
0
0
0
0
0
0
1
0
0
1
1
−1
1
0
0
0
1
1
−1





b
CoxI =


0
1
0
0
0
0
0
6
1
1
1
0
0
0
0
0
0
0
0
−1
−1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
−1
0
0
0
0
1
0
0
1
1
1
1
1
1
−1













b
CI =











1
0
1
1
0
0
0
0
1
1
1
0
0
0
−1
 0

 0
BI = 0
 −1
 0
1

0
−1
0
0
−1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
−1
−1
−1
−1
−1
−1
−1
1

0
0
1
0
0
0
0
0
0
0
0
−1
−1
1








0
0
1
0
−1
0
1









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 0,−1,−1,−2 ],
[ −1,−1, 0, 0, 0,−1,−1 ],
[ −1,−1, 0, 1, 0, 0,−1 ],
[ −1,−1, 1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 1,−1, 0, 0, 1, 1 ],
[ 1, 1, 0,−1, 0, 1, 1 ],
[ 1, 1, 0, 0, 0, 1, 2 ],
[ −1,−1, 0, 0,−1, 0,−2 ],
[ −1,−1, 0, 0, 0, 0,−1 ],
[ −1,−1, 0, 1, 0, 0, 0 ],
[ −1,−1, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1,−1,−1, 0, 0, 0 ],
[ 1, 1,−1, 0, 1, 0, 1 ],
[ 1, 1, 0,−1, 1, 0, 1 ],
[ 1, 1, 0, 0, 1, 0, 1 ],
[ −1,−1, 0, 0,−1, 0,−1 ],
[ −1,−1, 0, 1,−1, 0,−1 ],
[ −1,−1, 1, 0,−1, 0,−1 ],
[ −1,−1, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1,−1, 0, 0, 0, 0 ],
[ 1, 1, 0,−1, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 0, 1, 0, 2 ],
1
• I≡
∗
0 D3
A3 :
2
4
∗
3
5
6
41
[ −1,−1, 0, 0, 0,−1,−2 ],
[ −1,−1, 0, 1, 0,−1,−1 ],
[ −1,−1, 1, 0, 0,−1,−1 ],
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 1,−1, 0, 0, 0, 1 ],
[ 1, 1, 0,−1, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, 1, 1 ],
[ 1, 1, 0, 0, 1, 1, 2 ]




CI =






b
CoxI =


0
1
0
1
1
1
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
−1
1
1
1
0
0
0
0
0
0
0
−1
−1
−1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
−1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0













bI =
C



1
1
1
1
1
1
−1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
−1
0
0
0
0
0
1
0
 −1

 0
BI = 0
 0
 0
1










0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
−1
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1
0
0
0
−1
−1
−1
1









0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0,−1,−1, 0,−2 ],
[ −1,−1, 0, 0,−1,−1,−2 ],
[ −1,−1, 0, 0, 0,−1,−1 ],
[ −1,−1, 1, 0, 0,−1,−1 ],
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 1,−1, 0, 1, 0, 1 ],
[ 1, 1, 0, 0, 0, 1, 2 ],
[ 1, 1, 0, 1, 0, 0, 1 ],
[ −1,−1, 0,−1, 0,−1,−2 ],
[ −1,−1, 0, 0,−1, 0,−2 ],
[ −1,−1, 0, 0, 0, 0,−1 ],
[ −1,−1, 1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1,−1, 0, 0, 0, 0 ],
[ 1, 1,−1, 1, 0, 0, 1 ],
[ 1, 1, 0, 0, 1, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 2 ],
[ −1,−1, 0,−1, 0,0,−2 ],
[ −1,−1, 0, 0,−1,0,−1 ],
[ −1,−1, 1,−1, 0,0,−1 ],
[ −1,−1, 1, 0, 0,0, 0 ],
[ −1, 0, 0, 0, 0,0,−1 ],
[ 0,−1, 0, 0,−1,0,−1 ],
[ 0,−1, 1, 0, 0,0, 0 ],
[ 0, 0,−1, 0, 0,0,−1 ],
[ 0, 0, 0,−1, 0,1, 0 ],
[ 0, 0, 0, 0,−1,1, 0 ],
[ 0, 0, 0, 0, 0,0, 1 ],
[ 0, 0, 0, 0, 1,0, 0 ],
[ 0, 0, 0, 1, 0,0, 0 ],
[ 0, 0, 1, 0, 0,1, 1 ],
[ 0, 1, 0, 0, 0,0, 0 ],
[ 0, 1, 0, 1, 0,0, 1 ],
[ 1, 0, 0, 0, 0,1, 1 ],
[ 1, 1,−1, 0, 0,0, 1 ],
[ 1, 1, 0, 0, 0,0, 1 ],
[ 1, 1, 0, 0, 1,0, 2 ],
[ 1, 1, 0, 1, 0,1, 2 ],
[ −1,−1, 0,−1, 0, 0,−1 ],
[ −1,−1, 0, 0, 0,−1,−2 ],
[ −1,−1, 1, 0,−1, 0,−1 ],
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 1,−1, 0, 0, 1, 1 ],
[ 1, 1, 0, 0, 0, 1, 1 ],
[ 1, 1, 0, 0, 1, 1, 2 ],
[ 1, 1, 0, 1, 1, 0, 2 ]
1
• I≡
∗
0 D2
A4 :
∗
2
3
4




CI =


1
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1













bI =
C



42
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
1
1
1
1
−1
1
0
1
1
1
1
−1
1
1
0
0
0
0
−1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
−1













BI =


1
0
1
1
1
0
−1
0
1
1
1
1
0
−1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
−1
0
0
1
1
1
1
−1
1
1
2
2
1
0
−2









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1,−1,−1, 0, 0,−2 ],
[ −1,−1,−1, 0, 0, 0,−1 ],
[ −1,−1, 0,−1, 0, 0,−1 ],
[ −1,−1, 0, 0, 0,−1,−2 ],
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 1, 0, 0, 1, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 2 ],
[ 1, 1, 1, 0, 0, 0, 2 ],
[ −1,−1,−1, 0,−1, 0,−2 ],
[ −1,−1, 0,−1,−1, 0,−2 ],
[ −1,−1, 0, 0,−1,−1,−2 ],
[ −1,−1, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1,−1, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 0, 1, 0, 2 ],
[ 1, 1, 0, 1, 0, 1, 2 ],
[ 1, 1, 1, 0, 0, 1, 2 ],
1
• I ≡ 1 D∗6 A0 :




CI =





b
CoxI =


[ −1,−1,−1, 0, 0, 0,−2 ],
[ −1,−1, 0,−1, 0, 0,−2 ],
[ −1,−1, 0, 0,−1, 0,−1 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, 1, 2 ],
[ 1, 1, 0, 1, 0, 0, 1 ],
[ 1, 1, 1, 0, 0, 0, 1 ],
[ 1, 1, 1, 1, 0, 0, 2 ]
2
3

[ −1,−1,−1, 0, 0,−1,−2 ],
[ −1,−1, 0,−1, 0,−1,−2 ],
[ −1,−1, 0, 0,−1, 0,−2 ],
[ −1,−1, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 1, 0, 0, 0, 1, 1 ],
[ 1, 1, 0, 0, 1, 1, 2 ],
[ 1, 1, 0, 1, 1, 0, 2 ],
[ 1, 1, 1, 0, 1, 0, 2 ],
0
0
0
0
0
0
−1
4
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
5
1
0
1
0
0
0
0
−1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
∗
6
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1













b
CI =


1
1
1
1
1
1
−1

0
 0

 0
BI = −1
 0
 0
0








0
1
0
1
1
1
0

0
0
1
1
1
1
0
0
−1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
−1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
0
0
0
0
0
0
−1
−1
−1
−1
−1
−1
1

0
0
0
0
0
0
1
1
1
1
1
1
1
−1








0
0
0
0
1
0
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
43
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 1, 0,−1, 0, 0 ],
[ 0,−1,−1, 0, 0, 0,−1 ],
[ 0,−1,−1, 0, 1, 0, 0 ],
[ 0,−1,−1, 1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 1,−1, 0, 0, 0 ],
[ 0, 1, 1, 0,−1, 0, 1 ],
[ 1,−1,−1, 0, 0, 0,−1 ],
[ 1,−1,−1, 1, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0,−1, 0 ],
[ 0,−1,−1, 0, 0, 1,−1 ],
[ 0,−1,−1, 0, 1, 1, 0 ],
[ 0,−1,−1, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1,−1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0,−1, 0 ],
[ 1,−1,−1, 0, 0, 0, 0 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
1
• I≡
∗
1 D5
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 0 ],
[ 0,−1,−1, 0, 0, 1, 0 ],
[ 0,−1,−1, 1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 1,−1,−1, 0, 0 ],
[ 0, 1, 1, 0,−1,−1, 0 ],
[ 0, 1, 1, 0, 0,−1, 1 ],
[ 1,−1,−1, 0, 0, 1, 0 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 1,−1, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 1 ],
[ 0,−1,−1, 0, 1, 0,−1 ],
[ 0,−1,−1, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 1,−1, 0,−1, 0 ],
[ 0, 1, 1, 0,−1, 0, 0 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1,−1,−1, 0, 1, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ]
2
A1 :
3
4
∗
5
6




CI =






b I =
Cox



0
0
0
0
0
1
−1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
−1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
−1
1
1
1
1
1
1
1













bI =
C



1
1
1
1
1
1
−1
1
1
1
1
1
0
0













BI =


0
1
0
1
1
0
0
0
0
0
0
0
1
−1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
−1
−1
0
0
0
−1
1
0
0
0
0
1
0
0
−1
0
−1
0
0
−1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1
1
1
1
1
1
0
−1









0
0
0
1
0
0
0
−1
0
0
1
0
0
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 1, 0,−1, 0, 0 ],
[ 0,−1,−1, 0, 0,−1,−2 ],
[ 0,−1,−1, 0, 1, 0,−1 ],
[ 0,−1,−1, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 0 ],
[ 0,−1,−1, 0, 0,−1,−1 ],
[ 0,−1,−1, 0, 1, 0, 0 ],
[ 0,−1,−1, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 1 ],
[ 0,−1,−1, 0, 0, 0,−1 ],
[ 0,−1,−1, 1, 0,−1,−1 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 1,−1,−1, 0, 0 ],
44
[ −1, 0, 0, 0,
[ −1, 1, 1,−1,
[ −1, 1, 1, 0,
[ 0,−1,−1, 0,
[ 0,−1,−1, 1,
[ 0,−1, 0, 0,
[ 0, 0,−1, 0,
[ 0, 0,−1, 1,
[ 0, 0, 0,−1,
[ 0, 0, 0, 0,
[ 0, 0, 0, 0,
[ 0, 0, 0, 0,
[ 0, 0, 0, 1,
[ 0, 0, 1, 0,
[ 0, 1, 0, 0,
[ 0, 1, 1,−1,
1, 0, 0 ],
0, 0, 0 ],
0, 1, 1 ],
1,−1,−1 ],
0, 0,−1 ],
0, 0,−1 ],
0,−1,−1 ],
0, 0, 0 ],
1, 0, 0 ],
0,−1,−1 ],
0, 1, 0 ],
1, 1, 1 ],
0, 1, 1 ],
0, 0, 1 ],
0, 0, 0 ],
0, 0, 0 ],
[
[
[
[
[
0, 1, 1,−1, 0, 0, 1 ],
0, 1, 1, 0,−1, 1, 1 ],
1,−1,−1, 0, 0,−1,−1 ],
1,−1,−1, 1, 0, 0, 0 ],
1, 0, 0, 0,−1, 0, 0 ],
[
[
[
[
[
0, 1, 1,−1,
0, 1, 1, 0,
1,−1,−1, 0,
1,−1, 0, 0,
1, 0, 0, 0,
1
• I≡
∗
1 D4
3
1
0
0
0
0
0
0




CI =


0
0
0
0
1
1
−1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
[
[
[
[
[
0, 1, 1,
0, 1, 1,
1,−1,−1,
1, 0,−1,
1, 0, 0,
0,−1,
0, 0,
0, 0,
0, 0,
0, 0,
0,
1,
0,
0,
0,
0 ],
1 ],
0 ],
0 ],
1 ],
0
0
1
1
0
0
0
0
0
0
1
0
0
0
[
[
[
[
[
0, 1, 1, 0,−1,
0, 1, 1, 0, 0,
1,−1,−1, 0, 1,
1, 0, 0,−1, 0,
1, 0, 0, 0, 0,
0,
1,
0,
0,
1,
1 ],
2 ],
0 ],
0 ],
1]
∗
4
5



b
CoxI =


1, 1 ],
0, 1 ],
0,−1 ],
0, 0 ],
0, 0 ],
2
A2 :

0,
0,
0,
0,
0,
1
0
1
0
0
0
0
6
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
−1
0
0
0
0
0
0
1
1
1
1
0
0
−1
0
0
0
0
1
0
0
1
1
1
1
1
1
1













b
CI =


1
1
1
1
1
1
−1

0
 0

 0
BI = 0
 −1
 0
0









1
1
1
1
0
0
0
0
1
0
1
0
0
0
−1
0
−1
0
0
0
1
−1
−1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
−1
−1
−1
−1
−1
−1
−1
1
−1
0
0
0
0
0
0









0
0
0
0
−1
−1
1
−1
0
0
0
−1
0
1









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 0 ],
[ 0,−1,−1, 0,−1,−1,−2 ],
[ 0,−1,−1, 0, 0,−1,−1 ],
[ 0,−1,−1, 1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 1,−1, 0, 1, 1 ],
[ 0, 1, 1, 0, 0, 1, 2 ],
[ 1,−1,−1, 0,−1, 0,−1 ],
[ 1,−1,−1, 1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 1 ],
[ 0,−1,−1, 0,−1, 0,−2 ],
[ 0,−1,−1, 0, 0, 0,−1 ],
[ 0,−1,−1, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 1,−1, 1, 0, 1 ],
[ 0, 1, 1, 0, 1, 0, 1 ],
[ 1,−1,−1, 0, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
1
• I≡
∗
1 D3
A3 :
2
∗
3
4
5
6
45
[ −1, 0, 0, 0, 0,0,−1 ],
[ −1, 1, 0, 0, 0,0, 0 ],
[ −1, 1, 1, 0, 0,1, 1 ],
[ 0,−1,−1, 0,−1,0,−1 ],
[ 0,−1,−1, 1,−1,0,−1 ],
[ 0,−1, 0, 0,−1,0,−1 ],
[ 0,−1, 0, 1, 0,0, 0 ],
[ 0, 0,−1, 0, 0,0, 0 ],
[ 0, 0, 0,−1, 0,0,−1 ],
[ 0, 0, 0, 0,−1,1, 0 ],
[ 0, 0, 0, 0, 0,0, 1 ],
[ 0, 0, 0, 0, 1,0, 0 ],
[ 0, 0, 0, 1, 0,1, 1 ],
[ 0, 0, 1, 0, 0,0, 1 ],
[ 0, 1, 0, 0, 0,0, 0 ],
[ 0, 1, 1,−1, 0,0, 0 ],
[ 0, 1, 1, 0, 0,0, 1 ],
[ 0, 1, 1, 0, 1,0, 2 ],
[ 1,−1,−1, 0, 0,0,−1 ],
[ 1, 0,−1, 0, 0,0, 0 ],
[ 1, 0, 0, 0, 0,1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 1,−1, 0, 0, 0 ],
[ −1, 1, 1, 0, 1, 0, 1 ],
[ 0,−1,−1, 0, 0,−1,−2 ],
[ 0,−1,−1, 1, 0,−1,−1 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1,−1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 1, 1 ],
[ 0, 1, 1, 0, 1, 1, 2 ],
[ 1,−1,−1, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ]




CI =






b
CoxI =


0
0
0
1
1
1
−1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
−1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1













bI =
C



1
1
1
1
1
1
−1













BI =


1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
−1
0
0
0
1
1
1
0
1
1
0
1
0
0
−1
0
0
0
0
1
1
0
−1
−1
−1
−1
−1
−1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
−1
1
0
0
0
0
0
0









0
0
0
1
1
1
−1
2
1
1
1
1
0
−2









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 1 ],
[ 0,−1,−1,−1,−1, 0,−2 ],
[ 0,−1,−1, 0,−1,−1,−2 ],
[ 0,−1,−1, 0, 0,−1,−1 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 1, 0, 0, 1, 2 ],
[ 0, 1, 1, 1, 0, 0, 1 ],
[ 1,−1,−1,−1, 0, 0,−1 ],
[ 1,−1,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
• I ≡ 2 D∗6 A0 :
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 1, 1 ],
[ 0,−1,−1,−1, 0,−1,−2 ],
[ 0,−1,−1, 0,−1, 0,−2 ],
[ 0,−1,−1, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 1, 0, 1 ],
[ 0, 1, 1, 1, 0, 0, 2 ],
[ 1,−1,−1, 0,−1, 0,−1 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
1
2



CI =






b
CoxI =


0
0
0
0
0
0
−1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 1, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 1, 0, 0, 1 ],
[ 0,−1,−1,−1, 0, 0,−1 ],
[ 0,−1,−1, 0, 0,−1,−2 ],
[ 0,−1, 0, 0,−1, 0,−1 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 1, 0, 0, 1, 1 ],
[ 0, 1, 1, 0, 1, 1, 2 ],
[ 0, 1, 1, 1, 1, 0, 2 ],
[ 1,−1,−1, 0, 0, 0,−1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ]
3
4

[ −1, 0, 0, 0, 0,−1,−1 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 1, 0, 1 ],
[ 0,−1,−1,−1, 0, 0,−2 ],
[ 0,−1,−1, 0,−1, 0,−1 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 1, 0, 2 ],
[ 0, 1, 1, 1, 0, 1, 2 ],
[ 1,−1,−1, 0, 0,−1,−1 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
5
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
∗
6
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
−1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
−1













bI =
C



1
1
1
1
1
1
0













BI =


46
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
−1
−1
−1
0
0
0
0
0
0
0
0
1
1
0
−1
−1
0
−1
0
0
0
−1
−1
−1
−1
−1
−1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1









1
1
1
1
1
1
−1
0
0
0
0
1
0
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 1, 0,−1, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 0, 0 ],
[ 0, 0,−1,−1, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 1, 1,−1,−1, 0 ],
[ 0, 0, 1, 1, 0,−1, 1 ],
[ 0, 1,−1,−1, 0, 1, 0 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1,−1, 1, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 0, 1 ],
[ 0, 0,−1,−1, 1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 1,−1, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1,−1,−1, 1, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 1, 0,−1,−1, 0, 0,−1 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
1
• I≡
∗
2 D5
2
[ −1, 0, 0, 0, 0,0, 0 ],
[ −1, 0, 1, 0, 0,0, 0 ],
[ −1, 0, 1, 1, 0,0, 1 ],
[ 0,−1, 0, 0, 0,1, 0 ],
[ 0,−1, 1, 1,−1,0, 0 ],
[ 0, 0,−1,−1, 0,0,−1 ],
[ 0, 0,−1,−1, 1,0, 0 ],
[ 0, 0,−1, 0, 0,1, 0 ],
[ 0, 0, 0,−1, 0,1, 0 ],
[ 0, 0, 0, 0,−1,1, 0 ],
[ 0, 0, 0, 0, 0,0, 1 ],
[ 0, 0, 0, 0, 1,0, 0 ],
[ 0, 0, 0, 1, 0,0, 0 ],
[ 0, 0, 1, 0, 0,0, 0 ],
[ 0, 0, 1, 1,−1,0, 1 ],
[ 0, 1,−1,−1, 0,0,−1 ],
[ 0, 1,−1, 0, 0,0, 0 ],
[ 0, 1, 0, 0, 0,0, 0 ],
[ 1, 0,−1,−1, 0,0, 0 ],
[ 1, 0, 0,−1, 0,0, 0 ],
[ 1, 0, 0, 0, 0,0, 1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 1,−1, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 1, 1, 0,−1, 0 ],
[ 0, 0,−1,−1, 0, 1,−1 ],
[ 0, 0,−1,−1, 1, 1, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0,−1, 0 ],
[ 0, 1,−1,−1, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0,−1,−1, 0, 1, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 1,−1,−1, 0, 0, 0 ]
3
A1 :
4
∗
5
6




CI =






b I =
Cox



0
0
0
0
0
1
−1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
−1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
−1
0
0
0
0
0
1
0
1
1
1
1
1
1
1













b
CI =


1
1
1
1
1
1
−1













BI =


1
1
1
1
1
0
0
0
0
0
0
0
1
−1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
−1
0
0
0
0
1
1
0
0
−1
−1
0
−1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
0
0
0
1
−1
−1
−1
−1
−1
−1
1
1
1
1
1
1
0
−1









0
−1
0
0
0
0
0
−1
−1
0
0
0
0
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1,
[ −1, 0,
[ −1, 0,
[ 0,−1,
[ 0,−1,
[ 0,−1,
1,
0,
1,
0,
0,
1,
1,
0,
1,
0,
1,
1,
0, 0, 0 ],
1, 0, 0 ],
0, 0, 0 ],
0,−1,−1 ],
0, 0, 0 ],
0, 0, 1 ],
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ 0,−1,
[ 0,−1,
[ 0,−1,
0,
0,
1,
0,
1,
1,
0,
1,
1,
0,
0,
1,
0,−1,−1 ],
0, 0, 0 ],
0, 0, 1 ],
0, 0,−1 ],
0, 0, 0 ],
0, 1, 1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 1, 1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 1,−1, 0, 0 ],
[ 0, 0,−1,−1, 0,−1,−2 ],
47
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 1,−1, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 1, 1, 0, 0, 0 ],
[ 0, 0,−1,−1, 0,−1,−1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0,−1,−1, 0, 0,−1 ],
0, 0,−1, 0, 0,−1,−1 ],
0, 0, 0,−1, 0,−1,−1 ],
0, 0, 0, 0,−1,−1,−1 ],
0, 0, 0, 0, 0,−1, 0 ],
0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 1,−1, 0, 0 ],
0, 0, 1, 0,−1, 0, 0 ],
0, 0, 1, 1,−1, 0, 0 ],
0, 0, 1, 1, 0, 1, 1 ],
0, 1,−1,−1, 0, 0, 0 ],
0, 1, 0, 0,−1, 0, 0 ],
1,−1, 0, 0, 0, 0, 0 ],
1, 0,−1,−1, 1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1
• I≡
∗
2 D4
0,−1,−1, 1,−1,−1 ],
0,−1, 0, 0, 0,−1 ],
0, 0,−1, 0, 0,−1 ],
0, 0, 0,−1, 0,−1 ],
0, 0, 0, 0, 0,−1 ],
0, 0, 0, 1, 0, 0 ],
0, 0, 1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0 ],
0, 1, 1,−1, 0, 1 ],
0, 1, 1, 0, 1, 2 ],
1,−1,−1, 1, 0, 0 ],
1, 0, 0, 0, 0, 0 ],
0,−1,−1, 0,−1,−1 ],
0,−1, 0, 0, 0, 0 ],
0, 0, 0, 0, 0, 1 ],
2
A2 :



CI =






b I =
Cox



0
0
0
0
1
1
−1
1
0
0
0
0
0
0
0,−1,−1, 1, 0,−1 ],
0,−1, 0, 0, 0, 0 ],
0, 0,−1, 0, 0, 0 ],
0, 0, 0,−1, 0, 0 ],
0, 0, 0, 0, 0, 1 ],
0, 0, 0, 1, 0, 1 ],
0, 0, 1, 0, 0, 1 ],
0, 1, 0, 0, 0, 1 ],
0, 1, 1,−1, 1, 1 ],
1,−1,−1, 0,−1,−1 ],
1,−1, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 1 ],
0,−1,−1, 0, 0,−1 ],
0, 0,−1, 0, 0, 0 ],
0, 0, 0, 0, 1, 1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
0,−1,−1, 1, 0, 0 ],
0,−1, 0, 1, 0, 0 ],
0, 0,−1, 1, 0, 0 ],
0, 0, 0, 0,−1,−1 ],
0, 0, 0, 0, 1, 0 ],
0, 0, 0, 1, 1, 1 ],
0, 0, 1, 0, 1, 1 ],
0, 1, 0, 0, 1, 1 ],
0, 1, 1, 0, 0, 1 ],
1,−1,−1, 0, 0,−1 ],
1, 0,−1, 0, 0, 0 ],
1, 0, 0, 0, 1, 1 ],
0,−1,−1, 0, 0, 0 ],
0, 0, 0,−1, 0, 0 ],
1,−1,−1, 0, 0, 0 ]
∗
5
1
0
0
0
0
0
0
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
3
4

[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
6
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
−1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1













bI =
C



1
1
1
1
1
1
−1













BI =


1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
−1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
−1
0
0
0
−1
−1
−1
−1
−1
−1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0









0
0
0
0
1
1
−1
1
0
0
0
1
0
−1









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 1 ],
[ 0,−1, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 1, 1 ],
[ 0, 0,−1,−1,−1, 0,−1 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 1,−1,−1, 0, 0,−1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 1, 1 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 1, 0, 1 ],
[ 0, 0,−1,−1, 0,−1,−2 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 1, 1 ],
[ 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 1,−1,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0,−1,−1,−1, 0,−1 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ −1, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 1, 1, 0, 0, 0 ],
[ 0, 0,−1,−1,−1,−1,−2 ],
[ 0, 0,−1,−1, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, 1, 0, 1, 2 ],
[ 0, 1,−1,−1,−1, 0,−1 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 1, 0,−1,−1, 0,−1,−1 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
48
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 1, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 0, 1 ],
[ 0, 0,−1,−1,−1, 0,−2 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 1,−1,−1, 0,−1,−1 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 1, 0,−1,−1, 0, 0,−1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1,−1,−1, 0, 0, 0 ]
1
• I ≡ 3 D∗6 A0 :
2
3
4
5




CI =






b
CoxI =


0
0
0
0
0
0
−1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
∗
6
1
1
1
1
1
1
0
0
0
−1
0
0
0
0
1
1
1
1
1
1
1













b
CI =


1
1
1
1
1
1
−1













BI =


1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
−1
−1
−1
0
−1
0
1
0
0
0
0
0
0
−1
0
0
0
0
0
1
0
−1
−1
−1
−1
0
0
1
−1
−1
−1
−1
−1
−1
1









1
1
1
1
1
1
−1
0
0
−1
0
0
0
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 0, 0 ],
[ 0,−1,−1, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 1 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0,−1, 1, 1, 0, 0 ],
[ 0, 0, 0,−1,−1, 1, 0 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1, 1,−1, 1 ],
[ 0, 0, 1,−1,−1, 1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1,−1, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1,−1, 1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0,−1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0,−1, 1, 1, 0, 1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0,−1,−1, 1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
1
• I≡
∗
3 D5
2
3
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 1,−1, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1,−1,−1, 0,−1 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 0,−1,−1, 0,−1 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 1,−1,−1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1,−1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 1, 1,−1, 0 ],
[ 0, 0, 0,−1,−1, 1,−1 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1,−1, 0 ],
[ 0, 0, 1,−1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0,−1,−1, 0,−1 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 1,−1,−1, 0, 0 ],
[ 1, 0, 0,−1,−1, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 1, 0,−1,−1, 0, 0 ]
4
A1 :
∗
5
6




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1













b
CI =


49
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
0
0
0
1
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
−1
1
1
1
1
1
1
−1













BI =


1
1
1
1
1
0
−1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
−1
−1
−1
0
0
0
0
−1
−1
0
−1
0
0
0
0
0
0
0
1
−1
0
0
0
0
0
0
−1









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 1 ],
[ 0,−1,−1, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 1, 1, 1, 1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 1, 1, 0, 1 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 1,−1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0,−1,−1, 0,−1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
• I ≡ 4 D∗6 A0 :
[ −1, 0,−1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0,−1, 1, 1, 1, 1 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 2 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0,−1,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
1
2
3
4
[ −1, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 1, 1, 0, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1,−1,−1,−2 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1,−1,−1,−1,−1 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 1, 0, 0,−1,−1,−1,−1 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 1,−1,−1, 0, 0 ],
5
∗
6
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
−1




CI =






b
CoxI =


[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 1, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 1, 0, 0 ],
[ 0, 0, 0,−1,−1,−1,−1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1,−1,−1, 0,−1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1,−1,−1,−1 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 1,−1,−1, 0, 0 ],
[ 1, 0, 0,−1,−1, 0,−1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0,−1,−1, 0, 0 ]













b
CI =


1
1
1
1
1
1
0













BI =


0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1
−1
−1
−1
−1
0
−1
0
−1
−1
−1
−1
−1
0
0









−1
−1
−1
−1
−1
−1
1









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 0, 1, 1, 0 ],
[ −1, 0,−1, 0, 1, 1, 0 ],
[ −1, 0, 0,−1, 1, 1, 0 ],
50
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ 0,−1,−1, 0, 1, 1, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 1, 1 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1,−1,−1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0,−1,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0,−1,−1,−1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
b ∗ A1 :
• I≡D
5
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0,−1, 1, 1, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1,−1,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 1, 1,−1,−1, 0 ],
[ 0, 1, 0, 0,−1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 1,−1,−1, 0 ],
1
2
3
4
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 1, 0 ],
[ 0, 0,−1,−1, 1, 1, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 1, 1, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 1,−1,−1, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 1, 0,−1,−1, 0 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 1, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 1, 1 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0,−1,−1,−1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 1, 0,−1,−1, 0 ],
[ 1, 0, 0, 0,−1,−1,−1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0,−1,−1, 0 ]
∗
5
6
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
−1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
−1




CI =






b
CoxI =


0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
 −1

 −1
BI = 0
 0
 −1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
−1













b
CI =











1
1
1
1
1
1
0

−1
−1
−1
−1
−1
−1
1









1
1
1
1
0
1
−1
1
1
1
1
0
0
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 1, 0, 1, 1 ],
[ −1, 0, 1, 0, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 1, 0 ],
[ −1, 1, 1, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1,−1, 0,−1, 0,−1,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 1, 1 ],
[ −1, 1, 0, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1,−1, 0, 0,−1,−1,−1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 1, 1 ],
[ −1, 1, 0, 0, 1, 1, 1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 1,−1, 0, 0, 0,−1,−1 ],
51
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 1, 1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 1,−1,−1, 0, 0,−1,−1 ],
[ 1,−1, 0, 0, 0,−1, 0 ],
[
[
[
[
1,−1, 0, 0, 0, 0,
1, 0,−1, 0, 0,−1,
1, 0, 0,−1, 0,−1,
1, 0, 0, 0,−1, 0,
b ∗ A2 :
• I≡D
4
0 ],
0 ],
0 ],
0 ],
[
[
[
[
1,
1,
1,
1,
0,−1,−1,
0,−1, 0,
0, 0,−1,
0, 0, 0,
2
3
1
0,−1,−1 ],
0, 0, 0 ],
0, 0, 0 ],
0,−1, 0 ],



CI =






b I =
Cox



1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
−1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1,
1,
1,
1,
0,−1, 0,−1,−1,−1 ],
0, 0,−1,−1,−1,−1 ],
0, 0, 0,−1,−1,−1 ],
0, 0, 0, 0, 0, 0 ],
[
[
[
[
1,
1,
1,
1,
0,−1, 0, 0,−1,−1 ],
0, 0,−1, 0,−1,−1 ],
0, 0, 0,−1,−1, 0 ],
0, 0, 0, 0, 0, 1 ]
∗
4
5

[
[
[
[
6
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
−1
0
0
0
0
0
0
1
1
1
1
1
1
1
−1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
−1
 0

 0
BI = 0
 −1
 −1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
−1













bI =
C












1
1
1
1
0
1
0

−1
−1
−1
−1
−1
−1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0









1
1
0
0
1
1
−1
1
1
1
0
0
0
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1,−1, 0,−1, 0,−1,−1 ],
[ 1,−1, 0, 0, 1,−1, 0 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
b ∗ A3 :
• I≡D
3
[ −1, 0, 0, 0,−1, 1,−1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 1, 1 ],
[ −1, 0, 1, 0, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 1,−1, 0, 0, 0,−1,−1 ],
[ 1, 0,−1,−1, 0,−1,−1 ],
[ 1, 0,−1, 0, 1,−1, 0 ],
[ 1, 0, 0,−1, 1,−1, 0 ],
[ 1, 0, 0, 0, 1,−1, 0 ],
1
2
4
∗
3
5
[ −1, 0, 0, 0,−1, 1, 0 ],
[ −1, 0, 0, 1,−1, 1, 0 ],
[ −1, 0, 1, 0,−1, 1, 0 ],
[ −1, 0, 1, 1, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 1,−1, 0, 0, 0,−1, 0 ],
[ 1, 0,−1, 0, 0,−1,−1 ],
[ 1, 0, 0,−1, 0,−1,−1 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 1,−1, 1 ],
6
52
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 0, 0,−1, 1, 0 ],
[ −1, 1, 0, 1, 0, 1, 1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1,−1,−1, 0, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1, 0, 0,−1, 0 ],
[ 1, 0, 0,−1, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ]




CI =






b
CoxI =


1
0
0
0
0
0
0
0
0
0
1
1
0
−1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
−1
0
0
0
1
0
0
0
0
0
0
−1
0
0
1













bI =
C



1
1
1
1
1
1
−1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
 0

 0
BI = −1
 0
 0
1

0
0
0
1
0
0
0









0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0









0
0
0
1
1
0
−1
1
1
0
0
0
0
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0,−1,−1, 1,−1 ],
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 0, 0,−1, 1, 0 ],
[ −1, 1, 1, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 1,−1, 0, 0, 0,−1,−1 ],
[ 1,−1, 0, 1, 0,−1, 0 ],
[ 1, 0,−1, 0, 1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 1, 0,−1, 0 ],
b ∗ A4 :
• I≡D
2
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0,−1, 1,−1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 1,−1, 0, 0, 0,−1, 0 ],
[ 1, 0,−1, 0, 0,−1,−1 ],
[ 1, 0,−1, 1, 0,−1, 0 ],
[ 1, 0, 0, 0, 1,−1, 0 ],
[ 1, 0, 0, 1, 0,−1, 1 ],
1
3




CI =






b
CoxI =


0
0
1
1
1
0
−1
5
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
[ −1, 0, 0,−1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 1, 0,−1, 1, 0 ],
[ −1, 1, 0,−1, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1,−1,−1, 0, 0,−1,−1 ],
[ 1,−1, 0, 0, 1,−1, 0 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 0, 1, 1,−1, 1 ]
∗
2
4
[ −1, 0, 0,−1, 0, 1,−1 ],
[ −1, 0, 0, 0,−1, 1, 0 ],
[ −1, 0, 1,−1, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0,−1, 0,−1 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 1,−1, 1 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
6
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
−1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
−1
−1
0
0
1
1
1
1
1
1
1
1













bI =
C



1
1
1
1
1
1
−1
53
1
1
0
0
0
1
0













BI =


0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
−1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0









0
0
1
0
0
0
−1
1
0
0
0
0
0
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0,−1,−1, 0, 1,−1 ],
[ −1, 0,−1, 0, 0, 1, 0 ],
[ −1, 0, 0,−1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 1, 0,−1, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 1,−1, 0, 0, 0,−1, 0 ],
[ 1,−1, 1, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 1,−1, 0 ],
[ 1, 0, 0, 1, 0,−1, 1 ],
[ 1, 0, 1, 0, 0,−1, 1 ],
2.7.3
[ −1, 0,−1, 0,−1, 1,−1 ],
[ −1, 0, 0,−1,−1, 1,−1 ],
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0,−1, 1, 0 ],
[ 0,−1,−1, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 1,−1, 1 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0,−1, 1,−1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1,−1, 0, 0, 1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 0, 1, 1,−1, 1 ],
[ 1, 0, 1, 0, 1,−1, 1 ],
[ −1, 0,−1, 0, 0, 1,−1 ],
[ −1, 0, 0,−1, 0, 1,−1 ],
[ −1, 0, 0, 0,−1, 1, 0 ],
[ −1, 1,−1, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 1,−1, 0, 0, 0,−1,−1 ],
[ 1,−1, 0, 1, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 1, 0,−1, 0 ],
[ 1, 0, 1, 0, 0,−1, 0 ],
[ 1, 0, 1, 1, 0,−1, 1 ]
Posets of type E7
∗
6
5
• I ≡ P17 :
4
1
3
2




CI =






b I =
Cox



0
1
1
0
0
0
−1
1
0
0
0
0
0
0
1
0
0
0
0
0
−1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
−1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
−1













bI =
C



1
0
0
1
1
1
0













BI =


Number of sincere Tits roots of poset I sI = 6.
54
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
−1
0
0
−1
−1
0
0
0
0
0
0
0
1
0
0
0
−1
−1
0
0
0
−1
−1
−1
−1
−1
−1
1









0
0
0
0
0
0
−1
0
0
0
0
0
−1
0









Table of roots of qbI
[ −2,−2,−1, 1, 1, 1,−1 ],
[ 2, 1, 2,−1,−1,−1, 1 ],
[ −2, −1, −1, 1, 1, 0, −1 ],
[ −1, −1, −1, 0, 1, 1, −1 ],
[ −1, −1, −1, 1, 0, 1, 0 ],
[ −1, −1, 0, 0, 0, 0, −1 ],
[ −1, −1, 0, 0, 1, 0, 0 ],
[ −1, −1, 0, 1, 0, 1, 0 ],
[ −1, 0, −1, 0, 0, 1, 0 ],
[ −1, 0, −1, 1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 1, 0, 0, 0, −1, 0, 0 ],
[ 1, 0, 1, −1, −1, 0, 0 ],
[ 1, 0, 1, 0, −1, −1, 0 ],
[ 1, 0, 1, 0, 0, −1, 1 ],
[ 1, 1, 0, −1, 0, 0, 0 ],
[ 1, 1, 0, 0, −1, 0, 1 ],
[ 1, 1, 1, −1, −1, −1, 0 ],
[ 1, 1, 1, −1, 0, −1, 1 ],
[ 1, 1, 1, 0, −1, 0, 1 ],
[ 2, 1, 1, −1, 0, −1, 1 ],
[ −2,−1,−2, 1, 1, 1,−1 ],
[ 2, 2, 1,−1,−1,−1, 1 ],
[ −2, −1, −1, 1, 1, 1, 0 ],
[ −1, −1, −1, 0, 1, 1, 0 ],
[ −1, −1, −1, 1, 1, 0, −1 ],
[ −1, −1, 0, 0, 0, 1, −1 ],
[ −1, −1, 0, 0, 1, 1, 0 ],
[ −1, −1, 0, 1, 1, 0, 0 ],
[ −1, 0, −1, 0, 1, 0, −1 ],
[ −1, 0, −1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 0, 1, −1, 0, −1, 0 ],
[ 1, 0, 1, 0, −1, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 1, 0, −1, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, −1, 0 ],
[ 1, 1, 1, −1, −1, 0, 0 ],
[ 1, 1, 1, −1, 0, 0, 1 ],
[ 1, 1, 1, 0, 0, −1, 1 ],
[ 2, 1, 1, 0, −1, −1, 1 ]
[ −2,−1,−1, 1, 1, 1,−1 ],
[ −2, −1, −1, 0, 1, 1, −1 ],
[ −1, −1, −1, 0, 0, 1, −1 ],
[ −1, −1, −1, 1, 0, 0, −1 ],
[ −1, −1, −1, 1, 1, 0, 0 ],
[ −1, −1, 0, 0, 0, 1, 0 ],
[ −1, −1, 0, 1, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, −1, 0, 1, 0, 0 ],
[ −1, 0, −1, 1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1,−1, 0, 0, 0 ],
[ 1, 0, 1, 0,−1, 0, 1 ],
[ 1, 1, 0,−1,−1, 0, 0 ],
[ 1, 1, 0, 0,−1,−1, 0 ],
[ 1, 1, 0, 0, 0,−1, 1 ],
[ 1, 1, 1,−1,−1, 0, 1 ],
[ 1, 1, 1, 0,−1,−1, 0 ],
[ 2, 1, 1,−1,−1,−1, 0 ],
[ 2, 1, 1,−1,−1,−1, 1 ],
[ −2,−1,−1, 1, 0, 1,−1 ],
[ −1,−1,−1, 0, 1, 0,−1 ],
[ −1,−1,−1, 1, 0, 1,−1 ],
[ −1,−1,−1, 1, 1, 1, 0 ],
[ −1,−1, 0, 0, 1, 0,−1 ],
[ −1,−1, 0, 1, 0, 0, 0 ],
[ −1, 0,−1, 0, 0, 1,−1 ],
[ −1, 0,−1, 0, 1, 1, 0 ],
[ −1, 0,−1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, −1, 0, 0 ],
[ 1, 0, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, −1, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, −1, 0 ],
[ 1, 1, 0, −1, 0, −1, 0 ],
[ 1, 1, 0, 0, −1, 0, 0 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 1, −1, 0, −1, 0 ],
[ 1, 1, 1, 0, −1, −1, 1 ],
[ 2, 1, 1, −1, −1, 0, 1 ],
∗
6
• I ≡ P18 :
1
5
2
4
3




CI =






b I =
Cox



0
1
1
1
1
1
−1
1
0
0
0
0
0
0
1
0
1
1
0
0
−1
0
1
0
0
0
0
0
1
1
0
0
0
0
−1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
−1
0
−1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
−1













bI =
C



1
0
0
0
0
0
0













BI =


Number of sincere Tits roots of poset I sI = 10.
55
0
1
0
0
1
1
0
1
0
0
0
0
0
−1
0
0
1
1
1
1
0
0
0
0
0
−1
0
−1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
−1
0
0
0
0
0
1
0
0
0
−1
−1
−1
−1
0
−1
−1
−1
−1
−1
−1
1
0
−1
0
0
0
0
1









0
1
0
0
1
1
0
0
0
0
0
0
0
−1









Table of roots of qbI
[ −1,−2,−2,−1, 1, 1,−2 ],
[ −1,−1,−1,−1, 1, 1,−1 ],
[ 1, 2, 1, 2,−1,−1, 2 ],
[ −1, −1, −1, −1, 0, 0, −2 ],
[ −1, −1, −1, −1, 1, 0, −1 ],
[ −1, −1, −1, 0, 1, 0, −1 ],
[ −1, −1, 0, −1, 1, 0, −1 ],
[ −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −2, −1, −1, 1, 1, −1 ],
[ 0, −1, −1, −1, 1, 1, 0 ],
[ 0, −1, −1, 0, 1, 0, −1 ],
[ 0, −1, 0, −1, 0, 1, −1 ],
[ 0, −1, 0, −1, 1, 1, 0 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 1, −1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, −1, 0 ],
[ 0, 1, 1, 1, −1, −1, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 1, 0, 1, 0, −1, 1 ],
[ 1, 1, 1, 0, 0, −1, 1 ],
[ 1, 1, 1, 1, −1, 0, 2 ],
[ 1, 2, 1, 1, −1, 0, 2 ],
[ −1,−2,−1,−2, 1, 1,−2 ],
[ 1, 1, 1, 1,−1,−1, 1 ],
[ 1, 2, 2, 1,−1,−1, 2 ],
[ −1, −1, −1, −1, 0, 1, −2 ],
[ −1, −1, −1, 0, 0, 0, −2 ],
[ −1, −1, 0, −1, 0, 0, −2 ],
[ −1, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, −1, −1 ],
[ 0, −1, −1, −1, 0, 1, −1 ],
[ 0, −1, −1, 0, 0, 0, −1 ],
[ 0, −1, −1, 0, 1, 0, 0 ],
[ 0, −1, 0, −1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, −1, 0, 1 ],
[ 0, 1, 1, 0, −1, −1, 0 ],
[ 0, 1, 1, 0, 0, −1, 1 ],
[ 0, 1, 1, 1, −1, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 1 ],
[ 1, 1, 1, 0, 0, 0, 1 ],
[ 1, 1, 1, 1, 0, −1, 1 ],
[ 1, 2, 1, 1, 0, −1, 2 ]
[ −1,−2,−1,−1, 1, 1,−2 ],
[ 1, 2, 1, 1,−1,−1, 1 ],
[ −1, −2, −1, −1, 0, 1, −2 ],
[ −1, −1, −1, −1, 0, 1, −1 ],
[ −1, −1, −1, 0, 0, 0, −1 ],
[ −1, −1, 0, −1, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, −1, −1, 1, 0, −1 ],
[ 0, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, −1, 1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, −1, 0 ],
[ 0, 1, 1, 0, −1, 0, 0 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 0, −1, 1 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 2 ],
[ 1, 1, 1, 0, 0, 0, 2 ],
[ 1, 1, 1, 1, 0, −1, 2 ],
[ −1,−2,−1,−1, 1, 1,−1 ],
[ 1, 2, 1, 1,−1,−1, 2 ],
[ −1, −2, −1, −1, 1, 0, −2 ],
[ −1, −1, −1, −1, 1, 0, −2 ],
[ −1, −1, −1, 0, 0, 1, −1 ],
[ −1, −1, 0, −1, 0, 1, −1 ],
[ −1, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, 1, 1, −1 ],
[ 0, −1, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, −1, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 1, 0, 1, −1, −1, 0 ],
[ 0, 1, 0, 1, 0, −1, 1 ],
[ 0, 1, 1, 0, −1, 0, 1 ],
[ 0, 1, 1, 1, −1, −1, 0 ],
[ 0, 2, 1, 1, −1, −1, 1 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 1, 0, 1, −1, 0, 1 ],
[ 1, 1, 1, 0, −1, 0, 1 ],
[ 1, 1, 1, 1, −1, 0, 1 ],
[ 1, 1, 1, 1, 0, 0, 2 ],
∗
• I ≡ P19 :
3
6
2
5
1
4




CI =






b
CoxI =


0
0
1
1
1
1
−1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
−1
0
0
1
0
0
0
0
1
1
1
0
0
0
−1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
−1
−1
0
−1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
1
1













bI =
C



1
1
1
1
1
1
−1

0
 0

 0
BI = 0
 −1
 −1
0








0
1
0
0
0
0
0

Number of sincere Tits roots of poset I sI = 10.
Table of roots of qbI
56
0
0
1
0
0
1
0
1
1
0
0
0
0
−1
0
0
0
1
1
1
0
1
0
0
0
0
−1
−1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1
1
0
0
1
0
0
−1
0
0
1
0
0
0
−1









−1
0
−1
0
0
0
1
1
0
0
0
−1
−1
−1









[ −1,−1,−2,−2,−1, 1,−3 ],
[ −1,−1,−1,−1,−1, 1,−2 ],
[ 1, 1, 2, 1, 2,−1, 3 ],
[ −1, −1, −1, −1, −1, 0, −2 ],
[ −1, 0, −1, −1, −1, 0, −2 ],
[ −1, 0, −1, −1, 0, 0, −1 ],
[ −1, 0, −1, 0, −1, 1, −1 ],
[ −1, 0, 0, 0, 0, −1, −1 ],
[ 0, −1, −2, −1, −1, 1, −2 ],
[ 0, −1, −1, −1, 0, 0, −2 ],
[ 0, −1, −1, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, −1, 0, −1 ],
[ 0, 0, −1, −1, −1, 1, −1 ],
[ 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 1, 0, 2 ],
[ 0, 1, 1, 1, 1, −1, 1 ],
[ 1, −1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 1 ],
[ 1, 0, 1, 1, 0, 0, 2 ],
[ 1, 0, 2, 1, 1, −1, 2 ],
[ 1, 1, 1, 1, 1, 0, 3 ],
[ −1,−1,−2,−1,−2, 1,−3 ],
[ 1, 1, 1, 1, 1,−1, 2 ],
[ 1, 1, 2, 2, 1,−1, 3 ],
[ −1, −1, −1, −1, 0, 0, −2 ],
[ −1, 0, −1, −1, −1, 1, −2 ],
[ −1, 0, −1, −1, 0, 1, −1 ],
[ −1, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, −1, −1, −1, 0, −2 ],
[ 0, −1, −1, −1, 0, 0, −1 ],
[ 0, −1, −1, 0, −1, 1, −1 ],
[ 0, −1, 0, 0, 0, −1, −1 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 1, −1 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, −1, 0 ],
[ 0, 0, 1, 1, 0, −1, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 0, −1, 1 ],
[ 0, 1, 1, 1, 1, −1, 2 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 2 ],
[ 1, 0, 1, 1, 1, −1, 1 ],
[ 1, 1, 1, 0, 1, 0, 2 ],
[ 1, 1, 2, 1, 1, 0, 3 ]
[ −1,−1,−2,−1,−1, 1,−3 ],
[ 1, 1, 2, 1, 1,−1, 2 ],
[ −1, −1, −2, −1, −1, 0, −3 ],
[ −1, −1, −1, 0, −1, 0, −2 ],
[ −1, 0, −1, −1, −1, 1, −1 ],
[ −1, 0, −1, 0, −1, 0, −2 ],
[ −1, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, −1, 1, −2 ],
[ 0, −1, −1, −1, 0, 1, −1 ],
[ 0, −1, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, 0, −1, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, 0, 1, −1, 1 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 1, 0, 1, −1, 1 ],
[ 0, 1, 1, 1, 0, 0, 1 ],
[ 0, 1, 1, 1, 1, 0, 2 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 1, 1, 0, −1, 1 ],
[ 1, 0, 1, 1, 1, −1, 2 ],
[ 1, 1, 1, 1, 0, 0, 2 ],
[ −1,−1,−2,−1,−1, 1,−2 ],
[ 1, 1, 2, 1, 1,−1, 3 ],
[ −1, −1, −1, −1, −1, 0, −3 ],
[ −1, 0, −2, −1, −1, 1, −2 ],
[ −1, 0, −1, −1, 0, 0, −2 ],
[ −1, 0, −1, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, −1, 0, −1 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, −1, 1, −1 ],
[ 0, −1, −1, 0, −1, 0, −2 ],
[ 0, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, −1, 1 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 1, 0, 1, 0, 1 ],
[ 0, 1, 1, 1, 0, 0, 2 ],
[ 0, 1, 2, 1, 1, −1, 2 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 0, 1, 0, 1, −1, 1 ],
[ 1, 0, 1, 1, 0, 0, 1 ],
[ 1, 0, 1, 1, 1, 0, 2 ],
[ 1, 1, 1, 1, 1, 0, 2 ],
∗
1
• I ≡ P20 :
3
6
2
5
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
−1
0
1
0
0
0
0
0
1
1
1
0
0
0
−1




CI =






b
CoxI =


0
1
1
1
1
1
−1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1













b
CI =


1
1
1
1
1
1
−1













BI =


1
0
0
0
0
0
0
1
1
1
1
1
0
−2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
−1
Number of sincere Tits roots of poset I sI = 10.
Table of roots of qbI
57
0
0
0
1
1
1
0
1
0
0
1
0
0
−1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
−1
−1
−1
−1
−1
−1
−1
1
1
1
0
0
0
0
−1









0
0
0
1
1
1
−1
1
2
1
2
1
0
−3









[ −2,−2,−1,−1,−1,−1,−4 ],
[ −1,−1,−1,−1,−1,−1,−3 ],
[ 2, 1, 2, 1, 1, 1, 4 ],
[ −2, −1, −1, 0, −1, −1, −3 ],
[ −1, −1, −1, −1, 0, −1, −2 ],
[ −1, −1, −1, 0, −1, 0, −2 ],
[ −1, −1, 0, −1, 0, 0, −2 ],
[ −1, −1, 0, 0, −1, 0, −1 ],
[ −1, 0, −1, −1, −1, 0, −2 ],
[ −1, 0, −1, 0, −1, −1, −2 ],
[ −1, 0, −1, 0, 0, −1, −1 ],
[ −1, 0, 0, 0, 0, −1, −1 ],
[ 0, −1, 0, 0, −1, 0, −1 ],
[ 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, 0, 0, 1, 2 ],
[ 1, 0, 1, 1, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 0, 1, 0, 2 ],
[ 1, 1, 0, 1, 0, 1, 2 ],
[ 1, 1, 1, 0, 1, 1, 2 ],
[ 1, 1, 1, 1, 0, 1, 3 ],
[ 2, 1, 1, 1, 0, 1, 3 ],
[ −2,−1,−2,−1,−1,−1,−4 ],
[ 1, 1, 1, 1, 1, 1, 3 ],
[ 2, 2, 1, 1, 1, 1, 4 ],
[ −1, −1, −1, −1, −1, 0, −3 ],
[ −1, −1, −1, −1, 0, 0, −2 ],
[ −1, −1, −1, 0, 0, −1, −2 ],
[ −1, −1, 0, −1, 0, 0, −1 ],
[ −1, −1, 0, 0, 0, −1, −2 ],
[ −1, 0, −1, −1, 0, −1, −2 ],
[ −1, 0, −1, 0, −1, 0, −2 ],
[ −1, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, −1, −1 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 1 ],
[ 1, 0, 1, 1, 0, 0, 2 ],
[ 1, 1, 0, 0, 0, 1, 1 ],
[ 1, 1, 0, 0, 1, 1, 2 ],
[ 1, 1, 0, 1, 1, 0, 2 ],
[ 1, 1, 1, 0, 1, 1, 3 ],
[ 1, 1, 1, 1, 1, 0, 2 ],
[ 2, 1, 1, 1, 1, 0, 3 ]
[ −2,−1,−1,−1,−1,−1,−4 ],
[ 2, 1, 1, 1, 1, 1, 3 ],
[ −2, −1, −1, −1, −1, 0, −3 ],
[ −1, −1, −1, −1, −1, 0, −2 ],
[ −1, −1, −1, 0, −1, −1, −3 ],
[ −1, −1, 0, −1, −1, 0, −2 ],
[ −1, −1, 0, 0, −1, −1, −2 ],
[ −1, −1, 0, 0, 0, −1, −1 ],
[ −1, 0, −1, −1, 0, 0, −2 ],
[ −1, 0, −1, 0, −1, 0, −1 ],
[ −1, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 2 ],
[ 1, 0, 1, 1, 0, 1, 2 ],
[ 1, 1, 0, 0, 0, 1, 2 ],
[ 1, 1, 0, 1, 0, 0, 1 ],
[ 1, 1, 1, 0, 0, 1, 2 ],
[ 1, 1, 1, 1, 0, 0, 2 ],
[ 1, 1, 1, 1, 1, 0, 3 ],
[ −2,−1,−1,−1,−1,−1,−3 ],
[ 2, 1, 1, 1, 1, 1, 4 ],
[ −2, −1, −1, −1, 0, −1, −3 ],
[ −1, −1, −1, −1, 0, −1, −3 ],
[ −1, −1, −1, 0, −1, −1, −2 ],
[ −1, −1, 0, −1, 0, −1, −2 ],
[ −1, −1, 0, 0, −1, 0, −2 ],
[ −1, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, −1, −1, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, −1, −2 ],
[ −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, −1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 0, 1, 0, 0, 1, 1 ],
[ 1, 0, 1, 0, 1, 1, 2 ],
[ 1, 0, 1, 1, 1, 0, 2 ],
[ 1, 1, 0, 0, 1, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 2 ],
[ 1, 1, 1, 0, 1, 0, 2 ],
[ 1, 1, 1, 1, 0, 1, 2 ],
[ 2, 1, 1, 0, 1, 1, 3 ],
∗
6
5
• I ≡ P21 :
1
4
3
2




CI =






b I =
Cox



0
1
1
1
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
−1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
−1
−1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0













BI =


1
0
1
1
2
1
0
0
0
0
1
1
0
0
0
−1
0
0
0
0
1













b
CI =


1
1
1
1
1
1
−1
Number of sincere Tits roots of poset I sI = 10.
58
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
−1
−1
−1
−1
−1
−1
1
0
0
−1
−1
−1
−1
0









0
0
0
0
−1
0
−1
0
0
1
1
1
0
0









Table of roots of qbI
[ −2,−1,−1,−1, 1, 1,−2 ],
[ −1,−1,−1,−1, 1, 1,−1 ],
[ 2, 1, 1, 1,−1,−1, 1 ],
[ −2, 0, −1, −1, 1, 1, −1 ],
[ −1, −1, −1, 0, 1, 1, 0 ],
[ −1, −1, 0, −1, 1, 1, 0 ],
[ −1, −1, 0, 0, 1, 0, −1 ],
[ −1, 0, −1, −1, 1, 0, −1 ],
[ −1, 0, −1, 0, 0, 1, −1 ],
[ −1, 0, −1, 0, 1, 1, 0 ],
[ −1, 0, 0, −1, 1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 1, 0, −1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 1, 0, −1, 0 ],
[ 1, 0, 1, 0, −1, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 1, 1, 0, −1, 1 ],
[ 1, 1, 0, 0, 0, −1, 0 ],
[ 1, 1, 0, 1, −1, −1, 1 ],
[ 1, 1, 1, 0, −1, −1, 1 ],
[ 2, 1, 0, 1, −1, −1, 1 ],
[ −2,−1,−1,−1, 1, 1,−1 ],
[ 1, 1, 1, 1,−1,−1, 1 ],
[ 2, 1, 1, 1,−1,−1, 2 ],
[ −1, −1, −1, 0, 0, 1, −1 ],
[ −1, −1, 0, −1, 0, 1, −1 ],
[ −1, −1, 0, 0, 0, 0, −1 ],
[ −1, −1, 0, 0, 1, 0, 0 ],
[ −1, 0, −1, −1, 1, 1, −1 ],
[ −1, 0, −1, 0, 0, 1, 0 ],
[ −1, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, −1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, −1, 0, 0 ],
[ 1, 0, 0, 0, −1, 0, 0 ],
[ 1, 0, 0, 1, −1, −1, 0 ],
[ 1, 0, 0, 1, 0, −1, 1 ],
[ 1, 0, 1, 0, −1, 0, 1 ],
[ 1, 0, 1, 1, −1, −1, 0 ],
[ 1, 1, 0, 0, −1, −1, 0 ],
[ 1, 1, 0, 0, 0, −1, 1 ],
[ 1, 1, 0, 1, −1, 0, 1 ],
[ 1, 1, 1, 0, −1, 0, 1 ],
[ 2, 1, 1, 0, −1, −1, 1 ]
[ −2,−1,−1,−1, 1, 2,−1 ],
[ 2, 1, 1, 1,−2,−1, 1 ],
[ −2, −1, −1, 0, 1, 1, −1 ],
[ −1, −1, −1, 0, 1, 0, −1 ],
[ −1, −1, 0, −1, 1, 0, −1 ],
[ −1, −1, 0, 0, 0, 1, −1 ],
[ −1, −1, 0, 0, 1, 1, 0 ],
[ −1, 0, −1, −1, 1, 1, 0 ],
[ −1, 0, −1, 0, 1, 0, −1 ],
[ −1, 0, 0, −1, 0, 1, −1 ],
[ −1, 0, 0, −1, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 0, 0, 1, −1, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, −1, 0 ],
[ 1, 0, 1, 1, −1, −1, 1 ],
[ 1, 1, 0, 0, −1, 0, 0 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 1, 0, −1, 1 ],
[ 1, 1, 1, 0, 0, −1, 1 ],
[ −2,−1,−1,−1, 2, 1,−1 ],
[ 2, 1, 1, 1,−1,−2, 1 ],
[ −2, −1, 0, −1, 1, 1, −1 ],
[ −1, −1, −1, 0, 1, 1, −1 ],
[ −1, −1, 0, −1, 1, 1, −1 ],
[ −1, −1, 0, 0, 0, 1, 0 ],
[ −1, 0, −1, −1, 0, 1, −1 ],
[ −1, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, −1, 0, 1, 0, 0 ],
[ −1, 0, 0, −1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, −1, 0, 1 ],
[ 1, 0, 1, 0, −1, −1, 0 ],
[ 1, 0, 1, 0, 0, −1, 1 ],
[ 1, 0, 1, 1, −1, 0, 1 ],
[ 1, 1, 0, 0, −1, 0, 1 ],
[ 1, 1, 0, 1, −1, −1, 0 ],
[ 1, 1, 1, 0, −1, −1, 0 ],
[ 2, 0, 1, 1, −1, −1, 1 ],
∗
6
• I ≡ P22 :
2
1
5
4
3




CI =






b I =
Cox



0
1
1
1
1
1
−1
1
0
0
0
0
0
0
1
0
1
1
1
0
−1
0
1
0
0
0
0
0
1
1
0
0
0
0
−1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
−1
0
−1
−1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1













bI =
C



1
1
1
1
1
1
−1













BI =


Number of sincere Tits roots of poset I sI = 10.
59
1
0
0
0
0
0
0
1
0
0
0
0
−1
−1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
−2
0
0
0
1
1
1
0
0
0
1
1
1
0
−1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1
0
0
0
0
−1
−1
0
1
0
1
0
0
0
−1









−1
0
−1
−1
0
0
1
1
0
1
1
0
−1
−2









Table of roots of qbI
[ −2,−2,−1,−1,−1, 1,−3 ],
[ −1,−1,−1,−1,−1, 1,−2 ],
[ 1, 2, 1, 1, 1,−1, 3 ],
[ −1, −2, 0, −1, −1, 1, −2 ],
[ −1, −1, −1, 0, −1, 0, −2 ],
[ −1, −1, −1, 0, 0, 0, −1 ],
[ −1, −1, 0, −1, −1, 1, −1 ],
[ −1, −1, 0, 0, −1, 0, −2 ],
[ −1, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, −1, 1, −1 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 1, 1, −1, 1 ],
[ 0, 1, 1, 0, 1, −1, 1 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 1, 0, −1, 1 ],
[ 1, 1, 0, 1, 1, −1, 2 ],
[ 1, 1, 1, 0, 0, 0, 2 ],
[ 1, 1, 1, 1, 0, −1, 1 ],
[ 1, 2, 1, 0, 1, −1, 2 ],
[ −1,−2,−1,−1,−1, 1,−3 ],
[ 1, 1, 1, 1, 1,−1, 2 ],
[ 2, 2, 1, 1, 1,−1, 3 ],
[ −1, −1, −1, −1, 0, 0, −2 ],
[ −1, −1, −1, 0, −1, 1, −2 ],
[ −1, −1, −1, 0, 0, 1, −1 ],
[ −1, −1, 0, −1, 0, 0, −2 ],
[ −1, −1, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 1, −1 ],
[ 0, −1, 0, 0, −1, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, −1, 0 ],
[ 0, 1, 1, 0, 0, −1, 0 ],
[ 0, 1, 1, 1, 0, −1, 1 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 1, 0, 0, 1, −1, 1 ],
[ 1, 1, 0, 1, 0, 0, 1 ],
[ 1, 1, 0, 1, 1, 0, 2 ],
[ 1, 1, 1, 0, 1, −1, 1 ],
[ 1, 1, 1, 1, 0, −1, 2 ],
[ 1, 2, 1, 1, 0, −1, 2 ]
[ −1,−2,−1,−1,−1, 1,−2 ],
[ 1, 2, 1, 1, 1,−2, 2 ],
[ −1, −2, −1, −1, 0, 1, −2 ],
[ −1, −1, −1, −1, 0, 1, −2 ],
[ −1, −1, −1, 0, −1, 1, −1 ],
[ −1, −1, 0, −1, −1, 0, −2 ],
[ −1, −1, 0, −1, 0, 0, −1 ],
[ −1, −1, 0, 0, −1, 1, −1 ],
[ −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, −1, −1, 0, 1, −1 ],
[ 0, −1, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, −1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1, −1, 0 ],
[ 0, 1, 0, 1, 0, −1, 1 ],
[ 0, 1, 1, 0, 0, −1, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 1, 0, 0, 1, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 2 ],
[ 1, 1, 1, 0, 0, −1, 1 ],
[ 1, 1, 1, 0, 1, −1, 2 ],
[ 1, 1, 1, 1, 0, 0, 2 ],
[ −1,−2,−1,−1,−1, 2,−2 ],
[ 1, 2, 1, 1, 1,−1, 2 ],
[ −1, −2, −1, 0, −1, 1, −2 ],
[ −1, −1, −1, −1, 0, 1, −1 ],
[ −1, −1, −1, 0, 0, 0, −2 ],
[ −1, −1, 0, −1, −1, 1, −2 ],
[ −1, −1, 0, −1, 0, 1, −1 ],
[ −1, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, −1, −1 ],
[ 0, −1, −1, 0, −1, 1, −1 ],
[ 0, −1, 0, −1, −1, 1, −1 ],
[ 0, −1, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 1, −1, 1 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 1, 0, 0, 1, 0, 2 ],
[ 1, 1, 0, 1, 1, −1, 1 ],
[ 1, 1, 1, 0, 0, 0, 1 ],
[ 1, 1, 1, 0, 1, 0, 2 ],
[ 1, 2, 0, 1, 1, −1, 2 ],
∗
6
• I ≡ P23 :
3
5
2
4
1




CI =






b I =
Cox



0
0
0
1
1
0
−1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
−1
0
0
0
1
0
0
0
−1
−1
0
−1
0
0
1
1
1
1
1
1
1
1













bI =
C



1
1
1
1
1
1
−1













BI =


Number of sincere Tits roots of poset I sI = 10.
60
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
−1









0
0
0
0
0
−1
0









Table of roots of qbI
[ −1,−1,−1,−2,−1, 2,−2 ],
[ −1,−1,−1,−1,−1, 2,−1 ],
[ 1, 1, 1, 1, 2,−2, 2 ],
[ −1, −1, 0, −1, −1, 2, −1 ],
[ −1, 0, −1, −1, −1, 1, −1 ],
[ −1, 0, 0, −1, −1, 1, −1 ],
[ −1, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, −1, 1, −2 ],
[ 0, −1, −1, 0, −1, 1, −1 ],
[ 0, −1, 0, −1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, −1, −1, 1, −1 ],
[ 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, −1, 0 ],
[ 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, −1, 0 ],
[ 0, 1, 0, 1, 0, −1, 1 ],
[ 0, 1, 1, 1, 0, −1, 1 ],
[ 1, −1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 1, 0, −1, 0 ],
[ 1, 0, 1, 0, 1, −1, 1 ],
[ 1, 0, 1, 1, 1, −1, 2 ],
[ 1, 1, 0, 1, 1, −1, 1 ],
[ −1,−1,−1,−1,−2, 2,−2 ],
[ 1, 1, 1, 1, 1,−2, 1 ],
[ 1, 1, 1, 2, 1,−2, 2 ],
[ −1, −1, 0, −1, 0, 1, −1 ],
[ −1, 0, −1, −1, −1, 2, −1 ],
[ −1, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, −1, 1, −1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, −1, −1, −1, 1, −1 ],
[ 0, −1, 0, −1, −1, 1, −1 ],
[ 0, −1, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 1, −1 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, −1, 0 ],
[ 0, 0, 1, 1, 0, −1, 1 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 1, −1, 1 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 1, 1, −2, 1 ],
[ 1, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, −1, 0 ],
[ 1, 0, 0, 1, 0, −1, 1 ],
[ 1, 0, 1, 1, 0, −1, 1 ],
[ 1, 1, 0, 0, 1, −1, 1 ],
[ 1, 1, 0, 1, 1, −1, 2 ]
[ −1,−1,−1,−1,−1, 1,−2 ],
[ 1, 1, 1, 1, 1,−2, 2 ],
[ −1, −1, 0, −1, −1, 1, −2 ],
[ −1, −1, 0, 0, −1, 1, −1 ],
[ −1, 0, −1, −1, 0, 1, −1 ],
[ −1, 0, 0, −1, 0, 1, −1 ],
[ −1, 0, 0, 0, −1, 1, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, −1, 2, −1 ],
[ 0, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, −1, 1, −1 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, 0, −1, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, 0, 1, −1, 1 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 1, 1, −1, 1 ],
[ 0, 1, 1, 1, 1, −1, 1 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 0, 0, 0, 1, −1, 1 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 1, 1, −2, 1 ],
[ 1, 1, 0, 1, 0, −1, 1 ],
[ −1,−1,−1,−1,−1, 2,−2 ],
[ 1, 1, 1, 1, 1,−1, 2 ],
[ −1, −1, 0, −1, −1, 1, −1 ],
[ −1, 0, −1, −1, −1, 1, −2 ],
[ −1, 0, −1, 0, −1, 1, −1 ],
[ −1, 0, 0, −1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 1, −1 ],
[ 0, −1, 0, 0, −1, 1, 0 ],
[ 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, −1, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, −1, 0 ],
[ 0, 1, 1, 0, 1, −1, 1 ],
[ 0, 1, 1, 1, 1, −1, 2 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 0, 1, 1, −1, 1 ],
[ 1, 0, 1, 1, 1, −1, 1 ],
[ 1, 1, 0, 1, 1, −2, 1 ],
∗
• I ≡ P24 :
5
6
3
4
2
1




CI =






b I =
Cox



0
0
0
0
0
0
−1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1













bI =
C



1
1
1
1
1
1
−1













BI =


Number of sincere Tits roots of poset I sI = 10.
61
1
1
1
1
1
1
0
−1
−1
−1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
−1
0
0
0
1
0
1
0
1
1
1
1
0
0
−1
0
0
0
0
1
0
0
−1
−1
−1
−1
−1
−1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0









1
1
0
1
0
1
−1
2
1
1
1
1
0
−1









Table of roots of qbI
[ −2, 1, 1, 1, 1, 1, 1 ],
[ −1, 1, 1, 1, 1, 1, 2 ],
[ 2,−1,−1,−1,−1,−1,−2 ],
[ −2, 1, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 1, 0 ],
[ −1, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 2 ],
[ −1, 1, 0, 0, 1, 1, 1 ],
[ −1, 1, 1, 0, 0, 1, 1 ],
[ −1, 1, 1, 1, 0, 0, 1 ],
[ 0, −1, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1, −1, −1, 0, −1, −1, −2 ],
[ 1, −1, −1, 0, 0, 0, −1 ],
[ 1, −1, 0, 0, −1, 0, −1 ],
[ 1, 0, −1, −1, −1, −1, −1 ],
[ 1, 0, −1, −1, 0, 0, 0 ],
[ 1, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 2, −1, −1, 0, −1, −1, −1 ],
[ −2, 1, 1, 1, 1, 1, 2 ],
[ 1,−1,−1,−1,−1,−1,−2 ],
[ 2,−1,−1,−1,−1,−1,−1 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 0, 0, 1, 1 ],
[ −1, 0, 1, 1, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 1, 0, 1 ],
[ −1, 1, 1, 0, 1, 0, 1 ],
[ −1, 1, 1, 1, 1, 0, 1 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1, −1, −1, −1, −1, 0, −2 ],
[ 1, −1, −1, 0, −1, −1, −1 ],
[ 1, −1, −1, 0, 0, 0, 0 ],
[ 1, −1, 0, 0, −1, 0, 0 ],
[ 1, 0, −1, −1, −1, 0, −1 ],
[ 1, 0, −1, 0, −1, −1, −1 ],
[ 1, 0, 0, −1, −1, −1, −1 ],
[ 1, 0, 0, 0, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, −1, −1, −1, −1, −1 ]
[ −2, 1, 1, 1, 2, 1, 2 ],
[ 2,−1,−2,−1,−1,−1,−2 ],
[ −2, 0, 1, 1, 1, 1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ −1, 1, 0, 0, 1, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 1, 1, 1 ],
[ −1, 1, 1, 1, 1, 0, 2 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, −1, −1 ],
[ 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, −1, −1, −1, −1, 0, −1 ],
[ 1, −1, −1, 0, −1, 0, −1 ],
[ 1, −1, 0, −1, −1, 0, −1 ],
[ 1, −1, 0, 0, 0, 0, 0 ],
[ 1, 0, −1, −1, 0, −1, −1 ],
[ 1, 0, −1, 0, 0, −1, −1 ],
[ 1, 0, 0, −1, −1, 0, −1 ],
[ 1, 0, 0, 0, −1, −1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ −2, 1, 2, 1, 1, 1, 2 ],
[ 2,−1,−1,−1,−2,−1,−2 ],
[ −2, 1, 1, 0, 1, 1, 1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 1, 1 ],
[ −1, 1, 0, 0, 1, 0, 1 ],
[ −1, 1, 1, 0, 0, 0, 1 ],
[ −1, 1, 1, 0, 1, 1, 2 ],
[ 0, −1, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, −1, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 1, −1, −1, −1, 0, 0, −1 ],
[ 1, −1, −1, 0, 0, −1, −1 ],
[ 1, −1, 0, 0, −1, −1, −1 ],
[ 1, 0, −1, −1, −1, −1, −2 ],
[ 1, 0, −1, −1, 0, 0, −1 ],
[ 1, 0, −1, 0, 0, −1, 0 ],
[ 1, 0, 0, −1, −1, 0, 0 ],
[ 1, 0, 0, 0, −1, 0, 0 ],
[ 2, −1, −1, −1, −1, 0, −1 ],
∗
6
5
• I ≡ P25 :
2
4
3
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
−1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
−1
0
−1
0
0
0
0




CI =






b I =
Cox



1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













BI =


0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
−1













bI =
C



1
1
1
1
1
1
−1
62









0
0
0
0
0
−1
0









Number of sincere Tits roots of poset I sI = 6.
Table of roots of qbI
[ −1, 2, 1, 1,−1,−1, 1 ],
[ 1,−2,−1,−2, 1, 1,−1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 1 ],
[ −1, 1, 1, 0, 0, 0, 1 ],
[ −1, 1, 1, 1, 0, −1, 0 ],
[ −1, 2, 1, 1, −1, 0, 1 ],
[ 0, −1, −1, −1, 1, 0, −1 ],
[ 0, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, −1, 1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, −1, 0 ],
[ 0, 1, 1, 0, −1, 0, 0 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 0, −1, 1 ],
[ 1, −2, −1, −1, 1, 1, 0 ],
[ 1, −1, −1, −1, 1, 0, −1 ],
[ 1, −1, −1, 0, 0, 0, 0 ],
[ 1, −1, 0, −1, 0, 0, 0 ],
[ 1, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 2, 1, 2,−1,−1, 1 ],
[ 1,−2,−1,−1, 1, 1,−1 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 1, −1, 0, 0 ],
[ −1, 1, 1, 0, −1, 0, 0 ],
[ −1, 1, 1, 1, −1, −1, 0 ],
[ −1, 1, 1, 1, 0, −1, 1 ],
[ −1, 2, 1, 1, 0, −1, 1 ],
[ 0, −1, −1, −1, 1, 1, −1 ],
[ 0, −1, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, −1, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 1, 0, 1, −1, −1, 0 ],
[ 0, 1, 0, 1, 0, −1, 1 ],
[ 0, 1, 1, 0, −1, 0, 1 ],
[ 0, 1, 1, 1, −1, −1, 0 ],
[ 0, 2, 1, 1, −1, −1, 1 ],
[ 1, −1, −1, −1, 0, 0, −1 ],
[ 1, −1, −1, −1, 1, 0, 0 ],
[ 1, −1, −1, 0, 0, 1, 0 ],
[ 1, −1, 0, −1, 0, 1, 0 ],
[ 1, 0, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ]
[ −1, 2, 2, 1,−1,−1, 1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, −1, 0 ],
[ −1, 1, 1, 0, 0, −1, 0 ],
[ −1, 1, 1, 1, −1, 0, 0 ],
[ −1, 1, 1, 1, 0, 0, 1 ],
[ 0,−2,−1,−1, 1, 1,−1 ],
[ 0,−1,−1,−1, 1, 1, 0 ],
[ 0,−1,−1, 0, 1, 0,−1 ],
[ 0,−1, 0,−1, 0, 1,−1 ],
[ 0,−1, 0,−1, 1, 1, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 1, −1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, −1, 0 ],
[ 0, 1, 1, 1, −1, −1, 1 ],
[ 1,−2,−1,−1, 0, 1,−1 ],
[ 1,−1,−1,−1, 0, 1,−1 ],
[ 1,−1,−1,−1, 1, 1, 0 ],
[ 1,−1,−1, 0, 1, 0, 0 ],
[ 1,−1, 0,−1, 1, 0, 0 ],
[ 1, 0, 0, 0, −1, 0, 0 ],
[ 1,−2,−2,−1, 1, 1,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 1,−1, 0, 1 ],
[ −1, 2, 1, 1,−1,−1, 0 ],
[ 0, −1, −1, −1, 0, 1, −1 ],
[ 0, −1, −1, 0, 0, 0, −1 ],
[ 0, −1, −1, 0, 1, 0, 0 ],
[ 0, −1, 0, −1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1,−1, 0, 1 ],
[ 0, 1, 1, 0,−1,−1, 0 ],
[ 0, 1, 1, 0, 0,−1, 1 ],
[ 0, 1, 1, 1,−1, 0, 1 ],
[ 1, −2, −1, −1, 1, 0, −1 ],
[ 1, −1, −1, −1, 0, 1, 0 ],
[ 1, −1, −1, 0, 0, 0, −1 ],
[ 1, −1, 0, −1, 0, 0, −1 ],
[ 1, −1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
∗
6
• I ≡ P26 :
3
1
5
4
2




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1













bI =
C



63
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
1
1
1
1
−1
1
0
0
0
0
0
−1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
−1
0
−1
0
0
0
1
1
1
1
1
1
−1













BI =


1
0
0
0
0
0
−1
0
1
1
1
1
1
−1
0
0
0
−1
−1
−1
0
0
0
−1
0
0
−1
0
0
0
0
0
−1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
−1









Number of sincere Tits roots of poset I sI = 10.
Table of roots of qbI
[ −1, 1,−2,−2,−1, 1,−2 ],
[ −1, 1,−1,−1,−1, 1,−1 ],
[ 1,−1, 2, 1, 2,−1, 2 ],
[ −1, 0, −1, −1, −1, 0, −2 ],
[ −1, 0, −1, −1, 0, 0, −1 ],
[ −1, 0, −1, 0, −1, 1, −1 ],
[ −1, 0, 0, 0, 0, −1, −1 ],
[ −1, 1, −1, −1, −1, 0, −2 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 1, 0, 0, 0 ],
[ 0, −1, 1, 0, 1, 0, 1 ],
[ 0, −1, 1, 1, 1, −1, 0 ],
[ 0, 0, −1, −1, −1, 1, −1 ],
[ 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, −1, 0 ],
[ 0, 1, −2, −1, −1, 1, −1 ],
[ 0, 1, −1, −1, 0, 0, −1 ],
[ 0, 1, −1, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, −1, 0, 0 ],
[ 1, −1, 1, 0, 1, 0, 1 ],
[ 1, −1, 2, 1, 1, 0, 2 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 1 ],
[ 1, 0, 1, 1, 0, 0, 2 ],
[ 1, 0, 2, 1, 1, −1, 2 ],
[ −1, 1,−2,−1,−2, 1,−2 ],
[ 1,−1, 1, 1, 1,−1, 1 ],
[ 1,−1, 2, 2, 1,−1, 2 ],
[ −1, 0, −1, −1, −1, 1, −2 ],
[ −1, 0, −1, −1, 0, 1, −1 ],
[ −1, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 1, −1, −1, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, 0, 0, 0, 0 ],
[ 0, −1, 1, 1, 0, −1, 0 ],
[ 0, −1, 1, 1, 1, −1, 1 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 1, −1 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, −1, 0 ],
[ 0, 0, 1, 1, 0, −1, 1 ],
[ 0, 1, −1, −1, −1, 0, −1 ],
[ 0, 1, −1, −1, 0, 0, 0 ],
[ 0, 1, −1, 0, −1, 1, 0 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 1, −1, 1, 1, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 2 ],
[ 1, 0, 1, 1, 1, −1, 1 ],
[ 1, 1, 0, 0, 0, 0, 1 ]
[ −1, 1,−2,−1,−1, 1,−2 ],
[ 1,−1, 2, 1, 1,−1, 1 ],
[ −1, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, −1, −1, −1, 1, −1 ],
[ −1, 0, −1, 0, −1, 0, −2 ],
[ −1, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, −1, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, −1, 1, 0, 1, −1, 0 ],
[ 0, −1, 1, 1, 0, 0, 0 ],
[ 0, −1, 1, 1, 1, 0, 1 ],
[ 0, 0, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, 0, −1, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, 0, 1, −1, 1 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, −1, −1, −1, 1, −1 ],
[ 0, 1, −1, −1, 0, 1, 0 ],
[ 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1, −1, 1, 1, 1, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 1, 1, 0, −1, 1 ],
[ 1, 0, 1, 1, 1, −1, 2 ],
[ −1, 1,−2,−1,−1, 1,−1 ],
[ 1,−1, 2, 1, 1,−1, 2 ],
[ −1, 0, −2, −1, −1, 1, −2 ],
[ −1, 0, −1, −1, 0, 0, −2 ],
[ −1, 0, −1, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, −1, 0, −1 ],
[ −1, 1, −2, −1, −1, 0, −2 ],
[ −1, 1, −1, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, −1, 1, 0, 1, 0, 0 ],
[ 0, −1, 1, 1, 0, 0, 1 ],
[ 0, −1, 2, 1, 1, −1, 1 ],
[ 0, 0, −1, −1, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, −1, 1 ],
[ 0, 1, −1, −1, −1, 1, 0 ],
[ 0, 1, −1, 0, −1, 0, −1 ],
[ 0, 1, 0, −1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, −1, 1, 1, 1, 0, 2 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 0, 1, 0, 1, −1, 1 ],
[ 1, 0, 1, 1, 0, 0, 1 ],
[ 1, 0, 1, 1, 1, 0, 2 ],
∗
4
• I ≡ P27 :
6
5
3
2
1




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
1













b
CI =


64
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
0
0
1
0
−1
1
0
1
1
0
1
−1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
−1













BI =


0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
−1
1
0
0
1
0
0
−1
0
1
0
0
1
0
−1
0
0
0
0
0
−1
0
1
1
0
0
0
0
−1









Number of sincere Tits roots of poset I sI = 10.
Table of roots of qbI
[ −1, 1, 1, 1, 1, 1, 2 ],
[ −1, 1, 2, 2, 1, 1, 3 ],
[ 1,−1,−1,−2,−1,−1,−2 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 1, 0, 1, 0 ],
[ −1, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 1, 1 ],
[ −1, 1, 1, 1, 0, 0, 1 ],
[ 0, −1, −1, −2, −1, −1, −3 ],
[ 0, −1, −1, −1, 0, −1, −2 ],
[ 0, −1, 0, −1, −1, −1, −2 ],
[ 0, −1, 0, 0, 0, −1, −1 ],
[ 0, 0, −1, −1, −1, −1, −2 ],
[ 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, −1, −1, −2 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 1, 0, 2 ],
[ 1, −1, −1, −2, 0, −1, −2 ],
[ 1, −1, 0, −1, 0, −1, −1 ],
[ 1, 0, −1, −1, −1, 0, −1 ],
[ 1, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ −1, 1, 1, 2, 1, 1, 2 ],
[ 1,−1,−2,−2,−1,−1,−3 ],
[ 1,−1,−1,−1,−1,−1,−2 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 1, 1 ],
[ −1, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 2 ],
[ −1, 1, 1, 1, 0, 1, 1 ],
[ 0, −1, −1, −1, −1, −1, −3 ],
[ 0, −1, −1, −1, 0, 0, −2 ],
[ 0, −1, 0, −1, 0, −1, −2 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, −1, −1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 1, 1 ],
[ 0, 1, 1, 1, 0, 0, 1 ],
[ 0, 1, 1, 1, 1, 1, 2 ],
[ 1, −1, −1, −1, 0, −1, −2 ],
[ 1, 0, −1, −2, −1, −1, −2 ],
[ 1, 0, −1, −1, 0, −1, −1 ],
[ 1, 0, 0, −1, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 1, 0, 0, 0, 0, 1 ]
[ −1, 1, 1, 2, 1, 1, 3 ],
[ 1,−1,−1,−2,−1,−2,−3 ],
[ −1, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 1, 1, 0, 1, 1 ],
[ −1, 0, 1, 2, 1, 1, 2 ],
[ −1, 1, 1, 1, 0, 1, 2 ],
[ 0, −1, −1, −1, −1, −1, −2 ],
[ 0, −1, −1, −1, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, −1, −1 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, −1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 1, 2 ],
[ 0, 1, 1, 1, 0, 0, 2 ],
[ 0, 1, 1, 1, 1, 1, 3 ],
[ 1, −1, −1, −1, 0, −1, −1 ],
[ 1, 0, −1, −1, −1, −1, −2 ],
[ 1, 0, −1, −1, 0, 0, −1 ],
[ 1, 0, 0, −1, 0, −1, −1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 2, 1, 2, 3 ],
[ 1,−1,−1,−2,−1,−1,−3 ],
[ −1, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ −1, 1, 0, 1, 0, 1, 1 ],
[ −1, 1, 1, 2, 0, 1, 2 ],
[ 0, −1, −1, −1, −1, 0, −2 ],
[ 0, −1, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, −1, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 2 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 1, 1, 1, 2 ],
[ 0, 1, 1, 1, 0, 1, 2 ],
[ 0, 1, 1, 2, 1, 1, 3 ],
[ 1, −1, −1, −1, 0, 0, −1 ],
[ 1, 0, −1, −1, −1, −1, −1 ],
[ 1, 0, −1, −1, 0, 0, 0 ],
[ 1, 0, 0, −1, 0, −1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
∗
5
• I ≡ P28 :
6
4
3
2
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1













b
CI =


65
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
0
1
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
−1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
−1













BI =


1
1
1
0
1
1
−1
0
1
1
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
1
0
0
−1
0
−1
−1
0
0
−1
0
0
−1
0
0
−1
0
0
0
0
0
0
0
0
−1









Number of sincere Tits roots of poset I sI = 10.
Table of roots of qbI
[ −1,−1, 1, 1, 1, 1, 1 ],
[ −1,−1, 2, 1, 2, 1, 2 ],
[ 1, 1,−1,−1,−2,−1,−1 ],
[ −1, −1, 1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 1, 0, 1, 0, 0 ],
[ −1, 0, 1, 1, 1, 1, 1 ],
[ 0, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, −1, 1, 0, 0, 0, 0 ],
[ 0, −1, 1, 1, 1, 0, 1 ],
[ 0, 0, −1, −1, −1, −1, −2 ],
[ 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, −1, −1, −2 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, −1, −1, −2, −1, −2 ],
[ 0, 1, −1, 0, −1, −1, −1 ],
[ 0, 1, 0, −1, −1, −1, −1 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 1, −1, 0, 0, 0, 0, 0 ],
[ 1, 0, −1, −1, −1, 0, −1 ],
[ 1, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, −1, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 1, −1, 0, −1, 0, 0 ],
[ −1,−1, 1, 1, 2, 1, 1 ],
[ 1, 1,−2,−1,−2,−1,−2 ],
[ 1, 1,−1,−1,−1,−1,−1 ],
[ −1, −1, 1, 0, 1, 1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 2 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 1, 1, 0 ],
[ 0, −1, 1, 0, 1, 0, 0 ],
[ 0, −1, 1, 1, 1, 1, 1 ],
[ 0, 0, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, −1, −1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 1, −1, −1, −1, −1, −2 ],
[ 0, 1, −1, 0, −1, 0, −1 ],
[ 0, 1, 0, 0, −1, −1, −1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1, 0, −1, −1, −2, −1, −2 ],
[ 1, 0, −1, 0, −1, −1, −1 ],
[ 1, 0, 0, −1, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 1, −1, 0, −2, −1, −1 ],
[ 1, 1, 0, 0, −1, −1, 0 ]
[ −1,−1, 1, 1, 2, 1, 2 ],
[ 1, 1,−1,−1,−2,−2,−2 ],
[ −1, −1, 0, 0, 1, 1, 0 ],
[ −1, −1, 1, 0, 2, 1, 1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 1, 1, 2, 1, 2 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 1 ],
[ 0, −1, 1, 0, 1, 0, 1 ],
[ 0, −1, 1, 1, 1, 1, 2 ],
[ 0, 0, −1, −1, −1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 1, −1, −1, −1, −1, −1 ],
[ 0, 1, −1, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, −1, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, −1, −1, −1, −1, −2 ],
[ 1, 0, −1, 0, −1, 0, −1 ],
[ 1, 0, 0, 0, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, −1, 0, −1, −1, −1 ],
[ −1,−1, 1, 1, 2, 2, 2 ],
[ 1, 1,−1,−1,−2,−1,−2 ],
[ −1, −1, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 1, 1, 1, 1 ],
[ 0, −1, 1, 0, 1, 1, 1 ],
[ 0, −1, 1, 1, 2, 1, 2 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, −1, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 2 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 1, −1, −1, −1, 0, −1 ],
[ 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 1, 0, −1, −1, −1, −1, −1 ],
[ 1, 0, −1, 0, −1, 0, 0 ],
[ 1, 0, 0, 0, −1, −1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1, −1, 0, −1, −1, 0 ],
∗
6
2
• I ≡ P29 :
5
4
3
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1













bI =
C



66
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
0
0
0
0
−1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
−1
0
−1
−1
0
0
0
1
1
1
1
1
1
−1









−1
 0

 −1
BI = −1
 0
 0
1
2
1
1
1
0
0
−1

1
0
1
1
1
0
−1
0
0
0
0
−1
−1
0
1
0
1
0
0
0
0
−1
0
−1
−1
0
0
0
1
0
0
0
0
−1
0









Number of sincere Tits roots of poset I sI = 10.
Table of roots of qbI
[ −2, 2, 1, 1, 1,−1, 1 ],
[ −1, 2, 1, 1, 1,−1, 2 ],
[ 1,−1,−1,−1,−1, 1,−1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, −1, 0 ],
[ −1, 1, 0, 1, 1, −1, 1 ],
[ −1, 1, 1, 0, 0, 0, 1 ],
[ −1, 1, 1, 1, 0, −1, 0 ],
[ −1, 2, 1, 0, 1, −1, 1 ],
[ 0, −1, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, −1, 1, −1 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 1, 1, −1, 1 ],
[ 0, 1, 1, 0, 1, −1, 1 ],
[ 1, −2, 0, −1, −1, 1, −1 ],
[ 1, −1, −1, 0, −1, 0, −1 ],
[ 1, −1, −1, 0, 0, 0, 0 ],
[ 1, −1, 0, −1, −1, 1, 0 ],
[ 1, −1, 0, 0, −1, 0, −1 ],
[ 1, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 1, 1,−1, 1 ],
[ 1,−2,−1,−1,−1, 1,−2 ],
[ 2,−2,−1,−1,−1, 1,−1 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 0, 1, −1, 0 ],
[ −1, 1, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 1, 1, 0, 1 ],
[ −1, 1, 1, 0, 1, −1, 0 ],
[ −1, 1, 1, 1, 0, −1, 1 ],
[ −1, 2, 1, 1, 0, −1, 1 ],
[ 0, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 1, −1 ],
[ 0, −1, 0, 0, −1, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, −1, 0 ],
[ 0, 1, 1, 0, 0, −1, 0 ],
[ 0, 1, 1, 1, 0, −1, 1 ],
[ 1, −1, −1, −1, 0, 0, −1 ],
[ 1, −1, −1, 0, −1, 1, −1 ],
[ 1, −1, −1, 0, 0, 1, 0 ],
[ 1, −1, 0, −1, 0, 0, −1 ],
[ 1, −1, 0, 0, −1, 0, 0 ],
[ 1, 0, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ]
[ −1, 2, 1, 1, 1,−2, 1 ],
[ 1,−2,−1,−1,−1, 1,−1 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 1 ],
[ −1, 1, 1, 0, 0, −1, 0 ],
[ −1, 1, 1, 0, 1, −1, 1 ],
[ −1, 1, 1, 1, 0, 0, 1 ],
[ 0, −1, −1, −1, 0, 1, −1 ],
[ 0, −1, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, −1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1, −1, 0 ],
[ 0, 1, 0, 1, 0, −1, 1 ],
[ 0, 1, 1, 0, 0, −1, 1 ],
[ 1, −2, −1, −1, 0, 1, −1 ],
[ 1, −1, −1, −1, 0, 1, −1 ],
[ 1, −1, −1, 0, −1, 1, 0 ],
[ 1, −1, 0, −1, −1, 0, −1 ],
[ 1, −1, 0, −1, 0, 0, 0 ],
[ 1, −1, 0, 0, −1, 1, 0 ],
[ 1, 0, 0, 0, −1, 0, 0 ],
[ −1, 2, 1, 1, 1,−1, 1 ],
[ 1,−2,−1,−1,−1, 2,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 1 ],
[ −1, 1, 0, 1, 1, −1, 0 ],
[ −1, 1, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 1, 0, 1 ],
[ −1, 2, 0, 1, 1, −1, 1 ],
[ 0, −1, −1, 0, −1, 1, −1 ],
[ 0, −1, 0, −1, −1, 1, −1 ],
[ 0, −1, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 1, −1, 1 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1, −2, −1, 0, −1, 1, −1 ],
[ 1, −1, −1, −1, 0, 1, 0 ],
[ 1, −1, −1, 0, 0, 0, −1 ],
[ 1, −1, 0, −1, −1, 1, −1 ],
[ 1, −1, 0, −1, 0, 1, 0 ],
[ 1, −1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
∗
5
• I ≡ P30 :
6
4
3
2
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1













b
CI =


67
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
0
1
0
0
−1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
−1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
−1













BI =


−1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
−1
1
1
1
1
0
0
−1
2
1
1
0
1
0
−1
1
1
1
0
0
1
−1
2
2
1
1
1
0
−2









Number of sincere Tits roots of poset I sI = 10.
Table of roots of qbI
[ −2, 1, 1, 1, 2, 1, 2 ],
[ −1, 1, 1, 2, 2, 1, 3 ],
[ 1,−1,−1,−1,−1,−1,−2 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 2 ],
[ −1, 1, 0, 0, 1, 0, 1 ],
[ −1, 1, 0, 1, 1, 1, 2 ],
[ −1, 1, 1, 1, 1, 0, 2 ],
[ 0, −1, 0, −1, −1, 0, −2 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, −1, −1, −1, −2 ],
[ 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, −1, −1, −2 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 1, 1, 1, 2 ],
[ 1, −1, −1, −1, −1, 0, −1 ],
[ 1, −1, 0, −1, −1, −1, −1 ],
[ 1, −1, 0, 0, −1, 0, 0 ],
[ 1, 0, −1, −1, −1, −1, −1 ],
[ 1, 0, −1, 0, −1, 0, 0 ],
[ 1, 0, 0, 0, −1, −1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ −1, 1, 1, 1, 1, 1, 2 ],
[ 1,−1,−1,−2,−2,−1,−3 ],
[ 2,−1,−1,−1,−2,−1,−2 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 1, 1, 2, 1, 2 ],
[ −1, 1, 0, 0, 1, 1, 1 ],
[ −1, 1, 0, 1, 2, 1, 2 ],
[ −1, 1, 1, 1, 2, 0, 2 ],
[ 0, −1, 0, −1, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, −1, −1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 1, 1, 0, 2 ],
[ 1, −1, −1, 0, −1, 0, −1 ],
[ 1, −1, 0, −1, −1, 0, −1 ],
[ 1, −1, 0, 0, 0, 0, 0 ],
[ 1, 0, −1, −1, −1, 0, −1 ],
[ 1, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, −1, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ]
[ −1, 1, 1, 1, 2, 1, 2 ],
[ 1,−1,−1,−1,−2,−1,−3 ],
[ −1, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 1, 0, 1 ],
[ −1, 1, 1, 0, 1, 0, 1 ],
[ 0, −1, −1, −1, −1, 0, −2 ],
[ 0, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, −1, −1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 1, 0, 1 ],
[ 1, −1, −1, −1, −2, 0, −2 ],
[ 1, −1, 0, −1, −2, −1, −2 ],
[ 1, −1, 0, 0, −1, −1, −1 ],
[ 1, 0, −1, −1, −2, −1, −2 ],
[ 1, 0, −1, 0, −1, −1, −1 ],
[ 1, 0, 0, −1, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ −1, 1, 1, 1, 2, 1, 3 ],
[ 1,−1,−1,−1,−2,−1,−2 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 1, 0, 1, 0, 0 ],
[ −1, 0, 1, 1, 1, 1, 1 ],
[ −1, 1, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 1, 1, 1, 1 ],
[ −1, 1, 1, 1, 1, 0, 1 ],
[ 0, −1, 0, −1, −1, −1, −2 ],
[ 0, −1, 0, 0, −1, 0, −1 ],
[ 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, −1, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 2 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 1, 0, 2 ],
[ 1, −1, −1, −1, −1, 0, −2 ],
[ 1, −1, 0, −1, −1, −1, −2 ],
[ 1, −1, 0, 0, −1, 0, −1 ],
[ 1, 0, −1, −1, −1, −1, −2 ],
[ 1, 0, −1, 0, −1, 0, −1 ],
[ 1, 0, 0, 0, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
∗
5
6
4
• I ≡ P31 :
3
2
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1













bI =
C



68
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
−1









−1
 −1

 −1
BI = 0
 −1
 0
1
0
−1
0
0
0
0
0

0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
2
1
1
1
0
−1
1
1
1
1
0
1
−1
1
1
1
1
0
0
0









Number of sincere Tits roots of poset I sI = 10.
Table of roots of qbI
[ −2,−1, 1, 1, 2, 1, 1 ],
[ −1,−1, 1, 1, 2, 1, 2 ],
[ 1, 2,−1,−1,−2,−1,−1 ],
[ −1, −1, 0, 1, 1, 1, 0 ],
[ −1, −1, 1, 0, 1, 1, 0 ],
[ −1, −1, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 1, 0, 0, 0 ],
[ 0, −1, 1, 0, 0, 0, 0 ],
[ 0, −1, 1, 1, 1, 0, 1 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, −1, 0, −1, −1, −1 ],
[ 0, 1, 0, −1, −1, −1, −1 ],
[ 0, 1, 0, 0, −1, −1, −1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1, 0, −1, 0, −1, −1, −1 ],
[ 1, 0, 0, −1, −1, −1, −1 ],
[ 1, 0, 0, 0, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, −1, −1, −1, 0, 0 ],
[ 1, 1, −1, 0, −1, 0, 0 ],
[ 1, 1, 0, −1, −1, 0, 0 ],
[ −1,−2, 1, 1, 2, 1, 1 ],
[ 1, 1,−1,−1,−2,−1,−2 ],
[ 2, 1,−1,−1,−2,−1,−1 ],
[ −1, −1, 0, 1, 1, 1, 1 ],
[ −1, −1, 1, 0, 1, 1, 1 ],
[ −1, −1, 1, 1, 2, 0, 1 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 1, 1, 0, 0 ],
[ 0, −1, 1, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, −1, 0, −1, 0, −1 ],
[ 0, 1, 0, −1, −1, 0, −1 ],
[ 0, 1, 0, 0, −1, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, −1, 0, −1, 0, −1 ],
[ 1, 0, 0, −1, −1, 0, −1 ],
[ 1, 0, 0, 0, −1, −1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1, −1, 0, −2, −1, −1 ],
[ 1, 1, 0, −1, −2, −1, −1 ],
[ 1, 1, 0, 0, −1, −1, 0 ]
[ −1,−1, 1, 1, 1, 1, 1 ],
[ 1, 1,−1,−1,−2,−1,−1 ],
[ −1, −1, 0, 0, 1, 1, 0 ],
[ −1, −1, 0, 1, 2, 1, 1 ],
[ −1, −1, 1, 0, 2, 1, 1 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 0, 1, 0, 1 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 1, 1, 0 ],
[ 0, −1, 0, 1, 1, 0, 1 ],
[ 0, −1, 1, 0, 1, 0, 1 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, −1, 0, −1, 0, 0 ],
[ 0, 1, 0, −1, −1, 0, 0 ],
[ 0, 1, 0, 0, −1, 0, 0 ],
[ 1, −1, 0, 0, 0, 0, 0 ],
[ 1, 0, −1, 0, −1, 0, 0 ],
[ 1, 0, 0, −1, −1, 0, 0 ],
[ 1, 0, 0, 0, −1, 0, 0 ],
[ 1, 1, −1, −1, −2, 0, −1 ],
[ 1, 1, −1, 0, −1, −1, −1 ],
[ 1, 1, 0, −1, −1, −1, −1 ],
[ −1,−1, 1, 1, 2, 1, 1 ],
[ 1, 1,−1,−1,−1,−1,−1 ],
[ −1, −1, 0, 1, 1, 0, 0 ],
[ −1, −1, 1, 0, 1, 0, 0 ],
[ −1, −1, 1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 1, 1 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 1 ],
[ 0, −1, 0, 1, 1, 1, 1 ],
[ 0, −1, 1, 0, 1, 1, 1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 1, −1, −1, −1, 0, −1 ],
[ 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, −1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 1, 0, −1, −1, −1, 0, −1 ],
[ 1, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 1, −1, −1, −1, 0, −1 ],
[ 1, 1, −1, 0, −1, −1, 0 ],
[ 1, 1, 0, −1, −1, −1, 0 ],
∗
6
4
• I ≡ P32 :
5
3
2
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1













bI =
C



69
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
−1
−1
0
0
0
0
1
1
1
1
1
1
−1









0
 −1

 −1
BI = 0
 0
 0
0

−1
−1
0
−1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
−1
0









Number of sincere Tits roots of poset I sI = 6.
Table of roots of qbI
[ −1,−1, 1, 2, 1,−1, 1 ],
[ 1, 1,−1,−2,−2, 1,−1 ],
[ −1, −1, 1, 1, 1, −1, 0 ],
[ −1, −1, 1, 2, 1, 0, 1 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 2, 1, −1, 1 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 1, 1, 0, 0 ],
[ 0, −1, 1, 1, 0, 0, 0 ],
[ 0, −1, 1, 1, 1, 0, 1 ],
[ 0, 0, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, −1, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 0, 1, 1, −1, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, −1, −1, −1, 1, −1 ],
[ 0, 1, −1, −1, 0, 1, 0 ],
[ 0, 1, 0, −1, −1, 1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1, 0, −1, −1, −1, 0, −1 ],
[ 1, 0, −1, −1, 0, 0, 0 ],
[ 1, 0, 0, −1, −1, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 1, −1, −2, −1, 1, 0 ],
[ 1, 1, −1, −1, 0, 0, 0 ],
[ −1,−1, 1, 2, 2,−1, 1 ],
[ 1, 1,−1,−2,−1, 1,−1 ],
[ −1, −1, 1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, −1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 1, 1, 0, 1 ],
[ 0, −1, 1, 1, 0, 0, 1 ],
[ 0, −1, 1, 2, 1, −1, 1 ],
[ 0, 0, −1, −1, 0, 1, 0 ],
[ 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, −1, 1 ],
[ 0, 1, −1, −1, −1, 1, 0 ],
[ 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, −1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, −1, −1, −1, 1, −1 ],
[ 1, 0, −1, −1, 0, 1, 0 ],
[ 1, 0, 0, −1, −1, 1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, −1, −1, −1, 0, −1 ],
[ 1, 1, 0, −1, −1, 0, 0 ]
[ −1,−1, 2, 2, 1,−1, 1 ],
[ −1, −1, 0, 1, 1, 0, 0 ],
[ −1, −1, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, −1, 0 ],
[ −1, 0, 1, 1, 0, −1, 0 ],
[ −1, 0, 1, 1, 1, −1, 1 ],
[ 0, −1, 0, 0, 0, 0,−1 ],
[ 0, −1, 0, 1, 0, 0, 0 ],
[ 0, −1, 1, 0, 0, 0, 0 ],
[ 0, −1, 1, 1, 1, −1, 0 ],
[ 0, 0,−1,−1,−1, 1,−1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 1, 1, 0, −1, 0 ],
[ 0, 1,−1,−2,−1, 1,−1 ],
[ 0, 1,−1,−1, 0, 0,−1 ],
[ 0, 1, 0,−1,−1, 0,−1 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 1, −1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1,−1,−1, 1, 0 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1,−1,−1,−1, 0, 0 ],
[ 1, 1,−2,−2,−1, 1,−1 ],
[ −1,−1, 1, 1, 0, 0, 0 ],
[ −1,−1, 1, 2, 1,−1, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 1,−1, 0 ],
[ 0,−1, 1, 1, 0,−1, 0 ],
[ 0,−1, 1, 1, 1,−1, 1 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, 1, −1 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1,−1, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 1, 0,−1, 1 ],
[ 0, 1, −1, −1, −1, 0, −1 ],
[ 0, 1, −1, −1, 0, 0, 0 ],
[ 0, 1, 0, −1, −1, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 1, 0, −1, −2, −1, 1, −1 ],
[ 1, 0, −1, −1, 0, 0, −1 ],
[ 1, 0, 0, −1, −1, 0, −1 ],
[ 1, 0, 0, 0, −1, 0, 0 ],
[ 1, 1, −1, −2, −1, 0, −1 ],
[ 1, 1, −1, −1, −1, 1, 0 ],
∗
5
6
4
• I ≡ P33 :
3
2
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1













bI =
C



70
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
−1













BI =


0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
−1
−1
−2
−1
−1
−1
0
0
−1
−1
−1
0
−1
0
−1
−1
−1
−1
−1
0
0
−1
−1
−1
−1
−1
−1
1









Number of sincere Tits roots of poset I sI = 6.
Table of roots of qbI
[ −1,−1,−1, 1, 2, 1, 1 ],
[ 1, 1, 1,−1,−2,−2,−1 ],
[ −1, −1, 0, 0, 1, 1, 0 ],
[ −1, −1, 0, 1, 2, 1, 1 ],
[ −1, 0, −1, 1, 1, 1, 1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ 0, −1, −1, 1, 1, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 1 ],
[ 0, −1, 0, 1, 1, 1, 1 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, −1, −1, −1, −1 ],
[ 0, 0, 1, 0, −1, −1, −1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, −1, −1, 0, −1 ],
[ 0, 1, 0, 0, −1, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, −1, −1, 0, 0 ],
[ 1, 0, 0, −1, −1, −1, −1 ],
[ 1, 0, 0, 0, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, −1, −1, −1, 0 ],
[ 1, 1, 0, −1, −1, −1, −1 ],
[ 1, 1, 1, −1, −2, −1, 0 ],
[ −1,−1,−1, 1, 2, 2, 1 ],
[ 1, 1, 1,−1,−2,−1,−1 ],
[ −1, −1, 0, 1, 1, 0, 0 ],
[ −1, 0, −1, 0, 1, 1, 0 ],
[ −1, 0, −1, 1, 2, 1, 1 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, 1, 1, 1, 1 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 1, 0, 0, 0 ],
[ 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, −1, 1, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, −1, −1, 0, −1 ],
[ 0, 0, 1, 0, −1, −1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, −1, −1, 0, 0 ],
[ 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 1, 1, −1, −2, −1, −1 ],
[ 0, 1, 1, 0, −1, −1, 0 ],
[ 1, 0, 0, −1, −1, 0, −1 ],
[ 1, 0, 0, 0, −1, −1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, −1, −1, 0, 0 ],
[ 1, 1, 0, −1, −1, −1, 0 ],
[ 1, 1, 1, −1, −1, −1, 0 ]
[ −1,−1,−1, 2, 2, 1, 1 ],
[ −1, −1, −1, 1, 1, 1, 0 ],
[ −1, −1, 0, 1, 1, 1, 0 ],
[ −1, 0, −1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 1, 1, 0, 1 ],
[ 0, −1, −1, 0, 1, 1, 0 ],
[ 0, −1, −1, 1, 2, 1, 1 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 1, 1, 0, 0 ],
[ 0, 0, −1, 0, 0, 0,−1 ],
[ 0, 0, −1, 0, 1, 1, 0 ],
[ 0, 0, −1, 1, 1, 0, 1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1,−1,−1, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 1,−1,−1,−1,−1 ],
[ 1, −1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1,−1, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 1,−1,−2,−1,−1 ],
[ 1, 0, 1, 0,−1,−1, 0 ],
[ 1, 1, 0,−1,−1, 0, 0 ],
[ 1, 1, 1,−2,−2,−1,−1 ],
[ −1,−1,−1, 1, 2, 1, 0 ],
[ −1,−1, 0, 1, 1, 1, 1 ],
[ −1, 0,−1, 1, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ 0,−1,−1, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, −1 ],
[ 0,−1, 0, 0, 1, 1, 0 ],
[ 0,−1, 0, 1, 1, 0, 1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 1, 1 ],
[ 0, 0,−1, 1, 1, 1, 1 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 1, 0, −1, −1, −1, −1 ],
[ 0, 1, 0, 0, −1, −1, −1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, −1, −1, −1, 0 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 0, 1, −1, −1, −1, −1 ],
[ 1, 1, 0, −1, −2, −1, −1 ],
[ 1, 1, 0, 0, −1, −1, 0 ],
∗
6
• I ≡ P34 :
4
5
2
3
1




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1













b
CI =


71
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
0
0
0
0
−1
1
0
1
0
1
0
−1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
−1
0
−1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
−1













BI =


0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
−1
−1
0
1
0
1
0
0
0
−1
1
0
0
0
0
0
0
−1
0
−1
0
0
0
0
0
0
0
−1
0
−1
0









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 1, 1, 1, 1,−1, 1 ],
[ −1,−1, 0, 0, 0, 0,−1 ],
[ −1,−1, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, −1, 0 ],
[ 0,−1,−1,−1,−1, 1,−2 ],
[ 0,−1,−1, 0,−1, 1,−1 ],
[ 0,−1, 0,−1,−1, 1,−1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1,−1,−1, 1,−1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 1, 1, 0, −1, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, −1, 0 ],
[ 0, 1, 1, 0, 0, −1, 0 ],
[ 0, 1, 1, 1, 0, −1, 1 ],
[ 1, 0,−1,−2,−1, 1,−1 ],
[ 1, 0,−1,−1, 0, 0,−1 ],
[ 1, 0, 0,−1,−1, 0,−1 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 1,−1,−1, 0, 0, 0 ],
[ 1, 1, 0,−1, 0, 0, 1 ],
[ 1, 1, 0, 0, 1, −1, 1 ],
[ 1,−1,−1,−1,−1, 1,−1 ],
[ −1, −1, 0, 0, 0, 1, −1 ],
[ −1, −1, 0, 1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1,−1, 0 ],
[ −1, 0, 1, 1, 0,−1, 0 ],
[ −1, 0, 1, 1, 1,−1, 1 ],
[ 0, −1, −1, −1, −1, 1, −1 ],
[ 0, −1, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, 1, −1 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1,−1, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 1, 0,−1, 1 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 1,−1, 1 ],
[ 0, 1, 1, 0, 0,−1, 1 ],
[ 0, 1, 1, 1, 1,−2, 1 ],
[ 1, 0, −1, −1, −1, 0, −1 ],
[ 1, 0, −1, −1, 0, 0, 0 ],
[ 1, 0, 0, −1, −1, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 1, 0, −1, −1, 0, 0 ],
[ 1, 1, 0, 0, 0,−1, 0 ],
[ 1, 1, 1, 0, 0,−1, 1 ]
[ −1,−1,−1, 0, 0, 1,−1 ],
[ −1,−1, 0, 0, 0, 1, 0 ],
[ −1,−1, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ 0,−1,−1,−1,−1, 2,−1 ],
[ 0,−1,−1, 0, 0, 1,−1 ],
[ 0,−1, 0, 0,−1, 1,−1 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1,−1, 0, 1,−1 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1,−1, 1, 0 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1, 1,−1, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 1,−1, 1 ],
[ 1, 0,−1,−1,−1, 1,−1 ],
[ 1, 0,−1,−1, 0, 1, 0 ],
[ 1, 0, 0,−1,−1, 1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0,−1, 0,−1, 0 ],
[ 1, 1, 0, 0, 0,−1, 1 ],
[ −1,−1, 0, 0,−1, 1,−1 ],
[ −1,−1, 0, 1, 0, 0,−1 ],
[ −1,−1, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 2, 1,−1, 1 ],
[ 0,−1,−1,−1, 0, 1,−1 ],
[ 0,−1,−1, 0, 0, 1, 0 ],
[ 0,−1, 0, 0,−1, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1,−1, 0, 1, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1,−1, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 1,−1, 1 ],
[ 0, 1, 1, 0, 1,−1, 1 ],
[ 0, 1, 1, 1, 1,−1, 2 ],
[ 1, 0,−1,−1,−1, 1, 0 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1, 0,−1, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
∗
• I ≡ P35 :
5
6
2
3
4
1




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
1













b
CI =


72
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
0
1
0
0
−1
1
0
1
1
0
1
−1
1
0
0
0
1
0
0
1
1
1
0
1
1
−1
0
0
0
−1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
−1













BI =


1
0
0
0
1
0
0
1
1
1
0
1
0
−1
0
1
0
1
0
0
−1
1
0
1
1
0
0
−1
0
0
0
0
−1
0
0
1
0
1
0
0
1
−1
2
1
1
1
1
0
−2









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 1, 1, 1, 1, 1, 2 ],
[ −1,−1, 0,−1, 0, 0,−2 ],
[ −1,−1, 0, 0, 1, 0,−1 ],
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ 0,−1,−1,−2,−1,−1,−3 ],
[ 0,−1,−1,−1, 0,−1,−2 ],
[ 0,−1, 0,−1,−1,−1,−2 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1,−1,−1,−1,−2 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1,−1,−1,−2 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 1, 0, 2 ],
[ 1, 0,−1,−1,−2,−1,−2 ],
[ 1, 0,−1, 0,−1,−1,−1 ],
[ 1, 0, 0,−1,−1,−1,−1 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 1,−1, 0,−1, 0, 0 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 1, 0, 1, 2 ],
[ 1,−1,−1,−1,−1,−1,−2 ],
[ −1, −1, 0, −1, 0, 0, −1 ],
[ −1, −1, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 1, 0, 1, 0, 0 ],
[ −1, 0, 1, 1, 1, 1, 1 ],
[ 0, −1, −1, −1, −1, −1, −3 ],
[ 0, −1, −1, −1, 0, 0, −2 ],
[ 0, −1, 0, −1, 0, −1, −2 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, −1, −1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 1, 1 ],
[ 0, 1, 1, 1, 0, 0, 1 ],
[ 0, 1, 1, 1, 1, 1, 2 ],
[ 1, 0, −1, −1, −1, −1, −2 ],
[ 1, 0, −1, 0, −1, 0, −1 ],
[ 1, 0, 0, 0, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, −1, −1, 0 ],
[ 1, 1, 0, 1, −1, 0, 1 ],
[ 1, 1, 1, 1, 0, 0, 2 ]
[ −1,−1,−1,−1, 0, 0,−2 ],
[ −1,−1, 0,−1, 1, 0,−1 ],
[ −1,−1, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 2 ],
[ 0,−1,−1,−1,−1,−1,−2 ],
[ 0,−1,−1,−1, 0, 0,−1 ],
[ 0,−1, 0,−1, 0,−1,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1,−1,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 1, 2 ],
[ 0, 1, 1, 1, 0, 0, 2 ],
[ 0, 1, 1, 1, 1, 1, 3 ],
[ 1, 0,−1,−1,−1,−1,−1 ],
[ 1, 0,−1, 0,−1, 0, 0 ],
[ 1, 0, 0, 0,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 0,−1, 0, 0 ],
[ 1, 1, 0, 1, 0, 0, 1 ],
[ −1,−1, 0,−1, 0,−1,−2 ],
[ −1,−1, 0, 0, 0, 0,−1 ],
[ −1,−1, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 1, 1, 2, 1, 2 ],
[ 0,−1,−1,−1,−1, 0,−2 ],
[ 0,−1,−1, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 2 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 1, 1, 1, 2 ],
[ 0, 1, 1, 1, 0, 1, 2 ],
[ 0, 1, 1, 2, 1, 1, 3 ],
[ 1, 0,−1,−1,−1, 0,−1 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 1, 0, 0,−1, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 2 ],
∗
• I ≡ P36 :
5
6
3
4
2
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1













b
CI =


73
1
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
0
0
0
0
−1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
−1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
−1









−1
 −1

 −1
BI = 0
 −1
 0
1

0
1
0
0
1
0
0
1
1
1
1
1
0
−1
1
0
1
0
0
0
0
0
0
0
0
−1
0
0
1
1
0
1
0
1
−1
1
1
0
1
0
0
0









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1, 1, 1, 1, 1, 1 ],
[ −1, −1, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 0, 0, 1, 1 ],
[ −1, 0, 1, 1, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 1, 1 ],
[ 0, −1,−1, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 1 ],
[ 0, −1, 0, 1, 1, 1, 1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0,−1,−1, 0,−1 ],
[ 0, 1, 0, 0,−1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0,−1, 0, 1 ],
[ 1, −1,−1, 0, 0, 0,−1 ],
[ 1, 0,−1,−1,−1,−1,−2 ],
[ 1, 0,−1,−1, 0, 0,−1 ],
[ 1, 0,−1, 0, 0,−1, 0 ],
[ 1, 0, 0,−1,−1, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 1, 0,−1,−2,−1,−1 ],
[ 1, 1, 0, 0,−1,−1, 0 ],
[ 1, 1,−1,−1,−1,−1,−1 ],
[ −1,−1, 0, 1, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ −1, 1, 1, 0, −1, 0, 0 ],
[ −1, 1, 1, 1, 0, 0, 1 ],
[ 0,−1, −1, 0, 1, 1, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, −1, −1, 0, 0 ],
[ 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 1, 1, −1, −1, 0, 0 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1,−1, −1, 0, 0, 0, 0 ],
[ 1, 0, −1, −1, −1, −1, −1 ],
[ 1, 0, −1, −1, 0, 0, 0 ],
[ 1, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 1, 0, −1, −1, −1, −1 ],
[ 2, 0, −1, −1, −1, −1, −1 ]
[ −2, 0, 1, 1, 1, 1, 1 ],
[ −1,−1, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 1, 1 ],
[ −1, 1, 1, 0, 0, 0, 0 ],
[ 0,−1,−1, 0, 0, 0,−1 ],
[ 0,−1,−1, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 1, 0,−1,−1, 0 ],
[ 1,−1,−1,−1, 0, 0,−1 ],
[ 1,−1,−1, 0, 1, 0, 0 ],
[ 1, 0,−1,−1,−1, 0,−1 ],
[ 1, 0,−1, 0,−1,−1,−1 ],
[ 1, 0, 0,−1,−1,−1,−1 ],
[ 1, 0, 0, 0,−1,−1,−1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0,−1,−1,−1, 0 ],
[ −1,−1, 0, 0, 1, 1, 0 ],
[ −1,−1, 0, 1, 2, 1, 1 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 1, 0 ],
[ −1, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 2 ],
[ −1, 1, 1, 0, 0, 0, 1 ],
[ 0,−1,−1, 0, 1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 1, 0 ],
[ 0,−1, 0, 1, 1, 0, 1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1,−1,−1,−1 ],
[ 0, 1, 0, 0,−1,−1,−1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 0,−1, 0, 0 ],
[ 1,−1,−1, 0, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1,−1, 0,−1,−1 ],
[ 1, 0,−1, 0, 0,−1,−1 ],
[ 1, 0, 0,−1,−1, 0,−1 ],
[ 1, 0, 0, 0,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1, 0,−1,−1, 0, 0 ],
∗
• I ≡ P37 :
3
6
2
5
4
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1













b
CI =


74
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
0
0
0
0
−1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
−1
0
0
−1
0
0
0
1
1
1
1
1
1
−1









−1
 0

 0
BI = −1
 −1
 0
1
1
0
0
1
1
0
0

1
1
1
0
0
0
−1
1
1
0
1
1
1
−1
0
0
0
0
0
−1
0
0
0
0
0
−1
0
0
1
1
0
0
0
0
0









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 1, 1, 1, 1,−1, 1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 1 ],
[ −1, 1, 0, 0, 1, −1, 0 ],
[ −1, 1, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 1, 1, 0, 1 ],
[ −1, 1, 1, 1, 1, 0, 2 ],
[ 0,−1, 0,−1, 0, 1,−1 ],
[ 0,−1, 0, 0,−1, 1, 0 ],
[ 0,−1, 1,−1, 0, 1, 0 ],
[ 0,−1, 1, 0, 0, 1, 1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1,−1, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 1, −1, 1 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 1,−1,−1,−1,−1, 0,−1 ],
[ 1,−1, 0,−1,−1, 1,−1 ],
[ 1,−1, 0,−1, 0, 1, 0 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1,−1, 0, 0, 0 ],
[ 1, 0,−1, 0, 0, −1,−1 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 1,−1, 0, 0, −1, 0 ],
[ 1,−1,−1,−1,−1, 1,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 1 ],
[ −1, 0, 1, 1, 0, 1, 1 ],
[ −1, 1, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 1 ],
[ −1, 1, 1, 0, 1, 0, 1 ],
[ −1, 2, 0, 1, 1,−1, 1 ],
[ 0, −1, 0, −1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 1, 0, −1, 1, 0 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 1, 1,−1, 1 ],
[ 1, −1, −1, −1, 0, 0, −1 ],
[ 1, −1, 0, −1, −1, 1, 0 ],
[ 1, −1, 0, 0, −1, 0, −1 ],
[ 1, 0, −1, −1, −1, 0, −1 ],
[ 1, 0, −1, 0, −1,−1, −1 ],
[ 1, 0, −1, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 2, −1, −1, −1, −1, 0, −1 ]
[ −2, 1, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ −1, 1, 0, 0, 1, 0, 1 ],
[ −1, 1, 0, 1, 1,−1, 0 ],
[ −1, 1, 1, 1, 0, 0, 1 ],
[ 0,−1, 0,−1,−1, 1,−1 ],
[ 0,−1, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1,−1, 0, 1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0,−1, 0 ],
[ 1,−2, 0,−1,−1, 1,−1 ],
[ 1,−1,−1, 0,−1, 0,−1 ],
[ 1,−1, 0,−1, 0, 0,−1 ],
[ 1,−1, 0, 0,−1, 0, 0 ],
[ 1, 0,−1,−1, 0,−1,−1 ],
[ 1, 0,−1, 0,−1, 0,−1 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ −1,−1, 1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 1, 1 ],
[ −1, 0, 1, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0,−1, 0 ],
[ −1, 1, 0, 1, 1,−1, 1 ],
[ −1, 1, 1, 1, 1, 0, 1 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0,−1, 1,−1 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 1, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1,−1, 0, 0,−1,−1 ],
[ 0, 1,−1, 1, 0,−1, 0 ],
[ 0, 1, 0, 0, 1,−1, 0 ],
[ 0, 1, 0, 1, 0,−1, 1 ],
[ 1,−1,−1,−1,−1, 0,−2 ],
[ 1,−1, 0,−1,−1, 0,−1 ],
[ 1,−1, 0,−1, 0, 0, 0 ],
[ 1,−1, 0, 0,−1, 1, 0 ],
[ 1, 0,−1,−1, 0, 0,−1 ],
[ 1, 0,−1, 0,−1, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
∗
6
• I ≡ P38 :
2
5
1
4
3




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1













b
CI =


75
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
1
1
0
0
−1
1
0
0
0
1
0
0
1
1
0
0
0
0
−1
0
0
1
0
0
0
0
−1
0
0
0
0
0
0
0
0
−1
0
0
0
1
1
1
1
1
1
1
−1













BI =


0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
−1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
−1
0
0
0
1
1
0
0









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−1,−1, 1, 1,−1 ],
[ −1, −1, −1, −1, 0, 1, −1 ],
[ −1, 0, −1, −1, 0, 1, −1 ],
[ −1, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, −1, 0, 1, 0, 0 ],
[ −1, 0, 0, −1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 1, −1, 0, 1, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 0 ],
[ 0, −1, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0,−1, 1, −1 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 1, 1,−1, 1 ],
[ 0, 1, 1, 0, 1,−1, 1 ],
[ 1, −1, 0, 0,−1, 1, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 1,−1,−1, 0 ],
[ 1, 0, 0, 1, 0,−1, 1 ],
[ 1, 0, 1, 0,−1, 0, 1 ],
[ 1, 0, 1, 1,−1,−1, 0 ],
[ 1, 1, 0, 1, 0,−1, 1 ],
[ 1, 1, 1, 1, 0,−1, 2 ],
[ 1, 1, 1, 1,−1,−1, 1 ],
[ −1,−1,−1,−1, 0, 2,−1 ],
[ −1, 0,−1,−1, 1, 0,−1 ],
[ −1, 0,−1, 0, 0, 1,−1 ],
[ −1, 0,−1, 0, 1, 1, 0 ],
[ −1, 0, 0,−1, 1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0,−1, 1, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 1 ],
[ 0,−1,−1, 0, 0, 1,−1 ],
[ 0,−1, 0,−1, 0, 1,−1 ],
[ 0,−1, 0, 0, −1, 1, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, −1, 0 ],
[ 0, 1, 1, 0, 0, −1, 0 ],
[ 0, 1, 1, 1, 0, −1, 1 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 0, 0, 1, −1, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, −1, 0 ],
[ 1, 0, 1, 1, −1, −1, 1 ],
[ 1, 1, 1, 0, 0, −1, 1 ],
[ 2, 0, 1, 1, −1, −1, 1 ]
[ −2, 0,−1,−1, 1, 1,−1 ],
[ −1,−1,−1, 0, 0, 1,−1 ],
[ −1, 0,−1,−1, 1, 1,−1 ],
[ −1, 0,−1, 0, 0, 1, 0 ],
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0,−1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1,−1,−1, 0, 1,−1 ],
[ 0,−1,−1, 0, 0, 1, 0 ],
[ 0,−1, 0,−1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1,−1, 0 ],
[ 0, 1, 0, 1, 0,−1, 1 ],
[ 0, 1, 1, 0, 0,−1, 1 ],
[ 1,−1, 0, 0,−1, 0,−1 ],
[ 1,−1, 0, 1,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1,−1, 0, 1 ],
[ 1, 0, 1, 0,−1,−1, 0 ],
[ 1, 0, 1, 0, 0,−1, 1 ],
[ 1, 0, 1, 1,−1, 0, 1 ],
[ 1, 1, 1, 1, 0,−2, 1 ],
[ −1,−1,−1,−1, 0, 1,−2 ],
[ −1,−1, 0,−1, 0, 1,−1 ],
[ −1, 0,−1,−1, 1, 1, 0 ],
[ −1, 0,−1, 0, 1, 0,−1 ],
[ −1, 0, 0,−1, 0, 1,−1 ],
[ −1, 0, 0,−1, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 0, 1,−1, 0 ],
[ 0,−1,−1, 0,−1, 1,−1 ],
[ 0,−1, 0,−1,−1, 1,−1 ],
[ 0,−1, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 1,−1, 1 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1,−1, 0, 0,−1, 0, 0 ],
[ 1,−1, 1, 0,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 1, 0,−1, 0 ],
[ 1, 0, 1, 0,−1, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 1, 1, 0,−1, 1 ],
[ 1, 1, 1, 1, 0,−1, 1 ],
∗
• I ≡ P39 :
3
6
2
5
1
4




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1













b
CI =


76
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
1
1
1
1
−1
1
0
0
1
1
0
−1
0
1
0
0
0
1
0
1
1
1
0
0
0
−1
0
0
0
1
0
0
0
−1
0
0
−1
0
0
1
1
1
1
1
1
1
−1













BI =


1
1
0
0
0
0
−1
1
0
0
1
1
0
−1
0
1
1
0
0
0
−1
0
1
0
1
1
1
−1
0
0
0
0
0
−1
0
0
0
0
0
−1
0
0
1
1
0
1
1
0
−2









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−1,−1,−1, 1,−2 ],
[ −1, −1, −1, −1, −1, 0, −3 ],
[ −1, −1, 0, −1, −1, 0, −2 ],
[ −1, −1, 0, −1, 0, 0, −1 ],
[ −1, −1, 0, 0, −1, 1, −1 ],
[ −1, 0, −1, −1, 0, 0, −2 ],
[ −1, 0, −1, 0, −1, 0, −1 ],
[ −1, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, −1, 0, 1, −1 ],
[ 0, −1, 0, 0, −1, 1, 0 ],
[ 0, −1, 1, −1, 0, 1, 0 ],
[ 0, −1, 1, 0, 0, 1, 1 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, −1, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 1,−1, 1 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 2 ],
[ 1, 0, 1, 1, 0, 1, 2 ],
[ 1, 1, 0, 0, 1, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 2 ],
[ 1, 1, 1, 0, 1, 0, 2 ],
[ 1, 2, 0, 1, 1,−1, 2 ],
[ 1, 1, 1, 1, 1,−1, 2 ],
[ −1,−1,−1,−1,−1, 0,−2 ],
[ −1,−1, 0,−1,−1, 1,−2 ],
[ −1,−1, 0,−1, 0, 1,−1 ],
[ −1,−1, 0, 0, 0, 0,−1 ],
[ −1, 0,−1,−1, 0, 0,−1 ],
[ −1, 0,−1, 0, 0, −1,−2 ],
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 1,−1, 0, 0, −1,−1 ],
[ 0,−1, 0,−1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 1, 0,−1, 1, 0 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 1, 1, −1, 1 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 0, 1, 0, 0, 1, 1 ],
[ 1, 0, 1, 0, 1, 1, 2 ],
[ 1, 0, 1, 1, 1, 0, 2 ],
[ 1, 1, 0, 0, 1, 0, 2 ],
[ 1, 1, 0, 1, 1, −1, 1 ],
[ 1, 1, 1, 1, 0, 0, 2 ],
[ 2, 1, 1, 1, 1, 0, 3 ]
[ −2,−1,−1,−1,−1, 0,−3 ],
[ −1,−1,−1,−1, 0, 0,−2 ],
[ −1,−1, 0,−1,−1, 1,−1 ],
[ −1,−1, 0, 0,−1, 0,−2 ],
[ −1, 0,−1,−1,−1, 0,−2 ],
[ −1, 0,−1, 0,−1,−1,−2 ],
[ −1, 0,−1, 0, 0,−1,−1 ],
[ −1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0,−1,−1, 1,−1 ],
[ 0,−1, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1,−1, 0, 1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0,−1, 0 ],
[ 1,−1, 1, 0, 0, 1, 1 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, 0, 0, 1, 2 ],
[ 1, 0, 1, 1, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 1, 0,−1, 1 ],
[ 1, 1, 0, 1, 1,−1, 2 ],
[ 1, 1, 1, 1, 1, 0, 2 ],
[ −1,−2, 0,−1,−1, 1,−2 ],
[ −1,−1,−1, 0,−1, 0,−2 ],
[ −1,−1, 0,−1, 0, 0,−2 ],
[ −1,−1, 0, 0,−1, 0,−1 ],
[ −1, 0,−1,−1, 0,−1,−2 ],
[ −1, 0,−1, 0,−1, 0,−2 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0,−1, 1,−1 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 1, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1,−1, 0, 0,−1,−1 ],
[ 0, 1,−1, 1, 0,−1, 0 ],
[ 0, 1, 0, 0, 1,−1, 0 ],
[ 0, 1, 0, 1, 0,−1, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 1 ],
[ 1, 0, 1, 1, 0, 0, 2 ],
[ 1, 1, 0, 0, 1,−1, 1 ],
[ 1, 1, 0, 1, 0, 0, 1 ],
[ 1, 1, 0, 1, 1, 0, 2 ],
[ 1, 1, 1, 1, 1, 0, 3 ],
∗
• I ≡ P40 :
2
4
6
1
3
5




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1










bI =
C

77





1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
1
0
1
1
−1
1
0
0
1
0
0
0
1
1
0
0
1
0
−1
0
0
0
0
−1
0
1
1
1
1
1
0
0
−1
−1
−1
0
0
0
0
1
1
1
1
1
1
1
−1













BI =


0
0
0
0
1
0
0
1
1
0
0
0
0
−1
1
0
1
1
1
1
−1
0
0
0
0
−1
−1
0
1
0
0
0
0
0
0
−1
0
0
−1
0
0
0
1
0
0
0
1
0
−1









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1,−1, 0,−1, 0,−2 ],
[ −1, 0,−1, 0,−1, 1,−1 ],
[ −1, 0,−1, 1,−1, 1, 0 ],
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1,−1, 1, 0, 1, 1 ],
[ −1, 1, 0, 1, 0, 0, 1 ],
[ 0,−1,−1, 0,−1, 0,−2 ],
[ 0,−1, 0,−1,−1,−1,−2 ],
[ 0,−1, 0,−1, 0,−1,−1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 1,−1 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0,−1, 1, 0, 1, 1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1,−1, 1,−1, 0 ],
[ 0, 0, 1, 0, 1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 1, 1, 0, 2 ],
[ 0, 1, 1, 0, 1, 0, 1 ],
[ 1,−1, 0,−1, 0,−1,−1 ],
[ 1,−1, 1,−2, 0,−1,−1 ],
[ 1,−1, 1,−1, 1,−1, 0 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 0, 1,−1, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 2,−1, 1,−1, 1 ],
[ −1, 0,−2, 1,−1, 1,−1 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0,−1, 1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1,−1 ],
[ −1, 1,−1, 1,−1, 1, 0 ],
[ −1, 1,−1, 2, 0, 1, 1 ],
[ −1, 1, 0, 1, 0, 1, 1 ],
[ 0,−1,−1, 0,−1, 0,−1 ],
[ 0,−1, 0,−1,−1, 0,−2 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0,−1, 1, 0 ],
[ 0, 0,−1, 1,−1, 1, 0 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1,−1, 0,−1,−1 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 0, 1,−1, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 1, 1 ],
[ 0, 1, 0, 1, 1, 1, 2 ],
[ 0, 1, 1, 0, 1, 0, 2 ],
[ 1,−1, 0,−1, 0, 0,−1 ],
[ 1,−1, 1,−1, 0,−1,−1 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 1,−1, 1,−1, 0 ],
[ 1, 0, 1, 0, 1,−1, 1 ],
[ 1, 1, 1, 0, 1, 0, 2 ]
[ −1, 0,−1, 0,−1, 0,−2 ],
[ −1, 0,−1, 1,−1, 0,−1 ],
[ −1, 0,−1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 1,−1, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 1, 0, 1 ],
[ 0,−1,−1, 0,−1, 1,−1 ],
[ 0,−1, 0,−1,−1, 0,−1 ],
[ 0,−1, 0, 0,−1, 0,−1 ],
[ 0,−1, 1,−1, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1,−1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 1, 0, 1, 2 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 1, 0, 2 ],
[ 1,−1, 0,−1, 0, 0, 0 ],
[ 1,−1, 1,−1, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1,−1, 0,−1, 0 ],
[ 1, 0, 1,−1, 1,−1, 1 ],
[ 1, 0, 1, 0, 1, 0, 1 ],
[ −1, 0,−1, 0,−1, 0,−1 ],
[ −1, 0,−1, 1,−1, 1,−1 ],
[ −1, 0,−1, 1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1,−1, 1, 0, 1, 0 ],
[ −1, 1, 0, 1, 0, 0, 0 ],
[ 0,−1,−1,−1,−1, 0,−2 ],
[ 0,−1,−1, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 0,−1,−2 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 1, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1,−1, 1, 0, 1, 1 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 1, 1, 0, 1 ],
[ 0, 1, 1, 0, 1,−1, 1 ],
[ 1,−1, 0,−1,−1, 0,−1 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1,−1, 1,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1,−1, 0, 0, 0 ],
[ 1, 0, 1,−1, 1, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 2 ],
∗
• I ≡ P41 :
5
6
3
4
2
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1













b
CI =


78
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
0
1
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
−1
0
0
1
0
0
1
0
−1
−1
0
0
0
0
1
1
1
1
1
1
1
−1













BI =


0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
−1
0
0
−1
0
0
−1
−1
0
0
1
0
0
0
0









Number of sincere Tits roots of poset I sI = 6.
Table of roots of qbI
[ −1,−1,−1,−2, 1, 2,−1 ],
[ 1, 1, 1, 1,−1,−1, 1 ],
[ −1, −1, 0, −1, 0, 1, −1 ],
[ −1, −1, 0, 0, 1, 1, 0 ],
[ −1, 0, −1, −1, 1, 2, 0 ],
[ −1, 0, 0, −1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, 1, 1, 0 ],
[ 0, −1, 0, −1, 0, 1, −1 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 1 ],
[ 0, 0, −1, −1, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, −1, −1, −1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, −1, 1 ],
[ 0, 1, 0, 0, −1, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 1, −1, −1, 1 ],
[ 1, 0, 0, 0, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, −1, 1 ],
[ 1, 0, 1, 1, −1, −1, 0 ],
[ 1, 1, 0, 1, −1, −2, 0 ],
[ 1, 1, 1, 1, −2, −2, 0 ],
[ −1,−1,−1,−1, 1, 1,−1 ],
[ 1, 1, 1, 2,−1,−2, 1 ],
[ −1, −1, 0, −1, 1, 1, −1 ],
[ −1, 0, −1, −1, 0, 1, −1 ],
[ −1, 0, −1, 0, 1, 1, 0 ],
[ −1, 0, 0, −1, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, 1, 2, 0 ],
[ 0, −1, 0, −1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, 1, 1, 0 ],
[ 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, −1, −1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 1, 0, 1, −1, −1, 0 ],
[ 0, 1, 1, 0, −1, −1, 0 ],
[ 0, 1, 1, 1, 0, −1, 1 ],
[ 1, 0, 0, 0, −1, −1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 1, −1, −1, 1 ],
[ 1, 1, 0, 1, −1, −1, 0 ],
[ 1, 1, 1, 1, −1, −2, 0 ]
[ −1,−1,−1,−1, 1, 2,−1 ],
[ −1, −1, −1, −1, 1, 2, 0 ],
[ −1, −1, 0, −1, 1, 1, 0 ],
[ −1, 0, −1, −1, 1, 1, −1 ],
[ −1, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ 0, −1, −1, −1, 0, 1, −1 ],
[ 0, −1, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, −1, 1, 1, 0 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 1, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 1, 1,−1,−1, 0 ],
[ 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 1, 0,−1, 0 ],
[ 0, 1, 1, 1,−1,−2, 0 ],
[ 1, −1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 1,−1,−1, 0 ],
[ 1, 0, 1, 0,−1,−1, 0 ],
[ 1, 0, 1, 1, 0,−1, 1 ],
[ 1, 1, 0, 1,−1,−1, 1 ],
[ 1, 1, 1, 1,−1,−2, 1 ],
[ −1,−1,−1,−1, 2, 2, 0 ],
[ −1,−1, 0,−1, 1, 2, 0 ],
[ −1, 0,−1,−1, 1, 1, 0 ],
[ −1, 0, 0,−1, 0, 1,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ 0,−1,−1,−1, 1, 1,−1 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 1, 0 ],
[ 0, 0,−1,−1, 0, 1,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 1, 1 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, 1, 0, −1, 0 ],
[ 0, 1, 0, 0, −1, −1,−1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, −1, 1 ],
[ 0, 1, 1, 1, −1, −1, 0 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 0, 0, 1, 0, −1, 0 ],
[ 1, 0, 1, 1, −1, −2, 0 ],
[ 1, 1, 0, 0, −1, −1, 0 ],
[ 1, 1, 0, 1, 0, −1, 1 ],
∗
6
• I ≡ P42 :
5
4
2
3
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1













b
CI =


79
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
1
0
0
0
−1
1
0
0
1
1
1
0
1
1
0
0
0
0
−1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
−1









−1
 −1

 −1
BI = −1
 0
 0
1

1
1
1
1
1
0
−1
0
0
−1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
−1
1
0
0
1
1
0
0









Number of sincere Tits roots of poset I sI = 6.
Table of roots of qbI
[ −2, 1,−1, 1, 1, 1, 1 ],
[ 2,−2, 1,−1,−1,−1,−1 ],
[ −2, 1, −1, 1, 0, 1, 0 ],
[ −1, 0, −1, 0, 0, 1, −1 ],
[ −1, 0, −1, 0, 1, 1, 0 ],
[ −1, 0, −1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 1, −1, 0, 1, 1, 0 ],
[ −1, 1, −1, 1, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 1, 1, 1 ],
[ −1, 1, 0, 1, 1, 0, 1 ],
[ 0, −1, 0, 0, 0, −1, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 1, −1, 0, −1, 0, −1, −1 ],
[ 1, −1, 0, 0, −1, 0, −1 ],
[ 1, −1, 0, 0, 0, 0, 0 ],
[ 1, −1, 1, −1, 0, −1, 0 ],
[ 1, −1, 1, 0, −1, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 0, 1, −1, 0, −1, 0 ],
[ 1, 0, 1, 0, −1, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 2, −1, 1, 0, −1, −1, 0 ],
[ −2, 2,−1, 1, 1, 1, 1 ],
[ 2,−1, 1,−1,−1,−1,−1 ],
[ −2, 1, −1, 1, 1, 0, 0 ],
[ −1, 0, −1, 0, 0, 1, 0 ],
[ −1, 0, −1, 1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, −1, 0, 1, 1, 1 ],
[ −1, 1, −1, 1, 1, 0, 0 ],
[ −1, 1, 0, 0, 0, 1, 1 ],
[ −1, 1, 0, 1, 0, 0, 0 ],
[ 0, −1, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 1, −1, 0, −1, 0, 0, −1 ],
[ 1, −1, 0, 0, −1, 0, 0 ],
[ 1, −1, 1, −1, −1, 0, −1 ],
[ 1, −1, 1, −1, 0, 0, 0 ],
[ 1, −1, 1, 0, 0, −1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, −1, 0, 0, 0 ],
[ 1, 0, 1, 0, −1, 0, 1 ],
[ 2, −1, 1, −1, −1, −1, 0 ],
[ 2, −1, 2, −1, −1, −1, 0 ]
[ −1, 1,−1, 1, 1, 1, 1 ],
[ −2, 1, −2, 1, 1, 1, 0 ],
[ −2, 1, −1, 1, 1, 1, 0 ],
[ −1, 0, −1, 0, 1, 0,−1 ],
[ −1, 0, −1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, −1, 0, 0, 1, 0 ],
[ −1, 1, −1, 1, 0, 0, 0 ],
[ −1, 1, −1, 1, 1, 0, 1 ],
[ −1, 1, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 1 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1,−1, 0,−1, 0, 0, 0 ],
[ 1,−1, 0, 0, 0,−1,−1 ],
[ 1,−1, 1,−1,−1, 0, 0 ],
[ 1,−1, 1, 0,−1,−1,−1 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1,−1, 0, 0, 1 ],
[ 1, 0, 1, 0, 0,−1, 0 ],
[ 2,−1, 1,−1,−1, 0, 0 ],
[ 1,−1, 1,−1,−1,−1,−1 ],
[ −2, 1,−1, 0, 1, 1, 0 ],
[ −1, 0,−1, 0, 0, 0, −1 ],
[ −1, 0,−1, 0, 1, 0, 0 ],
[ −1, 0,−1, 1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 1,−1, 0, 1, 0, 0 ],
[ −1, 1,−1, 1, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 1 ],
[ −1, 1, 0, 1, 0, 1, 1 ],
[ 0, −1, 0, 0, −1, 0, −1 ],
[ 0, 0,−1, 0, 0, 0, −1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 1, −1, 0, −1, −1, 0, −1 ],
[ 1, −1, 0, 0, −1, −1, −1 ],
[ 1, −1, 0, 0, 0, −1, 0 ],
[ 1, −1, 1, −1, 0, −1, −1 ],
[ 1, −1, 1, 0, −1, −1, 0 ],
[ 1, 0, 0, 0, −1, 0, 0 ],
[ 1, 0, 1, −1, −1, 0, 0 ],
[ 1, 0, 1, 0, −1, −1, 0 ],
[ 1, 0, 1, 0, 0, −1, 1 ],
[ 2, −1, 1, −1, 0, −1, 0 ],
∗
6
• I ≡ P43 :
5
2
4
1
3




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1













b
CI =


80
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
1
0
0
0
−1
1
0
0
1
1
0
0
1
1
0
0
0
0
−1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
−1
0
0
−1
0
0
0
1
1
1
1
1
1
−1













BI =


−1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
−1
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −2, 1,−1, 1, 1, 0, 0 ],
[ −1, 0,−1, 0, 0, 1, 0 ],
[ −1, 0,−1, 1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1,−1, 1, 1, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 1 ],
[ −1, 2, 0, 1, 1,−1, 1 ],
[ 0,−1,−1, 0, 0, 1,−1 ],
[ 0,−1, 0,−1, 0, 1,−1 ],
[ 0,−1, 0, 0,−1, 1, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0,−1, 0 ],
[ 0, 1, 1, 0, 0,−1, 0 ],
[ 0, 1, 1, 1, 0,−1, 1 ],
[ 1,−1, 0,−1,−1, 1, 0 ],
[ 1,−1, 0, 0,−1, 0,−1 ],
[ 1,−1, 1,−1,−1, 0,−1 ],
[ 1,−1, 1, 0,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1,−1, 0, 0, 0 ],
[ 1, 0, 1, 0,−1, 0, 1 ],
[ 1, 1, 1, 0, 0,−1, 1 ],
[ −1,−1,−1, 0, 0, 1,−1 ],
[ −1, 0,−1, 0, 1, 0,−1 ],
[ −1, 0,−1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1,−1, 0, 1, 0, 0 ],
[ −1, 1,−1, 1, 1, 0, 1 ],
[ −1, 1, 0, 0, 1, 0, 1 ],
[ −1, 1, 0, 1, 1,−1, 0 ],
[ 0,−1,−1,−1, 0, 1,−1 ],
[ 0,−1,−1, 0, 0, 1, 0 ],
[ 0,−1, 0,−1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1,−1, 0 ],
[ 0, 1, 0, 1, 0,−1, 1 ],
[ 0, 1, 1, 0, 0,−1, 1 ],
[ 1,−2, 0,−1,−1, 1,−1 ],
[ 1,−1, 0,−1, 0, 0,−1 ],
[ 1,−1, 0, 0,−1, 0, 0 ],
[ 1,−1, 1,−1,−1, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1,−1, 0, 0, 1 ],
[ 1, 0, 1, 0, 0,−1, 0 ],
[ 2,−1, 1,−1,−1, 0, 0 ]
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0,−1, 0, 1, 0, 0 ],
[ −1, 0,−1, 1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 1,−1, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0,−1, 0 ],
[ −1, 1, 0, 1, 1,−1, 1 ],
[ 0,−1,−1, 0,−1, 1,−1 ],
[ 0,−1, 0,−1,−1, 1,−1 ],
[ 0,−1, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 1,−1, 1 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1,−1, 0,−1,−1, 0,−1 ],
[ 1,−1, 0,−1, 0, 0, 0 ],
[ 1,−1, 0, 0,−1, 1, 0 ],
[ 1,−1, 1,−1,−1, 1, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 1,−1,−1, 0, 0 ],
[ 1, 0, 1, 0,−1,−1, 0 ],
[ 1, 0, 1, 0, 0,−1, 1 ],
[ −1, 0,−1, 0, 0, 1,−1 ],
[ −1, 0,−1, 0, 1, 1, 0 ],
[ −1, 0,−1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 1,−1, 1, 1,−1, 0 ],
[ −1, 1, 0, 0, 1,−1, 0 ],
[ −1, 1, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 1, 1, 0, 1 ],
[ 0,−1,−1, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0,−1, 1,−1 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 1, 1,−1, 1 ],
[ 0, 1, 1, 0, 1,−1, 1 ],
[ 1,−1, 0,−1,−1, 1,−1 ],
[ 1,−1, 0,−1, 0, 1, 0 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1,−1, 1,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 1,−1, 0,−1, 0 ],
[ 1, 0, 1, 0,−1, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
∗
6
• I ≡ P44 :
3
5
2
4
1




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1













b
CI =


81
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
1
1
1
1
−1
1
0
0
1
0
0
−1
0
1
0
0
1
1
0
1
1
1
0
0
0
−1
−1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
−1













BI =


1
0
0
0
0
0
−1
0
1
1
1
1
0
−1
0
0
0
−1
−1
0
0
0
1
0
1
1
1
−1
0
−1
−1
−1
−1
−1
1
0
−1
0
0
−1
0
0
0
0
0
0
0
0
−1









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 1,−1, 1,−1,−1,−1 ],
[ −1,−1, 0,−1, 0, 0, −1 ],
[ −1, 0, −1,−1, −1, 0, −2 ],
[ −1, 0, −1, 0, −1, −1, −2 ],
[ −1, 0, −1, 0, 0, −1, −1 ],
[ −1, 0, 0, 0, 0, −1, −1 ],
[ −1, 1, −1, 0, −1, −1, −2 ],
[ 0,−2, 1,−1, 1, 1, 0 ],
[ 0,−1, 0,−1, 1, 0, −1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1,−1, 1, 0, 0 ],
[ 0,−1, 1, 0, 0, 1, 0 ],
[ 0,−1, 1, 0, 1, 1, 1 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, −1, 0, −1, 0, −1 ],
[ 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 1, −1, 1, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, −1, 0 ],
[ 1,−1, 1, 0, 0, 1, 1 ],
[ 1,−1, 2, 0, 1, 1, 2 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, 0, 0, 1, 2 ],
[ 1, 0, 1, 1, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 2 ],
[ 1,−1, 1,−1, 1, 1, 1 ],
[ −1, −1, 0, −1, 0, 1,−1 ],
[ −1, 0,−1, −1, 0,−1,−2 ],
[ −1, 0,−1, 0,−1, 0,−2 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 1,−1, 0,−1,−1,−1 ],
[ 0, −1, 0, −1, 0, 0,−1 ],
[ 0, −1, 0, −1, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, −1, 1, −1, 1, 1, 0 ],
[ 0, −1, 1, 0, 0, 1, 1 ],
[ 0, 0,−1, −1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1,−1, 0,−1, 0, 0 ],
[ 0, 1,−1, 1,−1,−1,−1 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 1,−1,−1, 0 ],
[ 0, 1, 0, 1, 0,−1, 1 ],
[ 1, −1, 1, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 1 ],
[ 1, 0, 1, 1, 0, 0, 2 ],
[ 1, 1, 0, 1,−1, 0, 1 ],
[ 1, 1, 1, 1, 0, 0, 2 ]
[ −1,−1,−1,−1, 0, 0,−2 ],
[ −1,−1, 0,−1, 1, 0,−1 ],
[ −1, 0,−1,−1, 0, 0,−2 ],
[ −1, 0,−1, 0,−1, 0,−1 ],
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1,−1, 0,−1, 0,−1 ],
[ 0,−1, 0,−1, 0, 1,−1 ],
[ 0,−1, 0,−1, 1, 1, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 1,−1, 1, 1, 1 ],
[ 0,−1, 1, 0, 1, 0, 0 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1,−1, 0, 0,−1,−1 ],
[ 0, 1,−1, 1,−1,−1, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 1,−1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 1,−1, 1, 0, 1, 1, 1 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 2 ],
[ 1, 0, 1, 1, 0, 1, 2 ],
[ 1, 1, 0, 1, 0,−1, 1 ],
[ −1,−1, 0,−1, 0, 0,−2 ],
[ −1,−1, 0, 0, 0, 0,−1 ],
[ −1, 0,−1,−1, 0, 0,−1 ],
[ −1, 0,−1, 0, 0,−1,−2 ],
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 1,−2, 0,−1,−1,−2 ],
[ −1, 1,−1, 0, 0,−1,−1 ],
[ 0,−1, 0,−1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 1,−1, 0, 1, 0 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 1, 0, 1 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1,−1, 0,−1,−1,−1 ],
[ 0, 1,−1, 0, 0,−1, 0 ],
[ 0, 1,−1, 1,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1,−1, 0, 1 ],
[ 0, 2,−1, 1,−1,−1, 0 ],
[ 1,−1, 1, 0, 1, 1, 2 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 0, 1, 0, 0, 1, 1 ],
[ 1, 0, 1, 0, 1, 1, 2 ],
[ 1, 0, 1, 1, 1, 0, 2 ],
[ 1, 1, 0, 1, 0, 0, 1 ],
∗
• I ≡ P45 :
6
5
4
3
2
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1













b
CI =


82
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
0
0
0
0
−1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
−1
−1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
−1









0
 −1

 0
BI = 0
 0
 0
0

−1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
−1
1
0
0
1
0
0
−1
0
0
1
0
0
0
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ −1, 1, 0, 1, 0, 0, 1 ],
[ −1, 1, 1, 1, 0,−1, 1 ],
[ 0,−1,−1,−1, 1, 1,−1 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 1, 0 ],
[ 0, 0,−1,−1, 0, 1,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 1, 1 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 1, 0,−1, 0 ],
[ 0, 1, 0, 0,−1,−1,−1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0,−1, 1 ],
[ 0, 1, 1, 1,−1,−1, 0 ],
[ 1,−1,−1,−1, 0, 0,−1 ],
[ 1,−1, 0,−1,−1, 0,−1 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1,−1, 0, 1, 0 ],
[ 1, 0, 0,−1,−1, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 1, 0,−1,−1, 0 ],
[ −1, 0,−1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 1, 1, 0,−1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 1, 0, 1 ],
[ −1, 1, 1, 1, 0, 0, 1 ],
[ 0,−1,−1,−1, 1, 1, 0 ],
[ 0,−1, 0,−1, 0, 1,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 1 ],
[ 0, 0,−1,−1, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0,−1,−1,−1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0,−1, 1 ],
[ 0, 1, 0, 0,−1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 1,−1,−1, 1 ],
[ 1,−1,−1,−1, 0, 1,−1 ],
[ 1,−1, 0,−1, 0, 0,−1 ],
[ 1, 0,−1,−1,−1, 0,−1 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 1, 0, 0,−1,−1, 0 ]
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 1, 0, 0, 0 ],
[ −1, 1, 0, 1, 0,−1, 0 ],
[ −1, 1, 1, 1,−1,−1, 0 ],
[ −1, 1, 1, 2, 0,−1, 1 ],
[ 0,−1,−1,−1, 1, 2, 0 ],
[ 0,−1, 0,−1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1,−1, 1, 1, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0,−1,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 1,−1,−1, 0 ],
[ 0, 1, 1, 0,−1,−1, 0 ],
[ 0, 1, 1, 1, 0,−1, 1 ],
[ 1,−1,−1,−1, 0, 1, 0 ],
[ 1,−1, 0,−1, 0, 0, 0 ],
[ 1, 0,−1,−1, 0, 0,−1 ],
[ 1, 0, 0,−1,−1,−1,−1 ],
[ 1, 0, 0, 0,−1,−1,−1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 1, 1, 0, 0, 1 ],
[ −1, 1, 0, 1, 0, 0, 0 ],
[ −1, 1, 1, 1, 0,−1, 0 ],
[ 0,−1,−1,−1, 0, 1,−1 ],
[ 0,−1,−1, 0, 1, 1, 0 ],
[ 0,−1, 0,−1, 1, 1, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 1, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 1, 1,−1,−1, 0 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 1, 0,−1, 0 ],
[ 0, 1, 1, 1,−1,−2, 0 ],
[ 1,−1,−1,−2, 0, 1,−1 ],
[ 1,−1,−1,−1, 1, 1, 0 ],
[ 1,−1, 0,−1, 0, 1, 0 ],
[ 1, 0,−1,−1, 0, 0, 0 ],
[ 1, 0, 0,−1,−1, 0,−1 ],
[ 1, 0, 0, 0,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
∗
6
• I ≡ P46 :
3
5
2
4
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1













b
CI =


83
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
0
0
0
0
−1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
−1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
−1









−1
−1
−1
0
0
0
1
0
 0

 0
BI = −1
 0
 0
0

−1
0
0
0
0
0
0
1
1
1
1
1
0
−1
1
1
1
0
0
0
0
1
1
0
1
1
1
−1
0
1
0
0
1
0
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 1,−1, 1, 1, 0 ],
[ −1,−1, 1, 0, 1, 1, 1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ −1, 1, 0, 1, 0, 0, 0 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0,−1, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 1,−1, 1, 1, 0 ],
[ 0,−1, 1, 0, 0, 1, 1 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1,−1, 0,−1, 0, 0 ],
[ 0, 1,−1, 1,−1,−1,−1 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 1,−1,−1, 0 ],
[ 0, 1, 0, 1, 0,−1, 1 ],
[ 1,−1, 0,−1, 0, 0,−1 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1,−1, 0, 0, 0 ],
[ 1, 0,−1, 0, 0,−1,−1 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 1,−2, 0,−1,−1,−1 ],
[ 1, 1,−1, 0, 0,−1, 0 ],
[ −1,−1, 1, 0, 0, 1, 0 ],
[ −1,−1, 2, 0, 1, 1, 1 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 1, 1 ],
[ −1, 0, 1, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 1 ],
[ 0,−1, 0,−1, 0, 1,−1 ],
[ 0,−1, 0,−1, 1, 1, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 1,−1, 1, 1, 1 ],
[ 0,−1, 1, 0, 1, 0, 0 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1,−1, 0, 0,−1,−1 ],
[ 0, 1,−1, 1,−1,−1, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 1,−1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 1,−1, 0,−1, 0, 0, 0 ],
[ 1, 0,−1,−1,−1, 0,−1 ],
[ 1, 0,−1, 0,−1,−1,−1 ],
[ 1, 0,−1, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 1,−1, 0,−1,−1,−1 ],
[ 1, 1,−1, 1,−1,−1, 0 ]
[ −1,−1, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 1 ],
[ −1, 1, 0, 1,−1, 0, 0 ],
[ −1, 1, 1, 1, 0, 0, 1 ],
[ 0,−1, 0,−1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 1,−1, 0, 1, 0 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 1, 0, 1 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1,−1, 0,−1,−1,−1 ],
[ 0, 1,−1, 0, 0,−1, 0 ],
[ 0, 1,−1, 1,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1,−1, 0, 1 ],
[ 0, 2,−1, 1,−1,−1, 0 ],
[ 1,−1, 0,−1, 0, 1, 0 ],
[ 1, 0,−1,−1, 0,−1,−1 ],
[ 1, 0,−1, 0,−1, 0,−1 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1,−1, 0,−1,−1, 0 ],
[ −1,−1, 1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 1 ],
[ −1, 0, 1, 1, 0, 1, 1 ],
[ −1, 1, 0, 1, 0,−1, 0 ],
[ 0,−2, 1,−1, 1, 1, 0 ],
[ 0,−1, 0,−1, 1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1,−1, 1, 0, 0 ],
[ 0,−1, 1, 0, 0, 1, 0 ],
[ 0,−1, 1, 0, 1, 1, 1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1,−1, 0,−1, 0,−1 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1,−1, 1, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0,−1, 0 ],
[ 1,−1,−1,−1, 0, 0,−1 ],
[ 1,−1, 0,−1, 1, 0, 0 ],
[ 1, 0,−1,−1, 0, 0,−1 ],
[ 1, 0,−1, 0,−1, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1,−1, 0,−1, 0, 0 ],
∗
6
• I ≡ P47 :
5
4
3
2
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1













b
CI =


84
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
1
0
0
0
−1
1
0
0
0
0
0
0
1
1
0
1
0
0
−1
−1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
−1
0
0
0
0
0
1
1
1
1
1
1
−1













BI =


0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
−1
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1,−2, 0, 1, 1,−1 ],
[ −1,−1,−1, 0, 1, 1, 0 ],
[ −1,−1,−1, 1, 2, 0, 0 ],
[ −1, 0,−1, 0, 0, 1,−1 ],
[ −1, 0,−1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 0, 0 ],
[ 0,−1,−1, 0, 0, 0,−1 ],
[ 0,−1,−1, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 1,−1, 0 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1,−1, 1,−1 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1,−1, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 1, 0,−1, 1 ],
[ 0, 1, 0,−1,−1, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 1, 0,−1,−1, 0 ],
[ 0, 1, 1, 0, 0,−1, 1 ],
[ 1, 0, 0,−1,−1, 0,−1 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 1,−1,−1, 0, 0 ],
[ 1, 0, 1, 0, 0,−1, 0 ],
[ 1, 1, 0,−1,−1, 0, 0 ],
[ 1, 1, 1,−1,−1, 0, 1 ],
[ 1, 1, 1, 0, 0,−1, 1 ],
[ −1,−1,−1, 0, 0, 1,−1 ],
[ −1,−1,−1, 1, 1, 0,−1 ],
[ −1,−1, 0, 1, 1, 0, 0 ],
[ −1, 0,−1, 0, 0, 1, 0 ],
[ −1, 0,−1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 1 ],
[ 0,−1,−1, 0, 0, 1,−1 ],
[ 0,−1,−1, 0, 1, 1, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 1, 0, 0 ],
[ 0, 0,−1,−1, 0, 1,−1 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1,−1, 1, 0 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1, 1,−1, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0,−1,−1, 1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 0,−1, 0, 0 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1, 0, 0,−1,−1, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 1, 0,−1,−1, 0 ],
[ 1, 0, 1, 0, 0,−1, 1 ],
[ 1, 1, 1,−1,−2, 0, 0 ],
[ 1, 1, 1, 0,−1,−1, 0 ],
[ 1, 1, 2, 0,−1,−1, 1 ]
[ −1,−1,−1, 0, 1, 0,−1 ],
[ −1,−1,−1, 1, 1, 0, 0 ],
[ −1, 0,−1,−1, 0, 1,−1 ],
[ −1, 0,−1, 0, 1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1,−1, 0, 0, 1, 0 ],
[ 0,−1,−1, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 1 ],
[ 0, 0,−1,−1, 0, 1, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1,−1, 1 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0,−1, 0, 1 ],
[ 0, 1, 1, 1, 0,−1, 1 ],
[ 1, 0, 0,−1,−1, 1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0,−1, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 1, 1,−1,−1,−1, 0 ],
[ 1, 1, 1, 0,−1,−1, 1 ],
[ −1,−1,−1, 0, 1, 1,−1 ],
[ −1,−1,−1, 1, 1, 1, 0 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0,−1, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1,−1, 0 ],
[ 0,−1,−1,−1, 0, 1,−1 ],
[ 0,−1,−1, 0, 1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1,−1,−1, 1,−1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 1, 1, 0,−1, 0 ],
[ 0, 1, 0,−1,−1, 0,−1 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 1,−1,−1, 0, 0 ],
[ 0, 1, 1, 0, 0,−1, 0 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0,−1, 0, 1 ],
[ 1, 0, 1, 1, 0,−1, 1 ],
[ 1, 1, 1,−1,−1, 0, 0 ],
[ 1, 1, 1, 0,−1, 0, 1 ],
∗
• I ≡ P48 :
6
5
3
2
4
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1













b
CI =


85
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
1
1
0
0
−1
1
0
0
0
0
0
0
1
1
0
1
1
0
−1
1
1
1
0
1
1
−1
0
1
0
0
0
1
0
−1
0
0
−1
0
0
1
1
1
1
1
1
1
−1













BI =


1
1
0
0
1
0
−1
0
0
0
0
−1
0
0
0
0
1
0
0
0
−1
0
0
0
1
0
0
−1
−1
−1
−1
0
0
−1
1
0
−1
0
0
0
0
0
0
0
0
0
0
0
−1









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−1,−1, 1, 1,−1 ],
[ −1, −1, −1, −1, 0, 1, −2 ],
[ −1, −1, −1, 0, 1, 1, 0 ],
[ −1, 0, −1, −1, 0, 0, −2 ],
[ −1, 0, −1, 0, 0, 1, −1 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ 0, −1, −1, −1,−1, 0, −2 ],
[ 0, −1, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, −1,−1,−1, −2 ],
[ 0, 0, −1, 0,−1, 0, −1 ],
[ 0, 0, 0, −1,−1,−1, −2 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, −1,−1,−1, −1 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 1, 0,−1,−1, 0 ],
[ 0, 1, 1, 1, 0,−1, 1 ],
[ 1, −1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 1, 1, 1, 0, 2 ],
[ 1, 1, 1, 0,−1,−1, 1 ],
[ 1, 1, 1, 1, 0, 0, 2 ],
[ 1, 1, 1, 1,−1,−1, 1 ],
[ −1,−1,−1,−1, 0, 1,−1 ],
[ −1,−1,−1, 0, 1, 2, 0 ],
[ −1, 0,−1,−1, 0, 0,−1 ],
[ −1, 0,−1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ 0,−1,−1,−1, 0, 0,−2 ],
[ 0,−1,−1, 0, 0, 1,−1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 1, 0 ],
[ 0, 0,−1,−1, −1, 0,−2 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, −1, −1,−1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, −1, −1,−1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 0, −1, 0 ],
[ 0, 1, 1, 1, 0, 0, 1 ],
[ 1, 0, 0,−1, −1, −1,−1 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 0, 1, 0, −1, −1, 0 ],
[ 1, 0, 1, 1, 0, −1, 1 ],
[ 1, 1, 0, 0, −1, −1, 0 ],
[ 1, 1, 1, 0, 0, −1, 1 ],
[ 1, 1, 2, 1, 0, −1, 2 ]
[ −1,−1,−2,−1, 0, 1,−2 ],
[ −1,−1,−1, 0, 0, 1,−1 ],
[ −1,−1, 0, 0, 1, 1, 0 ],
[ −1, 0,−1,−1, 0, 1,−1 ],
[ −1, 0,−1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ 0,−1,−1,−1, 0, 0,−1 ],
[ 0,−1,−1, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 1 ],
[ 0, 0,−1,−1,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 1, 0, 0,−1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0,−1, 1 ],
[ 0, 1, 1, 1, 0, 0, 2 ],
[ 1, 0, 0, 0,−1,−1,−1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 0,−1, 0 ],
[ 1, 0, 1, 1, 0, 0, 1 ],
[ 1, 1, 1, 0,−1,−2, 0 ],
[ 1, 1, 1, 1, 0,−1, 1 ],
[ −1,−1,−1,−1, 0, 0,−2 ],
[ −1,−1,−1, 0, 1, 1,−1 ],
[ −1, 0,−1,−1,−1, 0,−2 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1,−1,−1, 0, 1,−1 ],
[ 0,−1,−1, 0, 1, 1, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 1, 1, 1 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 2 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 1, 0, 2 ],
[ 1, 0, 0, 0,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 0,−1, 1 ],
[ 1, 0, 1, 1, 0, 0, 2 ],
[ 1, 1, 1, 0,−1,−1, 0 ],
[ 1, 1, 1, 1, 0,−1, 2 ],
∗
6
• I ≡ P49 :
4
5
2
3
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1













b
CI =


86
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
1
0
0
0
−1
1
0
0
0
0
0
0
1
1
0
1
0
1
−1
−1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
−1













BI =


−1
0
0
0
0
0
0
0
0
−1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
−1
1
1
0
1
0
1
−1
0
1
0
1
0
0
0









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−1, 1, 2, 1, 1 ],
[ −1, −1, −1, 0, 1, 0,−1 ],
[ −1, −1, −1, 1, 1, 0,−1 ],
[ −1, −1, −1, 1, 2, 1, 0 ],
[ −1, −1, 0, 1, 1, 1, 1 ],
[ −1, 0, −1, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ 0, −1, −1, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 1 ],
[ 0, −1, 0, 1, 1, 1, 1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0,−1,−1, 0,−1 ],
[ 0, 1, 0, 0,−1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0,−1, 0, 1 ],
[ 1, 0, 0,−1,−1, 0,−1 ],
[ 1, 0, 0, 0,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0,−1, 0, 1 ],
[ 1, 1, 0,−1,−1,−1, 0 ],
[ 1, 1, 1,−1,−2, 0, 0 ],
[ 1, 1, 1, 0,−2,−1, 0 ],
[ 1, 2, 1,−1,−2,−1, 0 ],
[ 1, 1, 1,−1,−2,−1,−1 ],
[ −1,−1,−1, 0, 1, 1, −1 ],
[ −1,−1,−1, 1, 1, 0, 0 ],
[ −1,−1, 0, 0, 1, 1, 0 ],
[ −1,−1, 0, 1, 2, 1, 1 ],
[ −1, 0,−1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1,−1, 0, 1, 1, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, −1, 0, 0, −1 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, −1, −1, 0, 0 ],
[ 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 1, 1, −1, −1, 0, 0 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1, 0, 0, −1, −1, 0, 0 ],
[ 1, 0, 0, 0, −1, 0, 0 ],
[ 1, 0, 1, −1, −1, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 1, 0, −1, −1, 0, 0 ],
[ 1, 1, 1, −1, −1, −1, 0 ],
[ 1, 1, 1, 0, −1, −1, 0 ],
[ 2, 1, 1, −1, −2, −1, 0 ]
[ −2,−1,−1, 1, 2, 1, 0 ],
[ −1,−1,−1, 0, 1, 1, 0 ],
[ −1,−1,−1, 1, 1, 1, 0 ],
[ −1,−1, 0, 1, 1, 0, 0 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0,−1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0 ],
[ 0,−1,−1, 0, 0, 0,−1 ],
[ 0,−1,−1, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 1, 0,−1,−1, 0 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 1, 0,−1,−1, 0 ],
[ 1, 1, 0,−1,−2,−1,−1 ],
[ 1, 1, 0, 0,−1,−1, 0 ],
[ 1, 1, 1,−1,−1, 0, 0 ],
[ 1, 1, 1, 0,−1,−1, 1 ],
[ −1,−2,−1, 1, 2, 1, 0 ],
[ −1,−1,−1, 0, 2, 1, 0 ],
[ −1,−1,−1, 1, 2, 0, 0 ],
[ −1,−1, 0, 1, 1, 1, 0 ],
[ −1, 0,−1, 0, 1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 1, 1, 0, 1 ],
[ 0,−1,−1, 0, 1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 1, 0 ],
[ 0,−1, 0, 1, 1, 0, 1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1,−1,−1,−1 ],
[ 0, 1, 0, 0,−1,−1,−1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 0,−1, 0, 0 ],
[ 1, 0, 0,−1,−1,−1,−1 ],
[ 1, 0, 0, 0,−1,−1,−1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0,−1, 0, 0 ],
[ 1, 1, 0,−1,−1,−1,−1 ],
[ 1, 1, 1,−1,−2,−1, 0 ],
[ 1, 1, 1,−1,−1, 0, 1 ],
[ 1, 1, 1, 0,−1, 0, 1 ],
∗
6
• I ≡ P50 :
5
2
4
1
3




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1













b
CI =


87
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
1
1
0
0
−1
1
0
0
0
1
1
0
1
1
0
0
0
0
−1
0
0
1
0
0
0
0
0
0
−1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
−1













BI =


0
0
0
0
1
0
1
1
1
0
0
0
0
−1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
−1
0
0
0
0
1
0
0
0
−1
1
0
0
0
1
0
0









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −2, 1,−1,−1, 1, 1,−1 ],
[ −2, 1, −1, −1, 1, 2, 0 ],
[ −1, 0, −1, −1, 0, 1, −1 ],
[ −1, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, −1, 0, 1, 0, 0 ],
[ −1, 0, 0, −1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 1, −1, −1, 1, 1, 0 ],
[ −1, 1, −1, 0, 1, 1, 1 ],
[ −1, 1, 0, −1, 1, 1, 1 ],
[ −1, 1, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, −1, 0, 0, −1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1,−1, 0, 0, 0,−1, −1 ],
[ 1,−1, 0, 1,−1,−1, 0 ],
[ 1,−1, 1, 0,−1,−1, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 1,−1,−1, 0 ],
[ 1, 0, 0, 1, 0,−1, 1 ],
[ 1, 0, 1, 0,−1, 0, 1 ],
[ 1, 0, 1, 1,−1,−1, 0 ],
[ 2,−1, 0, 1,−1,−1, 0 ],
[ 2,−1, 1, 1,−1,−1, 0 ],
[ 2,−1, 1, 1,−1,−1, 1 ],
[ −2, 1,−1,−1, 2, 1, 0 ],
[ −1, 0,−1,−1, 1, 0,−1 ],
[ −1, 0,−1, 0, 0, 1,−1 ],
[ −1, 0,−1, 0, 1, 1, 0 ],
[ −1, 0, 0,−1, 1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1,−1, 0, 0, 1, 0 ],
[ −1, 1, 0,−1, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 1 ],
[ 0, −1, 0, 0, −1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 1, −1, 0, 0, −1, −1,−1 ],
[ 1, −1, 0, 0, 0, −1, 0 ],
[ 1, −1, 0, 1, −1, 0, 0 ],
[ 1, −1, 1, 0, −1, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 0, 0, 1, −1, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, −1, 0 ],
[ 1, 0, 1, 1, −1, −1, 1 ],
[ 2, −1, 1, 0, −1, −1, 0 ],
[ 2, 0, 1, 1, −1, −1, 1 ]
[ −2, 0,−1,−1, 1, 1,−1 ],
[ −2, 1,−1, 0, 1, 1, 0 ],
[ −1, 0,−1,−1, 1, 1,−1 ],
[ −1, 0,−1, 0, 0, 1, 0 ],
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0,−1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 1,−1, 0, 1, 0, 0 ],
[ −1, 1, 0,−1, 1, 0, 0 ],
[ −1, 1, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 1, 1, 1 ],
[ 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 1,−1, 0, 0,−1, 0,−1 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1,−1, 0, 1, 0,−1, 0 ],
[ 1,−1, 1, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1,−1, 0, 1 ],
[ 1, 0, 1, 0,−1,−1, 0 ],
[ 1, 0, 1, 0, 0,−1, 1 ],
[ 1, 0, 1, 1,−1, 0, 1 ],
[ 2,−1, 1, 1,−2,−1, 0 ],
[ −2, 1,−1,−1, 1, 1, 0 ],
[ −2, 1, 0,−1, 1, 1, 0 ],
[ −1, 0,−1,−1, 1, 1, 0 ],
[ −1, 0,−1, 0, 1, 0,−1 ],
[ −1, 0, 0,−1, 0, 1,−1 ],
[ −1, 0, 0,−1, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 1,−1, 0, 1, 1, 0 ],
[ −1, 1, 0,−1, 1, 1, 0 ],
[ −1, 1, 0, 0, 0, 1, 1 ],
[ 0,−1,−1, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 1,−1, 0, 0,−1, 0, 0 ],
[ 1,−1, 0, 1,−1,−1,−1 ],
[ 1,−1, 1, 0,−1,−1,−1 ],
[ 1,−1, 1, 1,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 1, 0,−1, 0 ],
[ 1, 0, 1, 0,−1, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 1, 1, 0,−1, 1 ],
[ 2,−1, 1, 1,−1,−2, 0 ],
∗
6
• I ≡ P51 :
5
2
4
1
3




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1













b
CI =


88
1
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
1
0
0
0
−1
1
0
0
1
0
0
0
1
1
0
0
0
0
−1
−1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
−1













BI =


0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
−1
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
−1
0









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−1,−1, 1, 1,−1 ],
[ −1, −1, −1, 0, 1, 0, −1 ],
[ −1, 0, −1, 0, 0, 1, −1 ],
[ −1, 0, −1, 0, 1, 1, 0 ],
[ −1, 0, −1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 1,−1, 0, 0 ],
[ 0, −2, −1, −1, 1, 1, −1 ],
[ 0, −1, −1, −1, 1, 1, 0 ],
[ 0, −1, −1, 0, 1, 0, −1 ],
[ 0, −1, 0, −1, 0, 1, −1 ],
[ 0, −1, 0, −1, 1, 1, 0 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 1,−1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0,−1, 0 ],
[ 0, 1, 1, 1,−1,−1, 1 ],
[ 1, −1, 0, −1, 0, 0, −1 ],
[ 1, −1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 1, −1, 0,−1, 0 ],
[ 1, 0, 1, 0,−1, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 1, 1, 0, 0,−1, 1 ],
[ 1, 1, 1, 1,−1,−1, 1 ],
[ −1,−1,−1, 0, 1, 1,−1 ],
[ −1, 0,−1, 0, 0, 1, 0 ],
[ −1, 0,−1, 1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, −1, 0 ],
[ 0,−1,−1,−1, 0, 1,−1 ],
[ 0,−1,−1, 0, 0, 0,−1 ],
[ 0,−1,−1, 0, 1, 0, 0 ],
[ 0,−1, 0,−1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, −1, 0, 1 ],
[ 0, 1, 1, 0, −1, −1, 0 ],
[ 0, 1, 1, 0, 0, −1, 1 ],
[ 0, 1, 1, 1, −1, 0, 1 ],
[ 1,−1, 0,−1, 0, 0, 0 ],
[ 1,−1, 1,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1,−1, 0, 0, 0 ],
[ 1, 0, 1, 0, −1, 0, 1 ],
[ 1, 1, 1, 0, −1, −1, 0 ],
[ 1, 1, 2, 0, −1, −1, 1 ]
[ −1,−1,−2, 0, 1, 1,−1 ],
[ −1,−1,−1, 0, 1, 1, 0 ],
[ −1, 0,−1, 0, 1, 0,−1 ],
[ −1, 0,−1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1,−1, 1, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 0 ],
[ 0,−1,−1,−1, 1, 0,−1 ],
[ 0,−1,−1, 0, 0, 1,−1 ],
[ 0,−1,−1, 0, 1, 1, 0 ],
[ 0,−1, 0,−1, 1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0,−1, 0 ],
[ 0, 1, 1, 0,−1, 0, 0 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 0,−1, 1 ],
[ 1,−1, 0,−1, 0, 1, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1,−1, 0, 0, 1 ],
[ 1, 0, 1, 0, 0,−1, 0 ],
[ 1, 1, 1, 0,−1,−1, 1 ],
[ −1,−1,−1, 0, 0, 1,−1 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0,−1, 0, 1, 0, 0 ],
[ −1, 0,−1, 1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 1 ],
[ 0,−1,−1,−1, 1, 1,−1 ],
[ 0,−1,−1, 0, 0, 1, 0 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0,−1, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 1,−1,−1, 0 ],
[ 0, 1, 0, 1, 0,−1, 1 ],
[ 0, 1, 1, 0,−1, 0, 1 ],
[ 0, 1, 1, 1,−1,−1, 0 ],
[ 0, 2, 1, 1,−1,−1, 1 ],
[ 1,−1, 0,−1, 1, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 1,−1,−1, 0, 0 ],
[ 1, 0, 1, 0,−1,−1, 0 ],
[ 1, 0, 1, 0, 0,−1, 1 ],
[ 1, 1, 1, 0,−1, 0, 1 ],
∗
6
• I ≡ P52 :
3
5
2
4
1




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1













b
CI =


89
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
1
1
1
1
−1
1
0
0
1
0
0
−1
0
1
0
0
1
0
0
1
1
1
0
0
0
−1
−1
0
0
0
0
0
1
0
−1
0
0
0
0
0
1
1
1
1
1
1
−1













BI =


1
0
0
0
0
0
−1
0
1
1
0
0
0
−1
0
0
−1
0
0
0
0
0
0
0
1
0
0
−1
0
−1
−1
−1
−1
−1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
−1









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−1,−1,−1, 1,−2 ],
[ −1, −1, −1, −1, 0, 1, −2 ],
[ −1, −1, 0, −1, 0, 1, −1 ],
[ −1, 0, −1, −1, −1, 0, −2 ],
[ −1, 0, −1, −1, 0, 0, −1 ],
[ −1, 0, −1, 0, −1, 1, −1 ],
[ −1, 0, 0, 0, 0,−1, −1 ],
[ 0, −1, −1, −1, 0, 1, −1 ],
[ 0, −1, 0, −1, 1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, −1, 1, −1 ],
[ 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0,−1, 0 ],
[ 0, 1, −1, 0, −1, 0, −1 ],
[ 0, 1, −1, 1, −1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0,−1, 0 ],
[ 1, −1, 1, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 1 ],
[ 1, 0, 1, 1, 0, 0, 2 ],
[ 1, 0, 2, 1, 1,−1, 2 ],
[ 1, 1, 0, 1, 0, 0, 1 ],
[ 1, 1, 1, 1, 0, 0, 2 ],
[ 1, 1, 1, 1, 1,−1, 2 ],
[ −1,−1,−1,−1, 0, 1,−1 ],
[ −1,−1, 0,−1, 1, 0,−1 ],
[ −1, 0,−1,−1,−1, 1,−2 ],
[ −1, 0,−1,−1, 0, 1,−1 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0,−1, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 1, 0, 1, −1, 0 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 1,−1 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, −1, 0 ],
[ 0, 0, 1, 1, 0, −1, 1 ],
[ 0, 1,−1, 0,−1, 0, 0 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 1,−1, −1, 0 ],
[ 0, 1, 0, 1, 0, −1, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 2 ],
[ 1, 0, 1, 1, 1, −1, 1 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 2 ],
[ 1, 1, 1, 2, 0, −1, 2 ]
[ −1,−1,−1,−2, 0, 1,−2 ],
[ −1,−1, 0,−1, 0, 0,−2 ],
[ −1,−1, 0, 0, 0, 0,−1 ],
[ −1, 0,−1,−1,−1, 1,−1 ],
[ −1, 0,−1, 0,−1, 0,−2 ],
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0,−1, 0, 1,−1 ],
[ 0,−1, 0,−1, 1, 1, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 1, 0, 1, 0, 0 ],
[ 0, 0,−1,−1, 0, 1,−1 ],
[ 0, 0,−1, 0,−1, 1, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 0, 1,−1, 1 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1,−1, 0,−1, 1, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 1,−1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 1, 1, 0,−1, 1 ],
[ 1, 0, 1, 1, 1,−1, 2 ],
[ 1, 1, 0, 1,−1, 0, 1 ],
[ 1, 1, 1, 1, 0,−1, 1 ],
[ −1,−1,−1,−1, 0, 0,−2 ],
[ −1,−1, 0,−1, 0, 0,−1 ],
[ −1, 0,−2,−1,−1, 1,−2 ],
[ −1, 0,−1,−1, 0, 0,−2 ],
[ −1, 0,−1, 0,−1, 0,−1 ],
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 1,−1, 0,−1, 0,−1 ],
[ 0,−1, 0,−1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 1,−1, 1, 0, 0 ],
[ 0,−1, 1, 0, 1, 0, 1 ],
[ 0, 0,−1,−1, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1,−1, 1 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1,−1, 0, 1 ],
[ 0, 1, 1, 1, 0,−1, 1 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 0, 1, 0, 1,−1, 1 ],
[ 1, 0, 1, 1, 0, 0, 1 ],
[ 1, 0, 1, 1, 1, 0, 2 ],
[ 1, 1, 0, 1, 0,−1, 1 ],
[ 1, 1, 1, 1, 0,−1, 2 ],
∗
• I ≡ P53 :
6
4
2
5
3
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1










bI =
C

90





1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
1
1
1
1
−1
1
0
0
0
0
0
0
1
1
0
0
1
0
−1
0
0
1
0
0
1
0
1
1
1
1
0
0
−1
−1
−1
0
0
0
0
1
1
1
1
1
1
1
−1









0
 0

 0
BI = 0
 0
 −1
0
1
1
0
0
0
0
−1

1
0
1
1
0
0
−1
0
0
0
−1
0
0
0
−1
0
0
0
0
0
0
1
0
0
0
1
0
−1
1
0
0
0
0
−1
−1









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−1,−1,−1,−1,−3 ],
[ −1, −1, −1, −1, −1, 0, −2 ],
[ −1, −1, 0, −1, −1, −1, −2 ],
[ −1, 0, −1, 0, −1, 0, −2 ],
[ −1, 0, 0, −1, −1, −1, −2 ],
[ −1, 0, 0, −1, 0, −1, −1 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, −1, −1, −1, 0, −2 ],
[ 0, −1, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, −1, −2 ],
[ 0, −1, 0, 0, 0, −1, −1 ],
[ 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, −1, 1, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, −1, 1, 0, 1, 1 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 1, 1, 0, 1 ],
[ 0, 1, 1, 0, 1, −1, 1 ],
[ 1, −1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 0, 0, 1, 0, 1, 2 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 1, 1, 1, 0, 2 ],
[ 1, 1, 0, 1, 1, 1, 3 ],
[ 1, 1, 1, 1, 1, 0, 3 ],
[ 1, 1, 1, 1, 1, 1, 3 ],
[ −1,−1,−1, 0,−1, 0,−2 ],
[ −1,−1, 0,−1,−1, 0,−2 ],
[ −1, 0,−1, 0,−1, 0,−1 ],
[ −1, 0, 0,−1,−1, 0,−2 ],
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1,−1, 0,−1, 0,−2 ],
[ 0,−1, 0,−1,−1,−1,−2 ],
[ 0,−1, 0,−1, 0,−1,−1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 1,−1 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0,−1, 1, 0, 1, 1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1,−1, 1,−1, 0 ],
[ 0, 0, 1, 0, 1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 1, 1, 0, 2 ],
[ 0, 1, 1, 0, 1, 0, 1 ],
[ 1, 0,−1, 1, 0, 1, 1 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 0, 1, 1, 0, 1 ],
[ 1, 0, 1, 0, 1,−1, 1 ],
[ 1, 1, 0, 1, 0, 1, 2 ],
[ 1, 1, 0, 2, 1, 1, 3 ],
[ 1, 1, 1, 1, 2, 0, 3 ]
[ −1,−1,−1,−1,−2, 0,−3 ],
[ −1,−1, 0,−2,−1,−1,−3 ],
[ −1,−1, 0,−1, 0,−1,−2 ],
[ −1, 0,−1, 0,−1, 1,−1 ],
[ −1, 0, 0,−1,−1, 0,−1 ],
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 1,−1, 0,−1,−1 ],
[ 0,−1,−1, 0,−1, 0,−1 ],
[ 0,−1, 0,−1,−1, 0,−2 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0,−1, 1, 0 ],
[ 0, 0,−1, 1,−1, 1, 0 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1,−1, 0,−1,−1 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 0, 1,−1, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 1, 1 ],
[ 0, 1, 0, 1, 1, 1, 2 ],
[ 0, 1, 1, 0, 1, 0, 2 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 0, 1, 1, 0, 2 ],
[ 1, 0, 1, 0, 1, 0, 1 ],
[ 1, 1, 0, 1, 1, 0, 2 ],
[ 1, 1, 1, 0, 1, 0, 2 ],
[ −1,−1,−1,−1,−1, 0,−3 ],
[ −1,−1, 0,−1,−1,−1,−3 ],
[ −1, 0,−1,−1,−1, 0,−2 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0,−1, 0,−1,−2 ],
[ −1, 0, 0, 0, 0,−1,−1 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1,−1, 0,−1, 1,−1 ],
[ 0,−1, 0,−1,−1, 0,−1 ],
[ 0,−1, 0, 0,−1, 0,−1 ],
[ 0,−1, 1,−1, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1,−1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 1, 0, 1, 2 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 1, 0, 2 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 1, 0, 1, 1 ],
[ 1, 0, 0, 1, 1, 1, 2 ],
[ 1, 0, 1, 0, 1, 0, 2 ],
[ 1, 1, 0, 1, 1, 1, 2 ],
[ 1, 1, 1, 1, 1, 0, 2 ],
∗
6
• I ≡ P54 :
3
5
2
4
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1













b
CI =


91
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
0
0
0
0
−1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
−1
0
0
0
0
0
0
0
−1
0
0
0
0
0
1
1
1
1
1
1
−1
0
 −1

 0
BI = 0
 0
 0
0










−1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
−1
0









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 1, 1, 1, 1,−1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, −1, 0 ],
[ −1, 0, 1, 1, 1, −1, 1 ],
[ −1, 1, 0, 1,−1, 0, 0 ],
[ −1, 1, 1, 1, 0, −1, 0 ],
[ 0,−1,−1,−1, 0, 1,−1 ],
[ 0,−1, 0,−1, 1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1,−1,−1, 1,−1 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, −1, 0 ],
[ 0, 1,−1, 0,−1, 0,−1 ],
[ 0, 1,−1, 1,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, −1, 0 ],
[ 1,−1,−1,−2, 0, 1,−1 ],
[ 1,−1, 0,−1, 0, 0,−1 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1,−1,−1, 1, 0 ],
[ 1, 0,−1, 0,−1, 0,−1 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1,−1,−1,−1,−1, 1,−1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 1,−1, 0 ],
[ −1, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ −1, 1, 0, 1, 0,−1, 0 ],
[ −1, 1, 1, 1, 0,−1, 1 ],
[ 0, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, −1, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, −1, 1, 0, 1,−1, 0 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 1, −1 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1,−1, 0 ],
[ 0, 0, 1, 1, 0,−1, 1 ],
[ 0, 1, −1, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 1, 0, 1, −1,−1, 0 ],
[ 0, 1, 0, 1, 0,−1, 1 ],
[ 1, −1, −1, −1, 0, 0, −1 ],
[ 1, −1, 0, −1, 0, 0, 0 ],
[ 1, 0, −2, −1, −1, 1, −1 ],
[ 1, 0, −1, −1, 0, 0, −1 ],
[ 1, 0, −1, 0, −1, 0, 0 ],
[ 1, 0, 0, 0, −1, 0, 0 ],
[ 1, 1, −1, 0, −1, 0, 0 ]
[ −1,−1, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 2, 1, 1,−1, 1 ],
[ −1, 1, 0, 1, 0, 0, 0 ],
[ −1, 1, 1, 1, 0, 0, 1 ],
[ 0,−1, 0,−1, 0, 1,−1 ],
[ 0,−1, 0,−1, 1, 1, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 1, 0, 1, 0, 0 ],
[ 0, 0,−1,−1, 0, 1,−1 ],
[ 0, 0,−1, 0,−1, 1, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 0, 1,−1, 1 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1,−1, 0,−1, 1, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 1,−1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 1,−1,−1,−1, 0, 1,−1 ],
[ 1,−1, 0,−1, 0, 1, 0 ],
[ 1, 0,−1,−1,−1, 0,−1 ],
[ 1, 0,−1,−1, 0, 0, 0 ],
[ 1, 0,−1, 0,−1, 1, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 1 ],
[ −1, 0, 1, 1, 1,−1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 1 ],
[ −1, 1, 1, 2, 0,−1, 1 ],
[ 0,−1, 0,−1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 1,−1, 1, 0, 0 ],
[ 0,−1, 1, 0, 1, 0, 1 ],
[ 0, 0,−1,−1, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1,−1, 1 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1,−1, 0, 1 ],
[ 0, 1, 1, 1, 0,−1, 1 ],
[ 1,−1,−1,−1, 0, 1, 0 ],
[ 1,−1, 0,−1, 1, 0, 0 ],
[ 1, 0,−1,−1,−1, 1,−1 ],
[ 1, 0,−1,−1, 0, 1, 0 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
∗
• I ≡ P55 :
6
5
3
2
4
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1













b
CI =


92
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
0
1
0
0
−1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
−1
0
1
0
0
0
1
0
−1
0
0
0
0
0
0
1
1
1
1
1
1
−1













BI =


1
1
1
0
1
1
−1
0
0
0
0
0
−1
0
0
0
0
0
−1
0
0
0
0
0
1
0
0
−1
0
0
−1
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
0
0
0
−1









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 1, 1, 1, 1, 1, 2 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 1, 0, 1, 0, 0 ],
[ −1, 0, 1, 1, 1, 1, 1 ],
[ −1, 1, 1, 0, 0,−1, 0 ],
[ −1, 1, 1, 1, 0, 0, 1 ],
[ 0,−1,−1,−1,−1, 0,−2 ],
[ 0,−1,−1, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1,−1,−1,−1,−2 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1,−1,−1,−2 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0,−1,−1,−1,−1 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 1, 0,−1,−1, 0 ],
[ 0, 1, 1, 1, 0,−1, 1 ],
[ 1,−1,−2,−1,−1, 0,−2 ],
[ 1,−1,−1, 0,−1, 0,−1 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1,−1,−1, 0,−1 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1,−1,−1,−1,−1,−1,−2 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 2 ],
[ −1, 1, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 1, 1, 0, 1 ],
[ 0, −1, −1, −1, 0, 0, −2 ],
[ 0, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 1, 1, 0 ],
[ 0, 0, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, −1, −1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, −1, −1, −1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 0, −1, 0 ],
[ 0, 1, 1, 1, 0, 0, 1 ],
[ 1, −1, −1, −1, −1, 0, −2 ],
[ 1, −1, −1, 0, 0, 0, −1 ],
[ 1, 0, −1, −1, −2, −1, −2 ],
[ 1, 0, −1, 0, −1, −1, −1 ],
[ 1, 0, 0, −1, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 1, 0, 0, −1, −1, 0 ]
[ −1,−1, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 1, 1, 2, 1, 2 ],
[ −1, 1, 1, 0, 0, 0, 1 ],
[ −1, 1, 1, 1, 1, 0, 2 ],
[ 0,−1,−1,−1, 0, 0,−1 ],
[ 0,−1,−1, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 1 ],
[ 0, 0,−1,−1,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 1, 0, 0,−1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0,−1, 1 ],
[ 0, 1, 1, 1, 0, 0, 2 ],
[ 1,−1,−1,−1,−1, 0,−1 ],
[ 1,−1,−1, 0, 0, 0, 0 ],
[ 1, 0,−1,−1,−1,−1,−2 ],
[ 1, 0,−1, 0,−1, 0,−1 ],
[ 1, 0, 0, 0,−1,−1,−1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 1, 0, 1 ],
[ −1, 1, 2, 1, 1, 0, 2 ],
[ 0,−1,−1,−1, 0, 1,−1 ],
[ 0,−1,−1, 0, 1, 1, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 1, 1, 1 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 2 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 1, 0, 2 ],
[ 1,−1,−1,−1, 0, 0,−1 ],
[ 1,−1,−1, 0, 0, 1, 0 ],
[ 1, 0,−1,−1,−1,−1,−1 ],
[ 1, 0,−1, 0,−1, 0, 0 ],
[ 1, 0, 0, 0,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
∗
• I ≡ P56 :
6
5
4
3
2
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1













b
CI =


93
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
−1
0
0
0
0
0
1
1
1
1
1
1
−1









0
 −1

 0
BI = −1
 0
 0
0

−1
−1
−1
0
−1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
−1
1
1
1
1
0
1
−1
0
0
1
0
0
0
0









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1, 1, 1, 1, 1, 1 ],
[ −1, −1, 0, 1, 1, 1, 0 ],
[ −1, −1, 1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 1, 0, 0, 0 ],
[ 0, −1,−1, 0, 1, 1, 0 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 1, 1, 0, 0 ],
[ 0, −1, 1, 1, 0,−1, 0 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 1, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 1, 1,−1,−1, 0 ],
[ 0, 1,−1,−1,−1, 0,−1 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 1, −1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1,−1, 0, 1, 0 ],
[ 1, 0, 0,−1,−1, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 1, 0,−1,−1, 0 ],
[ 1, 1,−1,−1, 0, 0, 0 ],
[ 1, 1, 0,−1,−1, 0, 0 ],
[ 1, 1,−1,−1,−1,−1,−1 ],
[ −1,−1, 0, 1, 1, 1, 1 ],
[ −1,−1, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 1, 1, 0, 0, 1 ],
[ 0,−1, 0, 0, 0, 0, −1 ],
[ 0,−1, 0, 0, 1, 1, 0 ],
[ 0,−1, 0, 1, 1, 0, 1 ],
[ 0,−1, 1, 1, 0, 0, 0 ],
[ 0, 0, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 1, 1 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, 1, 0, −1, 0 ],
[ 0, 1, −1, −1, 0, 0, −1 ],
[ 0, 1, 0, −1, −1, −1, −1 ],
[ 0, 1, 0, 0, −1, −1, −1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1, 0, −1, −1, −1, 0, −1 ],
[ 1, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 1, −1, −2, −1, 0, −1 ],
[ 1, 1, 0, −1, −2, −1, −1 ],
[ 1, 1, 0, 0, −1, −1, 0 ]
[ −1,−1, 0, 0, 1, 1, 0 ],
[ −1,−1, 0, 1, 2, 1, 1 ],
[ −1,−1, 1, 2, 1, 0, 1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 1 ],
[ 0,−1, 0, 1, 1, 1, 1 ],
[ 0,−1, 1, 1, 0, 0, 1 ],
[ 0, 0,−1,−1, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0,−1,−1,−1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0,−1, 1 ],
[ 0, 1,−1,−1, 0, 0, 0 ],
[ 0, 1, 0,−1,−1, 0,−1 ],
[ 0, 1, 0, 0,−1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0,−1,−1, 0, 0,−1 ],
[ 1, 0, 0,−1,−1,−1,−1 ],
[ 1, 0, 0, 0,−1,−1,−1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1,−1,−1,−1, 0,−1 ],
[ 1, 1, 0,−1,−1,−1,−1 ],
[ −1,−1, 0, 1, 1, 0, 0 ],
[ −1,−1, 1, 1, 0, 0, 0 ],
[ −1, 0,−1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 1, 1, 0,−1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 1, 0, 1 ],
[ 0, 0,−1,−1, 1, 1, 0 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0,−1,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1,−1,−1, 0, 1, 0 ],
[ 0, 1, 0,−1,−1, 0, 0 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 1, 0,−1,−1, 0 ],
[ 1, 0,−1,−1, 0, 0, 0 ],
[ 1, 0, 0,−1,−1, 0,−1 ],
[ 1, 0, 0, 0,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1,−1,−1,−1, 0, 0 ],
[ 1, 1, 0,−1,−1,−1, 0 ],
∗
4
• I ≡ P57 :
6
5
3
2
1




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1













b
CI =


94
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
0
0
1
0
−1
1
0
1
1
0
0
−1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
−1
0
0
−1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
−1













BI =


0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
−1
0
0
0
0
0
−1
0
0
1
0
0
1
0
−1
0
0
0
−1
0
0
0
1
1
0
1
0
0
−1









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1, 1, 1, 1, 1, 1 ],
[ −1, −1, 0, 0, 0, 1,−1 ],
[ −1, −1, 0, 1, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 1, 0 ],
[ −1, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 1, 1 ],
[ 0, −1,−1,−1,−1, 0,−2 ],
[ 0, −1,−1, 0, 0, 0,−1 ],
[ 0, −1, 0,−1, 0, 0,−1 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1,−1,−1,−1,−2 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1,−1,−1,−2 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0,−1,−1,−1,−1 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 1, 0,−1,−1, 0 ],
[ 0, 1, 1, 1, 0,−1, 1 ],
[ 1, −1,−1,−1, 0, 0,−1 ],
[ 1, 0,−1,−1,−1, 0,−1 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 1, 0,−1, 0,−1, 0 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1,−1,−1,−1,−1,−1 ],
[ −1,−1, 0, 0, 0, 1, 0 ],
[ −1,−1, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 1, 1 ],
[ −1, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 2 ],
[ 0,−1, −1, −1, 0, 0, −2 ],
[ 0,−1, −1, 0, 0, 1, −1 ],
[ 0,−1, 0, 0, 0, 0, −1 ],
[ 0,−1, 0, 0, 1, 1, 0 ],
[ 0, 0, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, −1, −1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, −1, −1, −1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 0, −1, 0 ],
[ 0, 1, 1, 1, 0, 0, 1 ],
[ 1, 0, −1, −2, −1, −1, −2 ],
[ 1, 0, −1, −1, 0, −1, −1 ],
[ 1, 0, 0, −1, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 1, 0, −1, −1, −2, −1 ],
[ 1, 1, 0, 0, −1, −1, 0 ],
[ 1, 1, 1, 0, 0, −1, 1 ]
[ −1,−1,−1, 0, 0, 1,−1 ],
[ −1,−1, 0, 0, 1, 1, 0 ],
[ −1,−1, 0, 1, 1, 2, 1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 1, 1, 0, 1, 1 ],
[ −1, 0, 1, 2, 1, 1, 2 ],
[ 0,−1,−1,−1, 0, 0,−1 ],
[ 0,−1,−1, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 1 ],
[ 0, 0,−1,−1,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 1, 0, 0,−1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0,−1, 1 ],
[ 0, 1, 1, 1, 0, 0, 2 ],
[ 1, 0,−1,−1,−1,−1,−2 ],
[ 1, 0,−1,−1, 0, 0,−1 ],
[ 1, 0, 0,−1, 0,−1,−1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0,−1,−1,−1,−1 ],
[ 1, 1, 0, 0, 0,−1, 0 ],
[ −1,−1, 0, 0, 0, 0,−1 ],
[ −1,−1, 0, 1, 0, 1, 0 ],
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ −1, 1, 1, 1, 0, 0, 1 ],
[ 0,−1,−1,−1, 0, 1,−1 ],
[ 0,−1,−1, 0, 1, 1, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 1, 1, 1 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 2 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 1, 0, 2 ],
[ 1, 0,−1,−1,−1,−1,−1 ],
[ 1, 0,−1,−1, 0, 0, 0 ],
[ 1, 0, 0,−1, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1, 0,−1,−1,−1, 0 ],
[ 1, 1, 0, 0, 0,−1, 1 ],
∗
• I ≡ P58 :
1
4
6
3
5
2




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1













b
CI =


95
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
1
0
1
1
−1
1
0
0
0
1
0
−1
0
1
0
0
0
1
0
0
−1
0
0
−1
−1
1
−1
0
0
0
0
0
1
1
1
1
1
0
0
−1
1
1
1
1
1
1
−1













BI =


1
0
0
0
1
0
−1
0
1
1
0
1
1
−1
0
0
0
0
0
−1
0
0
0
0
0
−1
0
0
0
0
0
−1
0
0
0
0
0
−1
0
0
0
0
0
0
0
−1
1
0
−1









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−1, 1,−1, 1,−1 ],
[ −1, −1, −1, 0, −1, 0, −2 ],
[ −1, −1, 0, 0, −1, 0, −2 ],
[ −1, −1, 0, 1, −1, 0, −1 ],
[ −1, −1, 0, 1, 0, 0, 0 ],
[ −1, 0, −1, 0, −1, 0, −1 ],
[ −1, 0, −1, 1, −1, 0, −1 ],
[ −1, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, −1, 1, 0 ],
[ 0, −1, 0, 1, −1, 1, 0 ],
[ 0, −1, 1, 0, −1, 1, 0 ],
[ 0, −1, 1, 1, 0, 1, 1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, −1, 0, 0,−1, −1 ],
[ 0, 1, 0,−1, 0,−1, −1 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 1,−1, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1,−1, 0, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 2 ],
[ 1, 1, 0,−1, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 1,−1, 0, 0, 1 ],
[ 1, 2, 0,−1, 1,−1, 1 ],
[ 1, 1, 1,−1, 1,−1, 1 ],
[ −1,−1,−1, 1,−1, 0,−2 ],
[ −1,−1, 0, 0,−1, 0,−1 ],
[ −1,−1, 0, 1,−1, 1,−1 ],
[ −1,−1, 0, 1, 0, 1, 0 ],
[ −1, 0,−1, 0, 0, −1,−2 ],
[ −1, 0,−1, 1, 0, −1,−1 ],
[ −1, 0, 0, 0, 0, −1,−1 ],
[ −1, 1,−1, 0, 0, −1,−1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1,−1, 0, 0, −1, 0 ],
[ 0, 1, 0, −1, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, −1, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 1, 1 ],
[ 1, 0, 1, 0, 1, 1, 2 ],
[ 1, 1, 0, −1, 1, −1, 0 ],
[ 1, 1, 0, 0, 1, −1, 1 ],
[ 1, 1, 1, −1, 1, 0, 1 ],
[ 2, 1, 1, −1, 1, 0, 2 ]
[ −2,−1,−1, 1,−1, 0,−2 ],
[ −1,−1,−1, 1,−1, 0,−1 ],
[ −1,−1, 0, 0,−1, 1,−1 ],
[ −1,−1, 0, 1,−1, 1, 0 ],
[ −1, 0,−1, 0,−1,−1,−2 ],
[ −1, 0,−1, 0, 0,−1,−1 ],
[ −1, 0,−1, 1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 0, 1, 0 ],
[ 0,−1, 1, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1,−1, 1, 0, 0, 1, 1 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 0, 1,−1, 0, 1, 1 ],
[ 1, 0, 1, 0, 0, 1, 2 ],
[ 1, 1, 0,−1, 0,−1, 0 ],
[ 1, 1, 0,−1, 1,−1, 1 ],
[ 1, 1, 0, 0, 1, 0, 1 ],
[ 1, 1, 1,−1, 1, 0, 2 ],
[ −1,−2, 0, 1,−1, 1,−1 ],
[ −1,−1,−1, 1, 0, 0,−1 ],
[ −1,−1, 0, 0, 0, 0,−1 ],
[ −1,−1, 0, 1, 0, 0,−1 ],
[ −1, 0,−1, 0,−1, 0,−2 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0,−1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0,−1, 1,−1 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 1, 1 ],
[ 0,−1, 1, 0, 0, 1, 1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1,−1,−1, 0,−1,−1 ],
[ 0, 1,−1, 0, 1,−1, 0 ],
[ 0, 1, 0,−1, 1,−1, 0 ],
[ 0, 1, 0, 0, 1,−1, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 1,−1, 1, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 1 ],
[ 1, 1, 0,−1, 0, 0, 0 ],
[ 1, 1, 0,−1, 1, 0, 1 ],
[ 1, 1, 0, 0, 1, 0, 2 ],
[ 1, 1, 1, 0, 1, 0, 2 ],
∗
• I ≡ P59 :
1
4
6
3
5
2




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1













b
CI =


96
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
1
0
1
1
−1
1
0
0
0
0
0
−1
0
1
0
0
1
1
0
0
−1
0
0
−1
−1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
−1













BI =


0
0
0
0
1
0
0
−1
−1
0
0
−1
−1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
−1
1
0
0
0
0
0
0
0
1
1
0
1
1
−1
0
1
1
0
1
0
0









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 1,−1,−1,−1,−1,−2 ],
[ −1,−1, 0, 1, 0, 0, −1 ],
[ −1, 0, −1, 0, −1, −1, −2 ],
[ −1, 0, −1, 0, 0, −1, −1 ],
[ −1, 0, −1, 1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 1, −1, 0, −1, −1, −2 ],
[ 0,−2, 1, 1, 1, 1, 1 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 0 ],
[ 0,−1, 1, 0, 0, 1, 0 ],
[ 0,−1, 1, 0, 1, 1, 1 ],
[ 0,−1, 1, 1, 1, 1, 2 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, −1, −1, −1, −1, −1 ],
[ 0, 1, −1, 0, −1, 0, −1 ],
[ 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, −1, 0, −1, −1 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 1,−1, 1, 0, 0, 1, 1 ],
[ 1,−1, 2, 0, 1, 1, 2 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 0, 1, −1, 0, 1, 1 ],
[ 1, 0, 1, 0, 0, 1, 2 ],
[ 1, 1, 0, −1, −1, 0, 0 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1,−1, 1, 1, 1, 1, 2 ],
[ −1, −1, 0, 1, 0, 0, 0 ],
[ −1, 0,−1, 0,−1, 0,−2 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0,−1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1,−1, 0,−1,−1,−1 ],
[ 0, −1, 0, 0, 0, 0,−1 ],
[ 0, −1, 0, 1, 0, 0, 0 ],
[ 0, −1, 0, 1, 1, 0, 1 ],
[ 0, −1, 1, 0, 0, 1, 1 ],
[ 0, −1, 1, 1, 0, 1, 1 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1,−1,−1,−1, 0,−1 ],
[ 0, 1,−1, 0,−1, 0, 0 ],
[ 0, 1, 0,−1,−1,−1,−1 ],
[ 0, 1, 0,−1, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1, −1, 1, 0, 1, 0, 1 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 1,−1, 1, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 1 ],
[ 1, 1, 0,−1, 0,−1, 0 ],
[ 1, 1, 1,−1, 0, 0, 1 ]
[ −1,−1,−1, 1, 0, 0,−1 ],
[ −1,−1, 0, 1, 0, 1, 0 ],
[ −1, 0,−1, 0,−1, 0,−1 ],
[ −1, 0,−1, 1,−1, 0,−1 ],
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1,−1, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 0, 1, 0 ],
[ 0,−1, 0, 1, 1, 1, 1 ],
[ 0,−1, 1, 0, 1, 0, 0 ],
[ 0,−1, 1, 1, 1, 0, 1 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1,−1,−1, 0,−1,−1 ],
[ 0, 1,−1, 0, 0,−1,−1 ],
[ 0, 1, 0,−1,−1, 0,−1 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1,−1, 1, 0, 1, 1, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1,−1, 0, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 2 ],
[ 1, 1, 0,−1, 0, 0, 0 ],
[ −1,−1, 0, 0, 0, 0,−1 ],
[ −1,−1, 0, 1, 1, 0, 0 ],
[ −1, 0,−1, 0, 0,−1,−2 ],
[ −1, 0,−1, 1, 0,−1,−1 ],
[ −1, 0, 0, 0, 0,−1,−1 ],
[ −1, 1,−2, 0,−1,−1,−2 ],
[ −1, 1,−1, 0, 0,−1,−1 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 1, 1 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 1, 0, 1 ],
[ 0,−1, 1, 1, 1, 1, 1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1,−1,−1,−1,−1,−2 ],
[ 0, 1,−1, 0,−1,−1,−1 ],
[ 0, 1,−1, 0, 0,−1, 0 ],
[ 0, 1, 0,−1,−1, 0, 0 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 2,−1,−1,−1,−1,−1 ],
[ 1,−1, 1, 0, 1, 1, 2 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1,−1, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 1, 1 ],
[ 1, 0, 1, 0, 1, 1, 2 ],
[ 1, 1, 0,−1, 0, 0, 1 ],
∗
6
• I ≡ P60 :
4
3
2
1
5




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1













b
CI =


97
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
0
1
0
0
−1
1
0
1
0
1
0
−1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
−1
−1
0
0
−1
0
1
1
1
1
1
1
1
−1
−1
 0

 0
BI = 0
 −1
 0
1

1
0
1
0
0
1
0









1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
−1
0
1
0
0
0
0
−1
1
0
1
0
0
0
0









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−1,−1,−1, 1,−2 ],
[ −1, −1, −1, −1, 0, 2, −1 ],
[ −1, −1, 0, 0, 0, 1, −1 ],
[ −1, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 1, 0, 1, 0, 1 ],
[ 0, −1, −2, −1, −1, 1, −2 ],
[ 0, −1, −1, −1, 0, 1, −1 ],
[ 0, −1, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, −1, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 1, 0, 1,−1, 1 ],
[ 0, 1, 1, 1, 1,−1, 1 ],
[ 1, −1, −1, 0, −1, 0, −1 ],
[ 1, 0, −1, 0, −1, 0, 0 ],
[ 1, 0, 0, 0, −1, 0, 0 ],
[ 1, 0, 0, 1, −1,−1, 0 ],
[ 1, 0, 1, 1, 0,−1, 1 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 1, 1, 0,−1, 1 ],
[ 1, 1, 1, 1, 1,−1, 2 ],
[ −1,−1,−1, 0, 0, 1,−1 ],
[ −1,−1, 0, 0, 0, 1, 0 ],
[ −1, 0, 0,−1, 0, 1,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 1, 1 ],
[ 0,−1,−1,−1,−1, 0,−2 ],
[ 0,−1,−1, 0,−1, 0,−2 ],
[ 0,−1,−1, 0, 0, 1,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1,−1,−1, 0,−1 ],
[ 0, 0,−1,−1, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, −1, 1 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 1, 0, 0, −1, 0 ],
[ 0, 1, 1, 0, 1, 0, 1 ],
[ 0, 1, 1, 1, 1, −1, 2 ],
[ 1, 0,−1,−1,−1, 0,−1 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 0, 0, 1, 0, −1, 0 ],
[ 1, 1, 0, 0,−1, −1, 0 ],
[ 1, 1, 0, 1, 0, −1, 1 ],
[ 1, 1, 1, 1, 0, −1, 2 ]
[ −1,−1,−1,−1, 0, 1,−2 ],
[ −1,−1, 0,−1, 0, 1,−1 ],
[ −1,−1, 0, 0, 1, 1, 0 ],
[ −1, 0, 0,−1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ 0,−1,−1,−1,−1, 1,−2 ],
[ 0,−1,−1, 0,−1, 0,−1 ],
[ 0,−1,−1, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1,−1,−1, 1,−1 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 1, 0,−1, 0 ],
[ 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 0,−1, 1 ],
[ 0, 1, 1, 0, 1, 0, 2 ],
[ 0, 1, 1, 1, 1, 0, 2 ],
[ 1, 0,−1, 0,−1,−1,−1 ],
[ 1, 0, 0, 0,−1,−1,−1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0,−1, 1 ],
[ 1, 1, 0, 0, 0,−1, 0 ],
[ 1, 1, 1, 0, 0,−1, 1 ],
[ −1,−1,−1,−1, 0, 1,−1 ],
[ −1,−1, 0, 0, 0, 0,−1 ],
[ −1, 0,−1,−1, 0, 1,−1 ],
[ −1, 0, 0,−1, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 0 ],
[ −1, 1, 1, 0, 1, 0, 1 ],
[ 0,−1,−1,−1,−1, 1,−1 ],
[ 0,−1,−1, 0,−1, 1,−1 ],
[ 0,−1, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0,−1, 1 ],
[ 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 0,−1, 1 ],
[ 0, 1, 2, 1, 1,−1, 2 ],
[ 1, 0,−1, 0,−1, 0,−1 ],
[ 1, 0, 0, 0,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 1, 0, 0, 0,−1, 1 ],
[ 1, 1, 1, 1, 0,−2, 1 ],
∗
• I ≡ P61 :
6
5
3
2
4
1




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
1













b
CI =


98
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
0
1
0
0
−1
1
0
1
0
0
1
−1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
−1













BI =


0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
−1
1
0
1
0
0
1
−1
1
1
1
1
0
0
−1









Number of sincere Tits roots of poset I sI = 10.
Table of roots of qbI
[ −2,−1, 1, 1, 2, 1, 1 ],
[ −1,−1, 1, 2, 2, 1, 2 ],
[ 1, 1,−1,−1,−1,−1,−1 ],
[ −1, −1, 0, 0, 1, 0, 0 ],
[ −1, −1, 0, 1, 1, 1, 1 ],
[ −1, −1, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 2 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 1, 1, 0, 0 ],
[ 0, 0, −1, −1, −1, −1, −2 ],
[ 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, −1, −1, −2 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, −1, −1, −1, 0, −1 ],
[ 0, 1, 0, −1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 1, 0, −1, −1, −1, −1, −1 ],
[ 1, 0, −1, 0, −1, 0, 0 ],
[ 1, 0, 0, 0, −1, −1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1, −1, −1, −1, 0, 0 ],
[ 1, 1, 0, −1, −1, −1, 0 ],
[ 1, 1, 0, 0, −1, 0, 1 ],
[ −1,−1, 1, 1, 1, 1, 1 ],
[ 1, 1,−1,−2,−2,−1,−2 ],
[ 2, 1,−1,−1,−2,−1,−1 ],
[ −1, −1, 0, 0, 1, 1, 0 ],
[ −1, −1, 0, 1, 2, 1, 1 ],
[ −1, −1, 1, 1, 2, 0, 1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 1, 1, 2, 1, 2 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 1, 1, 0, 1 ],
[ 0, 0, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, −1, −1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 1, 0, −1, −1, −1, −1 ],
[ 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1, 0, −1, −1, −1, 0, −1 ],
[ 1, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, −1, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 1, −1, 0, −1, 0, 0 ],
[ 1, 1, 0, −1, −1, 0, 0 ],
[ 1, 1, 0, 0, 0, 0, 1 ]
[ −1,−1, 1, 1, 2, 1, 1 ],
[ 1, 1,−1,−1,−2,−1,−2 ],
[ −1, −1, 0, 0, 0, 0, −1 ],
[ −1, −1, 0, 1, 1, 0, 0 ],
[ −1, −1, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ 0, −1, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 1, 1, 1, 1 ],
[ 0, 0, −1, −1, −1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 1, 0, −1, −1, 0, −1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1, 0, −1, −1, −2, −1, −2 ],
[ 1, 0, −1, 0, −1, −1, −1 ],
[ 1, 0, 0, −1, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 1, −1, −1, −2, 0, −1 ],
[ 1, 1, 0, −1, −2, −1, −1 ],
[ 1, 1, 0, 0, −1, −1, 0 ],
[ −1,−1, 1, 1, 2, 1, 2 ],
[ 1, 1,−1,−1,−2,−1,−1 ],
[ −1, −1, 0, 0, 1, 0, −1 ],
[ −1, −1, 0, 1, 1, 1, 0 ],
[ −1, −1, 1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 1, 0, 1, 0, 0 ],
[ −1, 0, 1, 1, 1, 1, 1 ],
[ 0, −1, 0, 0, 0, −1, −1 ],
[ 0, −1, 0, 1, 0, 0, 0 ],
[ 0, −1, 1, 1, 1, 0, 1 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, −1, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 2 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 1, 0, −1, −1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, −1, −1, −1, −1, −2 ],
[ 1, 0, −1, 0, −1, 0, −1 ],
[ 1, 0, 0, 0, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, −1, −1, −1, 0, −1 ],
[ 1, 1, 0, −1, −1, −1, −1 ],
[ 1, 1, 0, 0, −1, 0, 0 ],
∗
• I ≡ P62 :
6
3
5
2
1
4




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1













b
CI =


99
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
0
1
1
1
−1
1
0
0
1
1
0
−1
0
0
0
−1
−1
0
1
1
1
1
0
0
0
−1
−1
0
0
−1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
−1













BI =


1
0
0
1
0
0
−1
0
1
0
1
0
0
−1
0
0
0
−1
0
0
0
0
0
−1
0
0
0
0
0
0
0
1
1
0
−1
0
−1
0
−1
−1
−1
1
0
0
−1
1
0
0
−1









Number of sincere Tits roots of poset I sI = 10.
Table of roots of qbI
[ −2,−2, 1,−1,−1, 1,−2 ],
[ −1,−1, 1,−1,−1, 1,−1 ],
[ 1, 2,−1, 1, 1,−1, 2 ],
[ −1, −2, 1, 0, −1, 1, −1 ],
[ −1, −1, 0, −1, 0, 0, −2 ],
[ −1, −1, 0, 0, −1, 0, −1 ],
[ −1, −1, 1, −1, 0, 1, −1 ],
[ −1, −1, 1, 0, −1, 1, 0 ],
[ −1, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, −1, 0, 1, −1 ],
[ 0, −1, 0, 0, −1, 1, 0 ],
[ 0, −1, 1, −1, 0, 1, 0 ],
[ 0, −1, 1, 0, 0, 1, 1 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, −1, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 1, −1, 1 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1, −1, 0, 0, −1, 0 ],
[ 1, 1, −1, 0, 1, −1, 1 ],
[ 1, 1, −1, 1, 0, 0, 1 ],
[ 1, 1, 0, 0, 1, 0, 2 ],
[ 1, 1, 0, 1, 1, −1, 1 ],
[ 1, 2, −1, 1, 0, −1, 1 ],
[ −1,−2, 1,−1,−1, 1,−2 ],
[ 1, 1,−1, 1, 1,−1, 1 ],
[ 2, 2,−1, 1, 1,−1, 2 ],
[ −1, −1, 0, −1, −1, 0, −2 ],
[ −1, −1, 0, −1, 0, 0, −1 ],
[ −1, −1, 0, 0, −1, 1, −1 ],
[ −1, −1, 1, −1, 0, 1, 0 ],
[ −1, −1, 1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ 0, −1, 0, −1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 1, 0, −1, 1, 0 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 1, 1, −1, 1 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 1, −1, 0, 0, 0, 0 ],
[ 1, 1, −1, 0, 1, 0, 1 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 1, 0, −1, 1 ],
[ 1, 1, 0, 1, 1, −1, 2 ],
[ 1, 2, 0, 1, 1, −1, 2 ]
[ −1,−2, 1,−1,−1, 1,−1 ],
[ 1, 2,−1, 1, 1,−2, 1 ],
[ −1, −2, 0, −1, −1, 1, −2 ],
[ −1, −1, 0, −1, −1, 1, −2 ],
[ −1, −1, 0, −1, 0, 1, −1 ],
[ −1, −1, 0, 0, 0, 0, −1 ],
[ −1, −1, 1, 0, −1, 0, −1 ],
[ −1, −1, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, −1, −1 ],
[ 0, −1, 0, −1, −1, 1, −1 ],
[ 0, −1, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, −1, 0, 1, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, −1, 0 ],
[ 1, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 1, −1, 0, 0, 0, 1 ],
[ 1, 1, −1, 1, 0, −1, 0 ],
[ 1, 1, 0, 0, 1, −1, 1 ],
[ 1, 1, 0, 1, 0, 0, 1 ],
[ 1, 1, 0, 1, 1, 0, 2 ],
[ −1,−2, 1,−1,−1, 2,−1 ],
[ 1, 2,−1, 1, 1,−1, 1 ],
[ −1, −2, 1, −1, 0, 1, −1 ],
[ −1, −1, 0, −1, −1, 1, −1 ],
[ −1, −1, 0, 0, −1, 0, −2 ],
[ −1, −1, 1, −1, 0, 0, −1 ],
[ −1, −1, 1, 0, −1, 1, −1 ],
[ −1, −1, 1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, −1, 1, −1 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, −1, 1, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, −1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, −1, 0, 0, −1, −1 ],
[ 0, 1, −1, 1, 0, −1, 0 ],
[ 0, 1, 0, 0, 1, −1, 0 ],
[ 0, 1, 0, 1, 0, −1, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 1, −1, 0, 1, −1, 0 ],
[ 1, 1, −1, 1, 0, −1, 1 ],
[ 1, 1, 0, 0, 1, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 2 ],
[ 1, 2, −1, 0, 1, −1, 1 ],
∗
6
• I ≡ P63 :
5
4
2
1
3




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1













b
CI =


100
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
0
0
1
0
−1
1
0
1
0
0
0
−1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
−1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
−1













BI =


0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
−1
0
1
0
1
0
0
0
−1
0
1
0
0
1
0
−1
0
0
−1
0
0
0
0
0
1
0
0
0
0
0









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1, 1, 1, 1, 1, 1 ],
[ −1, −1, 0, 0, 0, 0,−1 ],
[ −1, −1, 0, 1, 0, 0,−1 ],
[ −1, −1, 0, 1, 1, 1, 0 ],
[ −1, −1, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0,−1, 0 ],
[ 0, −1,−1,−1, 0, 1,−1 ],
[ 0, −1,−1, 0, 1, 1, 0 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 1, 1, 0, 0 ],
[ 0, 0,−1,−1,−1, 0,−2 ],
[ 0, 0,−1,−1, 0, 1,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1,−1,−1,−1, 0,−1 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 1, 0, 0,−1, 0 ],
[ 1, 0,−1,−1,−1, 0,−1 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1,−1,−1,−1, 0, 0 ],
[ 1, 1, 0,−1,−1, 0, 0 ],
[ 1, 1, 0, 0,−1,−1, 0 ],
[ 1, 1, 1, 0, 0,−1, 1 ],
[ 1, 1,−1,−1,−1,−1,−1 ],
[ −1,−1, 0, 0, 0, 1, −1 ],
[ −1,−1, 0, 1, 0, 0, 0 ],
[ −1,−1, 0, 1, 1, 1, 1 ],
[ −1,−1, 1, 2, 1, 0, 1 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 1, 0, 0, 0 ],
[ 0,−1, −1, 0, 0, 0, −1 ],
[ 0,−1, 0, 0, 0, 0, −1 ],
[ 0,−1, 0, 0, 1, 1, 0 ],
[ 0,−1, 0, 1, 1, 0, 1 ],
[ 0, 0, −1, −1, −1, 0, −1 ],
[ 0, 0, −1, −1, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, −1, 1 ],
[ 0, 1, 0, −1, −1, −1, −1 ],
[ 0, 1, 0, 0, −1, −1, −1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 0, −1, 1 ],
[ 1, 0, −1, −1, 0, 0, −1 ],
[ 1, 0, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 1, −1, −1, 0, 0, 0 ],
[ 1, 1, 0, −1, 0, −1, 0 ],
[ 1, 1, 0, 0, 0, −1, 0 ],
[ 1, 2, 0, −1, −1, −1, 0 ]
[ −1,−2, 0, 1, 1, 1, 0 ],
[ −1,−1, 0, 0, 0, 1, 0 ],
[ −1,−1, 0, 1, 0, 1, 0 ],
[ −1,−1, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 1 ],
[ 0,−1,−1, 0, 0, 1,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 1 ],
[ 0,−1, 0, 1, 1, 1, 1 ],
[ 0, 0,−1,−1,−1, 1,−1 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 1, 0,−1, 0 ],
[ 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 1, 0,−1,−1, 0,−1 ],
[ 0, 1, 0, 0,−1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1, 0,−1,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 1,−1,−2,−1, 0,−1 ],
[ 1, 1, 0,−1,−1,−1,−1 ],
[ 1, 1, 0,−1, 0, 0, 0 ],
[ 1, 1, 0, 0, 0,−1, 1 ],
[ −1,−1,−1, 0, 0, 1,−1 ],
[ −1,−1, 0, 0, 1, 1, 0 ],
[ −1,−1, 0, 1, 1, 0, 0 ],
[ −1,−1, 1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ 0,−1,−1, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0,−1, 1, 1, 1, 0, 1 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0,−1, 1 ],
[ 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 1, 0,−1,−1, 0, 0 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 1, 0,−1,−1, 0 ],
[ 0, 1, 1, 1, 0,−1, 1 ],
[ 1, 0,−1,−1, 0, 1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1,−1,−1,−1, 0,−1 ],
[ 1, 1, 0,−1,−1,−1, 0 ],
[ 1, 1, 0,−1, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
∗
• I ≡ P64 :
1
4
6
3
5
2




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1













b
CI =


101
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
1
0
1
1
−1
1
0
0
0
0
0
−1
0
1
0
0
1
0
0
0
−1
0
0
−1
0
1
0
1
1
1
0
0
0
0
−1
0
0
0
0
0
1
1
1
1
1
1
−1













BI =


1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
−1
0
0
0
0
0
−1
0
0
0
0
0
−1
0
0
0









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−1, 1,−1, 1,−1 ],
[ −1, −1, −1, 1, 0, 1, 0 ],
[ −1, −1, 0, 1, 0, 0, 0 ],
[ −1, 0, −1, 0, −1, 0, −2 ],
[ −1, 0, −1, 1, −1, 0, −1 ],
[ −1, 0, −1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, −1, 1, 0, 1, 0 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 1, 1, 0, 0 ],
[ 0, −1, 1, 0, 1,−1, 0 ],
[ 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, −1, 1, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, −1,−1, −1, 0, −1 ],
[ 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0,−1, −1 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 1, −1, 1, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 0, 1,−1, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 2,−1, 1,−1, 1 ],
[ 1, 1, 0,−1, 0, 0, 1 ],
[ 1, 1, 1,−1, 0,−1, 1 ],
[ 1, 1, 1,−1, 1,−1, 1 ],
[ −1,−1,−1, 2, 0, 1, 0 ],
[ −1,−1, 0, 1, 0, 1, 0 ],
[ −1, 0,−1, 0,−1, 0,−1 ],
[ −1, 0,−1, 1,−1, 1,−1 ],
[ −1, 0,−1, 1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 1 ],
[ 0,−1, 1, 0, 1, 0, 0 ],
[ 0, 0,−1, 0,−1, 1,−1 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0,−1, 1, 0, 1, 1 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, −1, 1, −1, 0 ],
[ 0, 0, 1, 0, 1, −1, 0 ],
[ 0, 1,−1, 0,−1, 0,−1 ],
[ 0, 1, 0, −1,−1, −1,−1 ],
[ 0, 1, 0, −1, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, −1, 1, −1, 0 ],
[ 1, 0, 1, 0, 1, −1, 1 ],
[ 1, 1, 0, −1,−1, 0, 0 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 1, −1, 0, 0, 1 ]
[ −1,−1,−1, 1, 0, 0,−1 ],
[ −1,−1, 0, 0, 0, 0,−1 ],
[ −1,−1, 0, 1, 1, 0, 0 ],
[ −1, 0,−1, 0,−1, 1,−1 ],
[ −1, 0,−1, 1,−1, 1, 0 ],
[ −1, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 0, 1, 0 ],
[ 0,−1, 0, 1, 1, 1, 1 ],
[ 0,−1, 1, 0, 1, 0, 1 ],
[ 0, 0,−1, 0,−1, 1, 0 ],
[ 0, 0,−1, 1,−1, 1, 0 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1,−1, 0,−1,−1 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 0, 1,−1, 1 ],
[ 0, 1,−1, 0,−1, 0, 0 ],
[ 0, 1, 0,−1,−1, 0,−1 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1,−1, 0,−1, 0 ],
[ 1, 0, 1,−1, 1,−1, 1 ],
[ 1, 0, 1, 0, 1, 0, 1 ],
[ 1, 1, 0,−1, 0,−1, 0 ],
[ 1, 1, 1,−2, 0,−1, 0 ],
[ −1,−1,−1, 1, 0, 1,−1 ],
[ −1,−1, 0, 1, 0, 0,−1 ],
[ −1, 0,−2, 1,−1, 1,−1 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0,−1, 1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1,−1 ],
[ −1, 1,−1, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 1, 1 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 1, 0, 1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1,−1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1,−1, 0,−1, 1, 0 ],
[ 0, 1, 0,−1,−1, 0, 0 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 1,−1, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1,−1, 0, 0, 0 ],
[ 1, 0, 1,−1, 1, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 2 ],
[ 1, 1, 0,−1, 0, 0, 0 ],
[ 1, 1, 1,−1, 0,−1, 0 ],
∗
• I ≡ P65 :
5
6
3
2
4
1




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1













b
CI =


102
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
0
1
0
0
−1
1
0
1
0
1
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
−1
0
0
0
0
0
1
1
1
1
1
1
1
−1













BI =


0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
−1
0
0
0
0
−1
0
0
1
0
0
0
0
0
−1
0
1
0
0
0
0
0









Number of sincere Tits roots of poset I sI = 4.
Table of roots of qbI
[ −1,−1,−1, 1, 1, 2, 1 ],
[ −1, −2, −1, 1, 1, 2, 0 ],
[ −1, −1, −1, 0, 1, 2, 0 ],
[ −1, −1, 0, 0, 0, 1,−1 ],
[ −1, −1, 0, 1, 1, 1, 0 ],
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ 0, −1, −1, 0, 1, 1, 0 ],
[ 0, −1, −1, 1, 1, 2, 1 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 1, 1, 1, 1 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, −1, 1, 1, 1, 1 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 2 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 1,−1, 0,−1, 0 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1, 0, 0, 0,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1, 0,−1,−1,−1,−1 ],
[ 1, 1, 0, 0, 0,−1, 0 ],
[ 1, 1, 1,−1,−1,−1, 0 ],
[ 1, 1, 1, 0, 0,−1, 1 ],
[ −1,−1,−1, 1, 2, 2, 1 ],
[ −1, −1, −1, 0, 0, 1,−1 ],
[ −1, −1, −1, 1, 1, 1, 0 ],
[ −1, −1, 0, 0, 0, 1, 0 ],
[ −1, −1, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ 0, −1, −1, 0, 0, 0,−1 ],
[ 0, −1, −1, 1, 0, 1, 0 ],
[ 0, −1, 0, 0,−1, 0,−1 ],
[ 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, −1,−1, 0, 0,−1 ],
[ 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1,−1,−1,−2 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1,−1,−1,−1,−1 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0,−1,−1,−1,−1 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 1,−1,−1,−2,−1 ],
[ 0, 1, 1, 0,−1,−1, 0 ],
[ 1, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 1, 0,−1,−1,−1, 0 ],
[ 1, 1, 0, 0, 0,−1, 1 ],
[ 1, 1, 1, 0,−1,−2, 0 ],
[ 1, 2, 1,−1,−1,−2, 0 ]
[ 1, 1, 1,−1,−2,−2,−1 ],
[ −1,−1,−1, 0, 1, 1, −1 ],
[ −1,−1,−1, 1, 1, 2, 0 ],
[ −1,−1, 0, 0, 1, 1, 0 ],
[ −1,−1, 0, 1, 1, 2, 1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ 0,−1,−1, 0, 0, 1, −1 ],
[ 0,−1,−1, 1, 1, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, −1 ],
[ 0,−1, 0, 1, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 0, −1 ],
[ 0, 0,−1, 0, 1, 1, 0 ],
[ 0, 0, 0, −1, −1, −1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, −1, −1, −1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, −1, 0, −1, −1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, −1, −1, −1, −1 ],
[ 0, 1, 1, 0, 0, −1, 0 ],
[ 1, 0, 0, −1, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 0, 1, 0, −1, −1, 0 ],
[ 1, 1, 0, −1, 0, −1, 0 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 1, 0, −1, −1, 0 ],
[ 1, 1, 1,−1,−1,−2,−1 ],
[ −1,−1,−1, 0, 1, 1, 0 ],
[ −1,−1, 0, 0, 0, 0, −1 ],
[ −1,−1, 0, 1, 0, 1, 0 ],
[ −1, 0,−1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ 0,−1,−1, 0, 0, 1, 0 ],
[ 0,−1,−1, 1, 1, 1, 1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 0, 1, 1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 1, 1 ],
[ 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 1, 0, −1, −1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, −1, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, −1, −1, −1, 0 ],
[ 0, 1, 1, 0, 0, −1, 1 ],
[ 1, 0, 0, 0, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, −1, −1, −2, −1 ],
[ 1, 1, 0, 0, −1, −1, 0 ],
[ 1, 1, 1, −1, −1, −2, 0 ],
[ 1, 1, 1, 0, −1, −1, 1 ],
∗
6
• I ≡ P66 :
1
3
5
2
4




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1













b
CI =


103
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
0
1
1
1
−1
1
0
0
1
0
0
−1
0
0
0
−1
0
0
1
1
1
1
0
0
0
−1
−1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
−1













BI =


1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
−1
0
1
0
0
1
0
0
0
−1
0
0
−1
−1
0
0
0
0
−1
−1
0
0
0
0
−1
0
0
0
0









Number of sincere Tits roots of poset I sI = 4.
Table of roots of qbI
[ −1,−2, 1,−2, 1, 1,−1 ],
[ −1, −2, 1, −1, 0, 1, −1 ],
[ −1, −1, 0, −1, 0, 0, −2 ],
[ −1, −1, 0, 0, 0, 0, −1 ],
[ −1, −1, 1, −1, 1, 0, −1 ],
[ −1, −1, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 0,−1, 0, −1 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ 0, −1, 0, −1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 1, −1, 0, 1, 0 ],
[ 0, −1, 1, 0, 0, 0, 0 ],
[ 0, −1, 1, 0, 1, 0, 1 ],
[ 0, 0,−1, 0, 0,−1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1,−1, 0,−1,−1, −1 ],
[ 0, 1,−1, 0, 0,−1, 0 ],
[ 0, 1,−1, 1,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1,−1, 0, 1 ],
[ 0, 2,−1, 1,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 1,−1, 0, 0,−1, 0 ],
[ 1, 1,−1, 1,−1, 0, 0 ],
[ 1, 1,−1, 1, 0, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 1 ],
[ 1, 2,−1, 1,−1, 0, 1 ],
[ −1,−2, 1,−1, 1, 1,−1 ],
[ −1, −2, 1, −1, 1, 0, −1 ],
[ −1, −1, 0, −1, 0, 0, −1 ],
[ −1, −1, 1, −1, 0, 0, −1 ],
[ −1, −1, 1, −1, 1, 0, 0 ],
[ −1, −1, 1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0,−1, −1 ],
[ 0, −2, 1, −1, 1, 1, 0 ],
[ 0, −1, 0, −1, 1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, −1, 1, 0, 0 ],
[ 0, −1, 1, 0, 0, 1, 0 ],
[ 0, −1, 1, 0, 1, 1, 1 ],
[ 0, 0,−1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1,−1, 0,−1, 0, −1 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1,−1, 1, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0,−1, 0 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 1,−1, 0, 0, 0, 0 ],
[ 1, 1,−1, 1,−1, 0, 1 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 2 ],
[ 1, 2,−1, 1, 0,−1, 1 ]
[ 1, 2,−1, 1,−1,−1, 1 ],
[ −1,−2, 1,−1, 1, 1, 0 ],
[ −1,−1, 0,−1, 0, 1,−1 ],
[ −1,−1, 1,−1, 0, 1,−1 ],
[ −1,−1, 1,−1, 1, 1, 0 ],
[ −1,−1, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0,−1, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 1,−1, 1, 1, 0 ],
[ 0,−1, 1, 0, 0, 1, 1 ],
[ 0, 0, −1,−1, 0, 0,−1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, −1, 0, −1, 0, 0 ],
[ 0, 1, −1, 1, −1, −1,−1 ],
[ 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 1, 0, 1, −1, −1, 0 ],
[ 0, 1, 0, 1, 0, −1, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 1, −1, 0, 0, 0, 1 ],
[ 1, 1, −1, 1, 0, −1, 0 ],
[ 1, 1, 0, 1, −1, 0, 1 ],
[ 1, 2, −2, 1, −1, −1, 0 ],
[ 1, 2,−1, 2,−1,−1, 1 ],
[ −1,−2, 2,−1, 1, 1, 0 ],
[ −1,−1, 0,−1, 1, 0,−1 ],
[ −1,−1, 1,−1, 0, 1, 0 ],
[ −1,−1, 1, 0, 0, 0,−1 ],
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0,−1, 0, 1,−1 ],
[ 0,−1, 0,−1, 1, 1, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 1,−1, 1, 1, 1 ],
[ 0,−1, 1, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, −1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, −1, 0,−1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, −1, 0, 0, −1,−1 ],
[ 0, 1, −1, 1, −1, −1, 0 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 1, −1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1, −1, 0, −1, 0, 0 ],
[ 1, 1, −1, 1, −1, −1, 0 ],
[ 1, 1, −1, 1, 0, −1, 1 ],
[ 1, 1, 0, 1, 0, −1, 1 ],
[ 1, 2, −1, 1, −1, −1, 0 ],
∗
• I ≡ P67 :
3
6
2
5
1
4




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1













b
CI =


104
1
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
0
1
0
0
−1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
−1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
−1









0
 0

 0
BI = −1
 0
 0
1

0
0
0
1
0
0
0
1
1
1
0
0
0
−1
0
1
0
0
0
0
0
1
0
0
1
1
1
−1
0
0
0
0
0
−1
0
1
1
0
0
0
0
0









Number of sincere Tits roots of poset I sI = 8.
Table of roots of qbI
[ −2, 1, 1,−1, 1, 1, 1 ],
[ 1,−1,−1, 1,−1,−1,−1 ],
[ −2, 0, 1, −1, 1, 1, 0 ],
[ −1, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, −1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, −1, 1, 1, 0 ],
[ −1, 0, 1, 0, 0, 1, 1 ],
[ −1, 1, 0, −1, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 1 ],
[ −1, 1, 1, 0, 1, 1, 1 ],
[ 0, −1, 0, 0, 0, −1, −1 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, −1, −1, 0, −1, −1, −2 ],
[ 1, −1, 0, 0, −1, −1, −1 ],
[ 1, −1, 0, 0, 0, −1, 0 ],
[ 1, −1, 0, 1, −1, 0, 0 ],
[ 1, 0, −1, 0, −1, 0, 0 ],
[ 1, 0, −1, 1, −1, −1, −1 ],
[ 1, 0, 0, 0, −1, 0, 0 ],
[ 1, 0, 0, 1, −1, −1, 0 ],
[ 1, 0, 0, 1, 0, −1, 1 ],
[ 2, −1, 0, 1, −1, −1, 0 ],
[ −2, 1, 1,−1, 1, 2, 1 ],
[ 2,−1,−1, 1,−2,−1,−1 ],
[ −2, 1, 0, −1, 1, 1, 0 ],
[ −1, 0, 0, −1, 0, 1, −1 ],
[ −1, 0, 0, −1, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, −1, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 0, 0 ],
[ −1, 1, 0, −1, 1, 0, 0 ],
[ −1, 1, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 1, 1, 1 ],
[ −1, 1, 1, 0, 1, 1, 2 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 1, 1 ],
[ 1, −1, −1, 0, −1, −1, −1 ],
[ 1, −1, 0, 0, −1, 0, −1 ],
[ 1, −1, 0, 0, 0, 0, 0 ],
[ 1, −1, 0, 1, 0, −1, 0 ],
[ 1, 0, −1, 0, 0, −1, −1 ],
[ 1, 0, −1, 1, −1, −1, 0 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 0, 0, 1, −1, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 2, 0, −1, 1, −1, −1, 0 ]
[ −2, 1, 1,−1, 2, 1, 1 ],
[ 2,−1,−1, 1,−1,−2,−1 ],
[ −2, 1, 1, −1, 1, 1, 0 ],
[ −1, 0, 0, −1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 1, −1, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 1 ],
[ −1, 1, 0, −1, 1, 1, 0 ],
[ −1, 1, 0, 0, 0, 1, 1 ],
[ −1, 1, 1, 0, 0, 1, 1 ],
[ 0, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, −1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 1, −1, −1, 0, −1, 0, −1 ],
[ 1, −1, 0, 0, −1, 0, 0 ],
[ 1, −1, 0, 1, −1, −1, −1 ],
[ 1, 0, −1, 0, −1, −1, −1 ],
[ 1, 0, −1, 0, 0, −1, 0 ],
[ 1, 0, −1, 1, −1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, −1, 0, 1 ],
[ 2, −1, −1, 0, −1, −1, −1 ],
[ −1, 1, 1,−1, 1, 1, 1 ],
[ 2,−1,−1, 1,−1,−1,−1 ],
[ −2, 1, 1, 0, 1, 1, 1 ],
[ −1, 0, 0, −1, 1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, −1, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 1, 1, 1 ],
[ −1, 1, 0, −1, 1, 1, 1 ],
[ −1, 1, 0, 0, 1, 0, 0 ],
[ −1, 1, 1, 0, 1, 0, 1 ],
[ 0, −1, 0, 0, −1, 0, −1 ],
[ 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 1, −1, −1, 0, 0, −1, −1 ],
[ 1, −1, 0, 0, 0, −1, −1 ],
[ 1, −1, 0, 1, −1, −1, 0 ],
[ 1, 0, −1, 0, −1, 0, −1 ],
[ 1, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, −1, 1, 0, −1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 1, 0, −1, 0 ],
[ 2, −1, −1, 1, −1, −1, 0 ],
∗
• I ≡ P68 :
5
6
3
4
1
2




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1













b
CI =


105
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
0
1
0
0
−1
1
0
1
0
1
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
−1
−1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
−1













BI =


0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
−1
−1
0
−1
0
0
−1
0
−1
0
−1
0
−1
0
0
0
0
0
−1
0
−1
0









Number of sincere Tits roots of poset I sI = 8.
Table of roots of qbI
[ −2,−1,−1,−1, 1, 2,−1 ],
[ 1, 1, 1, 1,−1,−2, 1 ],
[ −1, −1, −1, −1, 0, 1, −2 ],
[ −1, −1, −1, 0, 0, 1, −1 ],
[ −1, −1, 0, −1, 0, 1, −1 ],
[ −1, −1, 0, 0, 1, 1, 0 ],
[ −1, 0, −1, −1, 1, 2, 0 ],
[ −1, 0, 0, −1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ 0, −1, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 1, 1 ],
[ 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, 1, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 1, 0, −1, −1, 0 ],
[ 0, 1, 1, 1, 0, −1, 1 ],
[ 1, 0, 0, 0, −1, 0, 0 ],
[ 1, 0, 0, 1, −1, −1, 0 ],
[ 1, 0, 1, 0, −1, −1, 0 ],
[ 1, 0, 1, 1, 0, −1, 1 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 1, 0, −1, −1, 1 ],
[ 1, 1, 1, 1, 0, −1, 1 ],
[ −1,−1,−2,−1, 1, 2,−1 ],
[ 1, 1, 1, 1,−1,−1, 1 ],
[ −1, −1, −1, −1, 0, 1, −1 ],
[ −1, −1, −1, 0, 1, 1, −1 ],
[ −1, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, −1, −1, 0, 1, −1 ],
[ −1, 0, −1, 0, 1, 1, 0 ],
[ −1, 0, 0, −1, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, −1, −1, 0, 1, −1 ],
[ 0, −1, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, −1, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, −1, −1, −1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, −1, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 0, −1, 0 ],
[ 1, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, 0 ],
[ 1, 0, 0, 1, 0, −1, 0 ],
[ 1, 0, 1, 1, −1, −2, 0 ],
[ 1, 1, 0, 0, −1, −1, 0 ],
[ 1, 1, 0, 1, 0, −1, 1 ],
[ 1, 1, 1, 0, 0, −1, 1 ],
[ 1, 1, 1, 1, 0, −1, 2 ]
[ −1,−1,−1,−1, 1, 1,−1 ],
[ 1, 1, 2, 1,−1,−2, 1 ],
[ −1, −1, −1, −1, 0, 2, −1 ],
[ −1, −1, −1, 0, 1, 1, 0 ],
[ −1, −1, 0, 0, 0, 1, −1 ],
[ −1, 0, −1, −1, 1, 1, −1 ],
[ −1, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ 0, −1, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, −1, −1, 1, 1, 0 ],
[ 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, −1, −1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, −1, 1 ],
[ 1, 0, 0, 0, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, −1, 1 ],
[ 1, 0, 1, 1, −1, −1, 0 ],
[ 1, 1, 0, 0, 0, −1, 0 ],
[ 1, 1, 1, 0, −1, −2, 0 ],
[ 1, 1, 1, 1, −1, −2, 0 ],
[ −1,−1,−1,−1, 1, 2,−1 ],
[ 2, 1, 1, 1,−1,−2, 1 ],
[ −1, −1, −1, −1, 1, 2, 0 ],
[ −1, −1, −1, 0, 1, 2, 0 ],
[ −1, −1, 0, 0, 0, 1, 0 ],
[ −1, 0, −1, −1, 1, 1, 0 ],
[ −1, 0, 0, −1, 0, 1, −1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ 0, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 1, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 0, 1, 1, −1, −1, 0 ],
[ 0, 1, 0, −1, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, −1, −1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 1, −1, −1, 1 ],
[ 1, 1, 0, 0, 0, −1, 1 ],
[ 1, 1, 1, 0, −1, −1, 0 ],
[ 1, 1, 1, 1, 0, −2, 1 ],
∗
• I ≡ P69 :
3
6
2
5
1
4




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1













b
CI =


106
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
0
1
0
0
−1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
−1
0
0
0
0
0
0
1
−1
0
0
0
0
0
0
1
1
1
1
1
1
−1













BI =


−1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
−1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
−1
0
1
0
0
0
0
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −2, 0, 1,−1, 1, 1, 0 ],
[ −1,−1, 1,−1, 0, 2, 0 ],
[ −1, 0, 0,−1, 0, 1,−1 ],
[ −1, 0, 0,−1, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1,−1, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 1, 0, 1 ],
[ 0,−1, 0,−1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 1, 0,−1, 1, 0 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 1, 1,−1, 1 ],
[ 1,−1, 0, 0,−1, 1, 0 ],
[ 1, 0,−1, 0,−1, 0,−1 ],
[ 1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0,−1, 1, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 1, 0,−1, 0 ],
[ 1, 1,−1, 1,−1,−1, 0 ],
[ 1, 1, 0, 1, 0,−1, 1 ],
[ −1,−1, 0,−1, 0, 1,−1 ],
[ −1,−1, 1,−1, 1, 1, 0 ],
[ −1, 0, 0,−1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 1,−1, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 1 ],
[ −1, 1, 0, 0, 1,−1, 0 ],
[ 0,−1, 0,−1,−1, 1,−1 ],
[ 0,−1, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1,−1, 0, 1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0,−1, 0 ],
[ 1,−1,−1, 0,−1, 0,−1 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1, 0,−1, 0, 0 ],
[ 1, 0,−1, 1,−1,−1,−1 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 1,−1,−1, 0 ],
[ 1, 0, 0, 1, 0,−1, 1 ],
[ 1, 1,−1, 1, 0,−2, 0 ],
[ 2, 0,−1, 1,−1,−1, 0 ]
[ −1,−1, 1,−1, 0, 1,−1 ],
[ −1,−1, 1, 0, 0, 1, 0 ],
[ −1, 0, 0,−1, 1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1,−1, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 1, 1, 1 ],
[ −1, 1, 0, 0, 1, 0, 0 ],
[ 0,−1, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0,−1, 1,−1 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 1, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1,−1, 0, 0,−1,−1 ],
[ 0, 1,−1, 1, 0,−1, 0 ],
[ 0, 1, 0, 0, 1,−1, 0 ],
[ 0, 1, 0, 1, 0,−1, 1 ],
[ 1,−1, 0, 0,−1, 0,−1 ],
[ 1,−1, 0, 1,−1, 0, 0 ],
[ 1, 0,−1, 0, 0,−1,−1 ],
[ 1, 0,−1, 1,−1,−1, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 1,−1, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 1,−1, 1, 0,−1, 0 ],
[ −1,−1, 1,−1, 0, 1, 0 ],
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0,−1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 1,−1, 1, 1, 0 ],
[ −1, 0, 1, 0, 0, 1, 1 ],
[ −1, 1, 0,−1, 1, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 1 ],
[ 0,−1, 0,−1, 0, 1,−1 ],
[ 0,−1, 0, 0,−1, 1, 0 ],
[ 0,−1, 1,−1, 0, 1, 0 ],
[ 0,−1, 1, 0, 0, 1, 1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1,−1, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 1,−1, 1 ],
[ 0, 1, 0, 1, 0, 0, 1 ],
[ 1,−1, 0, 0,−1, 0, 0 ],
[ 1, 0,−1, 0,−1,−1,−1 ],
[ 1, 0,−1, 0, 0,−1, 0 ],
[ 1, 0,−1, 1,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1,−1, 0, 1 ],
[ 1, 1,−1, 0, 0,−1, 0 ],
[ 1, 1,−1, 1, 0,−1, 1 ],
∗
6
• I ≡ P70 :
3
5
4
2
1




CI =


1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1













b
CI =


107
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
0
1
0
0
0
−1
1
0
0
0
0
0
0
1
1
0
1
1
0
−1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
−1
−1
0
0
−1
0
1
1
1
1
1
1
1
−1













BI =


0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
−1
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1,−1, 0, 0, 1,−1 ],
[ −1,−1,−1, 1, 1, 1, 0 ],
[ −1,−1, 0, 1, 1, 1, 1 ],
[ −1, 0,−1, 0, 0, 1,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1 ],
[ 0,−1,−1, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 1, 0 ],
[ 0,−1, 0, 1, 1, 0, 1 ],
[ 0, 0,−1,−1,−1, 0,−1 ],
[ 0, 0,−1,−1, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1,−1, 1 ],
[ 0, 1, 0,−1,−1,−1,−1 ],
[ 0, 1, 0, 0,−1,−1,−1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 0,−1, 1 ],
[ 1, 0,−1,−1,−1, 0,−1 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 1, 0, 0,−1, 0 ],
[ 1, 1, 0,−1,−2,−1,−1 ],
[ 1, 1, 0, 0,−1,−1, 0 ],
[ 1, 1, 1, 0,−1,−1, 1 ],
[ −1,−1,−1, 0, 1, 1,−1 ],
[ −1,−1, 0, 0, 1, 1, 0 ],
[ −1,−1, 0, 1, 2, 1, 1 ],
[ −1, 0,−1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 1 ],
[ 0,−1,−1, 0, 0, 1,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 1 ],
[ 0,−1, 0, 1, 1, 1, 1 ],
[ 0, 0,−1,−1,−1, 1,−1 ],
[ 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 1, 0,−1, 0 ],
[ 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 1, 0,−1,−1, 0,−1 ],
[ 0, 1, 0, 0,−1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1 ],
[ 1, 0, 0,−1,−1,−1,−1 ],
[ 1, 0, 0, 0,−1,−1,−1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 0,−1, 1 ],
[ 1, 1, 0,−1,−1,−1,−1 ],
[ 1, 1, 1,−1,−1,−1, 0 ],
[ 1, 1, 1, 0, 0,−1, 1 ]
[ −1,−1,−1, 0, 1, 1, 0 ],
[ −1,−1, 0, 1, 1, 0, 0 ],
[ −1, 0,−1,−1, 0, 1,−1 ],
[ −1, 0,−1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1,−1, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0,−1, 1, 1, 1, 0, 1 ],
[ 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0,−1, 1 ],
[ 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 1, 0,−1,−1, 0, 0 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 1, 0,−1,−1, 0 ],
[ 0, 1, 1, 1, 0,−1, 1 ],
[ 1, 0, 0,−1,−1, 0,−1 ],
[ 1, 0, 0, 0,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 1, 0,−1,−1,−1, 0 ],
[ 1, 1, 1, 0,−1,−2, 0 ],
[ −1,−1,−1, 0, 1, 2, 0 ],
[ −1,−1, 0, 1, 1, 1, 0 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 1, 1, 0, 1 ],
[ 0,−1,−1,−1, 0, 1,−1 ],
[ 0,−1,−1, 0, 1, 1, 0 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 0 ],
[ 0, 0,−1,−1,−1, 0,−2 ],
[ 0, 0,−1,−1, 0, 1,−1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 1,−1,−1,−1, 0,−1 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 1, 0, 0,−1, 0 ],
[ 1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1,−1, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 1, 0,−1,−1, 0 ],
[ 1, 0, 1, 1, 0,−1, 1 ],
[ 1, 1, 0,−1,−1, 0, 0 ],
[ 1, 1, 1, 0,−1,−1, 0 ],
∗
5
• I ≡ P71 :
6
4
1
3
2




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
1













b
CI =


108
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
1
0
0
1
−1
1
0
0
0
0
0
−1
0
1
0
0
0
1
0
0
−1
0
0
0
−1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
−1
0
 −1

 0
BI = 0
 0
 0
0










−1
0
0
0
0
0
0
0
−1
0
0
0
−1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
−1
1
0
0
1
0
0
0
0
0
1
1
0
0
0









Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −2,−1,−1, 1, 1, 0,−1 ],
[ −1,−1,−1, 1, 1, 0,−1 ],
[ −1,−1, 0, 0, 1, 0,−1 ],
[ −1,−1, 0, 1, 0, 0, 0 ],
[ −1,−1, 0, 1, 1, 1, 1 ],
[ −1, 0,−1, 0, 1,−1,−1 ],
[ −1, 0,−1, 1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 1,−1, 0, 0,−1,−1 ],
[ 0,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 1, 0, 1, 0 ],
[ 0,−1, 1, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1,−1, 0, 0,−1,−1 ],
[ 0, 1, 0,−1, 0,−1,−1 ],
[ 0, 1, 0, 0,−1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1,−1, 0, 0, 0 ],
[ 1, 0, 1, 0,−1, 0, 1 ],
[ 1, 0, 1, 0, 0, 1, 2 ],
[ 1, 1, 0,−1, 0,−1, 0 ],
[ 1, 1, 0, 0,−1, 0, 0 ],
[ 1, 1, 1,−1,−1, 0, 0 ],
[ 1, 2, 0,−1,−1,−1, 0 ],
[ −1,−2, 0, 1, 1, 1, 0 ],
[ −1,−1,−1, 1, 1, 0, 0 ],
[ −1,−1, 0, 0, 1, 0, 0 ],
[ −1,−1, 0, 1, 0, 1, 0 ],
[ −1, 0,−1, 0, 0,−1,−2 ],
[ −1, 0,−1, 0, 1, 0,−1 ],
[ −1, 0,−1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 1, 0 ],
[ 0,−1, 0, 1, 0, 1, 1 ],
[ 0,−1, 1, 0, 0, 1, 1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1,−1, 0, 0,−1, 0 ],
[ 0, 1, 0,−1, 0,−1, 0 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 1,−1, 1, 0, 0, 1, 1 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1,−1, 0, 0, 1 ],
[ 1, 0, 1, 0,−1, 1, 1 ],
[ 1, 1, 0,−1,−1,−1,−1 ],
[ 1, 1, 0,−1, 0, 0, 0 ],
[ 1, 1, 0, 0,−1, 0, 1 ],
[ 1, 1, 1,−1,−1, 0, 1 ],
[ 2, 1, 1,−1,−1, 0, 1 ]
[ −1,−1,−1, 0, 1, 0,−1 ],
[ −1,−1,−1, 1, 1, 1, 0 ],
[ −1,−1, 0, 0, 1, 1, 0 ],
[ −1,−1, 0, 1, 1, 0, 0 ],
[ −1, 0,−1, 0, 0,−1,−1 ],
[ −1, 0,−1, 0, 1, 0, 0 ],
[ −1, 0,−1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 1 ],
[ 0,−1, 0, 1, 1, 1, 1 ],
[ 0,−1, 1, 0, 1, 1, 1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1,−1,−1, 0,−1,−1 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 0, 1,−1, 0, 1, 1 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 1, 0,−1,−1,−1, 0 ],
[ 1, 1, 0,−1, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 1,−1, 0, 0, 1 ],
[ −1,−1,−1, 1, 0, 0,−1 ],
[ −1,−1, 0, 0, 0, 0,−1 ],
[ −1,−1, 0, 1, 0, 0,−1 ],
[ −1,−1, 0, 1, 1, 1, 0 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0,−1, 1, 0,−1,−1 ],
[ −1, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 1, 1 ],
[ 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1,−1, 0,−1,−1,−1 ],
[ 0, 1, 0,−1,−1,−1,−1 ],
[ 0, 1, 0, 0,−1,−1,−1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 1,−1,−1, 0, 0 ],
[ 1, 0, 1, 0,−1, 0, 0 ],
[ 1, 0, 1, 0, 0, 1, 1 ],
[ 1, 1, 0,−1,−1, 0, 0 ],
[ 1, 1, 0, 0,−1,−1, 0 ],
[ 1, 1, 1,−1,−1,−1, 0 ],
[ 1, 1, 1, 0,−1, 0, 1 ],
∗
5
• I ≡ P72 :
1
6
4
3
2




CI =


1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
1













b
CI =


109
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
1













b I =
Cox



0
1
1
1
0
1
−1
1
0
0
0
0
0
−1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
−1
−1
0
0
−1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
−1













BI =


1
1
0
0
0
1
−1
0
0
0
1
0
0
0
0
1
1
0
0
1
−1
0
1
0
0
0
0
0
0
−1
0
0
0
−1
0
0
0
0
−1
−1
0
0
0
1
0
0
−1
1
−1









Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 1,−1,−1, 1,−1,−1 ],
[ −1,−1, 0, −1, 1, 0, −1 ],
[ −1,−1, 0, 0, 1, 1, 0 ],
[ −1, 0, −1, −1, 1, 0, −1 ],
[ −1, 0, −1, 0, 1, −1, −1 ],
[ −1, 0, 0, −1, 0, −1, −1 ],
[ −1, 0, 0, −1, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 1, −1, 0, 0, −1, −1 ],
[ 0,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 1, 1 ],
[ 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, −1, 0,−1, −1, −1 ],
[ 0, 1, 0, −1,−1, −1, −1 ],
[ 0, 1, 0, 0,−1, −1, −1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 1,−1, 1, 1, 0, 1, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1,−1, 0, 1 ],
[ 1, 0, 0, 1, 0, 1, 2 ],
[ 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 1, 1,−1, 1, 1 ],
[ 1, 1, 0, 0,−1, 0, 0 ],
[ 1, 1, 1, 0,−1, 0, 1 ],
2.8
2.8.1
[ 1,−1, 1, 1,−1, 1, 1 ],
[ −1, −1, 0, 0, 0, 0,−1 ],
[ −1, 0,−1,−1, 0,−1,−2 ],
[ −1, 0,−1, 0, 0,−1,−2 ],
[ −1, 0,−1, 0, 1, 0,−1 ],
[ −1, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1,−1 ],
[ −1, 1,−1,−1, 0,−2,−2 ],
[ −1, 1, 0,−1, 0,−1,−1 ],
[ 0, −1, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 1, 0, 1, 0 ],
[ 0, −1, 1, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 1,−1, 0, 0,−1,−1 ],
[ 0, 1, 0,−1, 0,−1,−1 ],
[ 0, 1, 0, 0, −1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 1 ],
[ 1, −1, 1, 1, 0, 1, 2 ],
[ 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 1, −1, 1, 1 ],
[ 1, 0, 1, 0, −1, 0, 0 ],
[ 1, 0, 1, 0, 0, 1, 1 ],
[ 1, 0, 1, 1, −1, 1, 2 ],
[ 1, 1, 0, 0, −1, 0, 1 ],
[ 2, 0, 1, 1, −1, 1, 2 ]
[ −2, 0,−1,−1, 1,−1,−2 ],
[ −1,−1, 0, 0, 1, 0,−1 ],
[ −1, 0,−1,−1, 1,−1,−2 ],
[ −1, 0,−1, 0, 0,−1,−1 ],
[ −1, 0,−1, 0, 1, 0, 0 ],
[ −1, 0, 0,−1, 1,−1,−1 ],
[ −1, 0, 0, 0, 0, 0,−1 ],
[ −1, 1,−1,−1, 0,−1,−2 ],
[ 0,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 1, 0 ],
[ 0,−1, 0, 1, 0, 1, 1 ],
[ 0,−1, 1, 0, 0, 1, 1 ],
[ 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 1,−1, 0, 0,−1, 0 ],
[ 0, 1, 0,−1, 0,−1, 0 ],
[ 0, 1, 0, 0,−1, 0, 0 ],
[ 1,−1, 0, 1, 0, 1, 1 ],
[ 1,−1, 1, 1, 0, 2, 2 ],
[ 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 0,−1, 0, 1 ],
[ 1, 0, 1, 0, 0, 1, 2 ],
[ 1, 0, 1, 1, 0, 1, 2 ],
[ 1, 1, 0, 0, 0, 0, 1 ],
[ −1,−1,−1, 0, 1, 0,−1 ],
[ −1,−1, 0, 0, 1, 0, 0 ],
[ −1, 0,−1,−1, 1,−1,−1 ],
[ −1, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0,−1, 0,−1,−2 ],
[ −1, 0, 0,−1, 1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1,−1,−1, 0,−1,−1 ],
[ 0,−1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 1 ],
[ 0,−1, 0, 1, 1, 1, 1 ],
[ 0,−1, 1, 0, 1, 1, 1 ],
[ 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 1,−1,−1, 0,−1,−1 ],
[ 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0 ],
[ 1,−1, 1, 0, 0, 1, 1 ],
[ 1, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 1,−1, 0, 0 ],
[ 1, 0, 0, 1, 0, 1, 1 ],
[ 1, 0, 1, 0,−1, 1, 1 ],
[ 1, 0, 1, 1,−1, 0, 1 ],
[ 1, 1, 0, 0,−1,−1, 0 ],
[ 1, 1, 0, 1,−1, 0, 1 ],
Posets with 8 vertices
Posets of type A8
• I ≡ 0 A∗7 :
1
2





CI =



1
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
4
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
5
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
6
1
1
1
1
1
1
1
1
∗
7
















b
CI =



110
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1
0
 0

 0

BI = −10

 0
 0
0

0
0
0
−1
0
0
0
0











0
0
−1
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
−1
0
0
0
0
0
1
0
0

0
0
0
1
1
0
0
0











Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0,−1, 0 ],
• I ≡ 6 A∗7 :
1
2
3
[ −1, 0, 0, 0, 0, 0, 0,0 ],
[ −1, 0, 0, 0, 1, 0, 0,0 ],
[ −1, 1, 0, 0, 0, 0, 0,0 ],
[ 0,−1, 0, 0, 0, 0, 1,0 ],
[ 0,−1, 0, 1, 0, 0, 0,0 ],
[ 0, 0,−1, 0, 0, 0, 0,0 ],
[ 0, 0,−1, 0, 1, 0, 0,0 ],
[ 0, 0, 0,−1, 0, 0, 0,0 ],
[ 0, 0, 0,−1, 1, 0, 0,0 ],
[ 0, 0, 0, 0,−1, 0, 1,0 ],
[ 0, 0, 0, 0, 0,−1, 0,0 ],
[ 0, 0, 0, 0, 0, 0,−1,0 ],
[ 0, 0, 0, 0, 0, 0, 1,0 ],
[ 0, 0, 0, 0, 0, 1, 0,0 ],
[ 0, 0, 0, 0, 1, 0,−1,0 ],
[ 0, 0, 0, 1,−1, 0, 0,0 ],
[ 0, 0, 0, 1, 0, 0, 0,0 ],
[ 0, 0, 1, 0,−1, 0, 0,0 ],
[ 0, 0, 1, 0, 0, 0, 0,0 ],
[ 0, 1, 0,−1, 0, 0, 0,0 ],
[ 0, 1, 0, 0, 0, 0,−1,0 ],
[ 1,−1, 0, 0, 0, 0, 0,0 ],
[ 1, 0, 0, 0,−1, 0, 0,0 ],
[ 1, 0, 0, 0, 0, 0, 0,0 ],
4
5
[ −1, 0, 0, 0, 0, 0,1, 0 ],
[ −1, 0, 0, 1, 0, 0,0, 0 ],
[ 0,−1, 0, 0, 0, 0,0,−1 ],
[ 0,−1, 0, 0, 0, 1,0, 0 ],
[ 0,−1, 1, 0, 0, 0,0, 0 ],
[ 0, 0,−1, 0, 0, 0,1, 0 ],
[ 0, 0,−1, 1, 0, 0,0, 0 ],
[ 0, 0, 0,−1, 0, 0,1, 0 ],
[ 0, 0, 0, 0,−1, 0,0,−1 ],
[ 0, 0, 0, 0,−1, 1,0, 0 ],
[ 0, 0, 0, 0, 0,−1,1, 0 ],
[ 0, 0, 0, 0, 0, 0,0,−1 ],
[ 0, 0, 0, 0, 0, 0,1, 1 ],
[ 0, 0, 0, 0, 0, 1,0, 1 ],
[ 0, 0, 0, 0, 1, 0,0, 0 ],
[ 0, 0, 0, 1, 0,−1,0, 0 ],
[ 0, 0, 0, 1, 0, 0,0, 1 ],
[ 0, 0, 1, 0, 0,−1,0, 0 ],
[ 0, 0, 1, 0, 0, 0,0, 1 ],
[ 0, 1, 0, 0,−1, 0,0, 0 ],
[ 0, 1, 0, 0, 0, 0,0, 0 ],
[ 1, 0,−1, 0, 0, 0,0, 0 ],
[ 1, 0, 0, 0, 0,−1,0, 0 ],
[ 1, 0, 0, 0, 0, 0,0, 1 ]
∗
6
7





CI =








b
CoxI =



0
0
0
0
0
0
1
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
−1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
















BI =



Number of sincere Tits roots of poset I sI = 0.
111
1
1
1
1
1
1
0
0
0
0
−1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
−1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
−1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
−1











0
0
0
0
1
0
0
0










Table of roots of qbI
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
• I ≡ 5 A∗7 :
1
2
3
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
4





CI =








b
CoxI =



0
0
0
0
0
1
1
−1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
∗
5
6
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1, 1 ]
7
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
−1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
















BI =



−1
0
0
0
0
0
0
0
















b
CI =



0
0
1
1
1
0
0
0
0
0
0
0
0
−1
−1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
−1
−1
−1
−1
−1
−1
−1
−1
1

0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0










Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0,
[ −1, 0, 0, 0,
[ −1, 0, 1, 0,
[ 0,−1, 0, 0,
[ 0,−1, 0, 0,
[ 0, 0,−1, 0,
[ 0, 0,−1, 0,
[ 0, 0, 0,−1,
[ 0, 0, 0,−1,
0,−1, 0,−1 ],
0, 0, 0, 0 ],
0, 0, 0, 0 ],
0, 0,−1,−1 ],
1, 0, 0, 0 ],
0,−1, 0,−1 ],
0, 0, 0, 0 ],
0,−1, 0,−1 ],
0, 0, 0, 0 ],
[ −1, 0, 0, 0,
[ −1, 0, 0, 0,
[ −1, 1, 0, 0,
[ 0,−1, 0, 0,
[ 0,−1, 0, 1,
[ 0, 0,−1, 0,
[ 0, 0,−1, 0,
[ 0, 0, 0,−1,
[ 0, 0, 0,−1,
112
0,
1,
0,
0,
0,
0,
1,
0,
1,
0,−1,−1 ],
0, 0, 0 ],
0, 0, 0 ],
0, 0,−1 ],
0, 0, 0 ],
0,−1,−1 ],
0, 0, 0 ],
0,−1,−1 ],
0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,0,−1 ],
[ −1, 0, 0, 1, 0, 0,0, 0 ],
[ 0,−1, 0, 0, 0,−1,0,−1 ],
[ 0,−1, 0, 0, 0, 0,0, 0 ],
[ 0,−1, 1, 0, 0, 0,0, 0 ],
[ 0, 0,−1, 0, 0, 0,0,−1 ],
[ 0, 0,−1, 1, 0, 0,0, 0 ],
[ 0, 0, 0,−1, 0, 0,0,−1 ],
[ 0, 0, 0, 0,−1,−1,0,−1 ],
0
1
1
1
0
0
0
0











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
• I ≡ 4 A∗7 :
0, 0, 0,−1, 0,−1,−1 ],
0, 0, 0, 0,−1, 0,−1 ],
0, 0, 0, 0, 0,−1,−1 ],
0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 1,−1, 0 ],
0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 1, 0, 1 ],
0, 0, 1, 0, 0, 0, 1 ],
0, 1,−1, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 1 ],
1,−1, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 1, 0, 1 ],
0, 0,−1, 0, 0, 0, 0 ],
0, 0, 0, 0, 0, 0, 1 ],
1
2
3
5




b
CoxI =



0, 0,−1, 0, 0,−1 ],
0, 0, 0,−1, 0, 0 ],
0, 0, 0, 0,−1, 0 ],
0, 0, 0, 0, 1, 0 ],
0, 0, 0, 1, 0, 0 ],
0, 0, 1, 0, 0, 1 ],
0, 1,−1, 0, 0, 0 ],
0, 1, 0, 0, 1, 1 ],
1, 0,−1, 0, 0, 0 ],
1, 0, 0, 0, 1, 1 ],
0,−1, 0, 0, 0, 0 ],
0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 0 ],
0, 0,−1, 0, 0, 0 ],
0, 0, 0, 0, 1, 1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 1,
0, 1,
1, 0,
1, 0,
0,−1,
0, 0,
0, 0,
0,−1, 0,0, 0 ],
0, 0,−1,1, 0 ],
0, 0, 0,0,−1 ],
0, 0, 0,1, 1 ],
0, 0, 1,0, 1 ],
0, 1, 0,1, 1 ],
1, 0, 0,0, 0 ],
1, 0, 1,0, 1 ],
0, 0, 0,0, 0 ],
0, 0, 1,0, 1 ],
0,−1, 0,0, 0 ],
0, 0, 0,1, 1 ],
0, 0, 0,0, 0 ],
0, 0, 0,0, 0 ],
0, 0, 1,0, 1 ]
∗
7
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
−1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
−1




CI =



0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 1,
0, 1,
1,−1,
1, 0,
1, 0,
4
6
1
0
0
0
0
0
0
0


[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
















BI =



0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
−1
















bI =
C




1
1
1
1
1
1
1
−1
0
0
0
0
0
1
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0











1
1
1
0
1
1
1
−1
Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
113
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],











[
[
[
[
2.8.2
0,
0,
1,
1,
1,
1,
0,
0,
0, 0,
0, 0,
0,−1,
0, 0,
0,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1 ],
1 ],
0 ],
1 ],
[
[
[
[
0, 1,
1,−1,
1, 0,
1, 0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
0,
0,
0,
1 ],
0 ],
0 ],
1 ],
[
[
[
[
0,
1,
1,
1,
1, 0,
0,−1,
0, 0,
0, 0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
1 ],
0 ],
1 ],
1]
Posets of type D8
• I ≡ D∗7 :
2
3
4
5
6
∗
7
1





CI =



1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0





b
CoxI =



0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
−1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
−1
















b
CI =



0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
−1
−1
−1
−1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
−1
0
0
0
1
1
1
1
0






















Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1,−1, 0, 0, 0, 1,−1 ],
[ −1,−1, 0, 0, 0,−1, 1,−1 ],
[ −1,−1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0,−1, 0, 0,−1, 1,−1 ],
[ −1, 0,−1, 0, 0, 0, 1, 0 ],
[ −1, 0, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0,−1,−1, 1,−1 ],
[ −1, 0, 0, 0,−1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0,−1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0,−1, 0 ],
[ −1,−1, 0,−1, 0, 0,
[ −1,−1, 0, 0, 0, 0,
[ −1, 0,−1,−1, 0, 0,
[ −1, 0,−1, 0, 0, 0,
[ −1, 0, 0,−1,−1, 0,
[ −1, 0, 0,−1, 0, 0,
[ −1, 0, 0, 0,−1, 0,
[ −1, 0, 0, 0, 0,−1,
[ −1, 0, 0, 0, 0, 0,
[ 0,−1, 0, 0, 0, 0,
[ 0,−1, 0, 0, 0, 1,
[ 0,−1, 1, 0, 0, 0,
[ 0, 0,−1, 0, 0, 0,
[ 0, 0,−1, 1, 0, 0,
[ 0, 0, 0,−1, 0, 0,
[ 0, 0, 0, 0,−1, 0,
[ 0, 0, 0, 0,−1, 1,
[ 0, 0, 0, 0, 0,−1,
[ 0, 0, 0, 0, 0, 0,
[ 0, 0, 0, 0, 0, 0,
[ 0, 0, 0, 0, 0, 1,
[ 0, 0, 0, 0, 1, 0,
[ 0, 0, 0, 1, 0,−1,
[ 0, 0, 0, 1, 0, 0,
[ 0, 0, 1, 0, 0,−1,
[ 0, 0, 1, 0, 0, 0,
[ 0, 1, 0, 0,−1, 0,
[ 0, 1, 0, 0, 0, 0,
[ 1, 0, 0, 0, 0, 0,
114
1,−1 ],
0,−1 ],
1,−1 ],
0,−1 ],
1,−1 ],
1,−1 ],
0,−1 ],
0,−1 ],
0,−1 ],
0,−1 ],
0, 0 ],
0, 0 ],
1, 0 ],
0, 0 ],
1, 0 ],
0,−1 ],
0, 0 ],
1, 0 ],
0,−1 ],
1, 1 ],
0, 1 ],
0, 0 ],
0, 0 ],
0, 1 ],
0, 0 ],
0, 1 ],
0, 0 ],
0, 0 ],
0, 0 ],
[ −1,−1, 0, 0,−1, 0, 1,−1 ],
[ −1,−1, 0, 0, 0, 0, 1,−1 ],
[ −1, 0,−1, 0,−1, 0, 1,−1 ],
[ −1, 0,−1, 0, 0, 0, 1,−1 ],
[ −1, 0, 0,−1, 0,−1, 1,−1 ],
[ −1, 0, 0,−1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0,−1, 0, 1,−1 ],
[ −1, 0, 0, 0, 0,−1, 1,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[
[
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
1,
1,
1,
0,
0,
0,
0,
1,
1,
0,
0,
1,
0,
0,
0,
1,
0,
0,
0,
0,
0,
0,
1,
1,
0,
0,
0,
0,
0,
0,
1,−1,
0,−1,
1,−1,
0, 0,
0,−1,
1,−1,
0,−1,
1,−1,
0,−1,
0 ],
0 ],
1 ],
1 ],
0 ],
1 ],
0 ],
1 ],
1]
[
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
1,
1,
0,
0,
0,
0,
1,
1,
0,
0,
0,
0,
1,
1,
0,
0,
0,
0,
0,
1,
0,
0,
0,
1,
0,
1,
1,−1,
0,−1,
0,−1,
1,−1,
0,−1,
0,−1,
0,−1,
0,−1,
1 ],
1 ],
0 ],
1 ],
1 ],
1 ],
1 ],
1 ],
[
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
1,
1,
0,
0,
0,
0,
1,
1,
0,
0,
0,
0,
1,
1,
0,
1,
0,
1,
0,
1,
0,
1,
0,
0,
0,
0,
1, 0,
0, 0,
0,−1,
0,−1,
0, 0,
0,−1,
0, 0,
0,−1,
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1
• I ≡ 0 D∗7 A0 :
2





CI =



3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
5
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0





b I =
Cox




6
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
−1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
−1
∗
7
















bI =
C




0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
−1
0
0
0
1
1
1
1
0
−1
−1
−1
−1
−1
−1
−1
1






















Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 0, 0, 0, 0,−1 ],
[ −1,−1, 0, 0, 0, 1, 0,−1 ],
[ −1,−1, 0, 0, 1, 0, 0,−1 ],
[ −1,−1, 0, 0, 1, 1, 0, 0 ],
[ −1,−1, 0, 1, 0, 0, 1, 0 ],
[ −1,−1, 1, 0, 0, 0, 0,−1 ],
[ −1,−1, 1, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ −1,−1, 0, 0, 0, 0,
[ −1,−1, 0, 0, 0, 1,
[ −1,−1, 0, 0, 1, 0,
[ −1,−1, 0, 1, 0, 0,
[ −1,−1, 0, 1, 0, 1,
[ −1,−1, 1, 0, 0, 0,
[ −1,−1, 1, 0, 1, 0,
[ −1, 0, 0, 0, 0, 0,
[ −1, 0, 0, 0, 1, 0,
[ 0,−1, 0, 0, 0, 0,
[ 0,−1, 0, 0, 0, 1,
[ 0,−1, 1, 0, 0, 0,
[ 0, 0,−1, 0, 0, 0,
[ 0, 0,−1, 1, 0, 0,
[ 0, 0, 0,−1, 0, 0,
[ 0, 0, 0, 0,−1, 0,
[ 0, 0, 0, 0,−1, 1,
[ 0, 0, 0, 0, 0,−1,
[ 0, 0, 0, 0, 0, 0,
[ 0, 0, 0, 0, 0, 0,
[ 0, 0, 0, 0, 0, 1,
[ 0, 0, 0, 0, 1, 0,
[ 0, 0, 0, 1, 0,−1,
[ 0, 0, 0, 1, 0, 0,
[ 0, 0, 1, 0, 0,−1,
[ 0, 0, 1, 0, 0, 0,
115
1,−1 ],
0, 0 ],
0, 0 ],
0,−1 ],
0, 0 ],
0, 0 ],
0, 0 ],
0, 0 ],
0, 0 ],
0,−1 ],
0, 0 ],
0, 0 ],
1, 0 ],
0, 0 ],
1, 0 ],
0,−1 ],
0, 0 ],
1, 0 ],
0,−1 ],
1, 1 ],
0, 1 ],
0, 0 ],
0, 0 ],
0, 1 ],
0, 0 ],
0, 1 ],
[ −1,−1, 0, 0, 0, 0, 1, 0 ],
[ −1,−1, 0, 0, 0, 1, 1, 0 ],
[ −1,−1, 0, 0, 1, 0, 1, 0 ],
[ −1,−1, 0, 1, 0, 0, 0, 0 ],
[ −1,−1, 0, 1, 1, 0, 0, 0 ],
[ −1,−1, 1, 0, 0, 0, 1, 0 ],
[ −1,−1, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1, 0,−1, 0, 0, 0,
1, 0, 0, 0, 0,−1,
0,−1, 0, 0, 0, 0,
0, 0, 0, 0,−1, 0,
0, 0, 0, 0, 0, 0,
1,−1, 0, 0,−1, 0,
1,−1, 0, 0, 0, 0,
1, 0,−1, 0, 0,−1,
1, 0, 0,−1,−1, 0,
1, 0, 0,−1, 0, 0,
1, 0, 0, 0,−1, 0,
1, 0, 0, 0, 0, 0,
0 ],
0 ],
0 ],
0 ],
1 ],
0 ],
1 ],
0 ],
0 ],
1 ],
1 ],
1]
[
[
[
[
[
[
[
[
[
[
[
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1, 0, 0,−1, 0, 0,
1, 0, 0, 0, 0, 0,
0, 0,−1, 0, 0, 0,
0, 0, 0, 0, 0,−1,
1,−1,−1, 0, 0, 0,
1,−1, 0, 0, 0,−1,
1, 0,−1,−1, 0, 0,
1, 0,−1, 0, 0, 0,
1, 0, 0,−1, 0,−1,
1, 0, 0, 0,−1,−1,
1, 0, 0, 0, 0,−1,
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
[
[
[
[
[
[
[
[
[
[
[
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1, 0, 0, 0,−1, 0,
1, 0, 0, 0, 0, 0,
0, 0, 0,−1, 0, 0,
0, 0, 0, 0, 0, 0,
1,−1, 0,−1, 0, 0,
1,−1, 0, 0, 0, 0,
1, 0,−1, 0,−1, 0,
1, 0,−1, 0, 0, 0,
1, 0, 0,−1, 0, 0,
1, 0, 0, 0,−1, 0,
1, 0, 0, 0, 0,−1,
0 ],
1 ],
0 ],
0 ],
0 ],
0 ],
0 ],
1 ],
0 ],
0 ],
1 ],
1
• I≡
∗
0 D6
A1 :
2
3
4
5
∗
6
7





CI =



1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0

0
1
0
0
0
0
1
−1




b
CoxI =



0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
−1
















b
CI =



0
0
0
0
0
0
−1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
−1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
−1

0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1





















Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 0, 0, 0,−1,−2 ],
[ −1,−1, 0, 0, 0, 1,−1,−1 ],
[ −1,−1, 0, 0, 1, 0,−1,−1 ],
[ −1,−1, 0, 0, 1, 1, 0, 0 ],
[ −1,−1, 0, 1, 0, 0, 0, 0 ],
[ −1,−1, 1, 0, 0, 0,−1,−1 ],
[ −1,−1, 1, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ −1,−1, 0, 0, 0, 0,−1,−1 ],
[ −1,−1, 0, 0, 0, 1, 0,−1 ],
[ −1,−1, 0, 0, 1, 0, 0,−1 ],
[ −1,−1, 0, 1, 0, 0,−1,−1 ],
[ −1,−1, 0, 1, 0, 1, 0, 0 ],
[ −1,−1, 1, 0, 0, 0, 0,−1 ],
[ −1,−1, 1, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
116
[ −1,−1, 0, 0, 0, 0, 0,−1 ],
[ −1,−1, 0, 0, 0, 1, 0, 0 ],
[ −1,−1, 0, 0, 1, 0, 0, 0 ],
[ −1,−1, 0, 1, 0, 0, 0,−1 ],
[ −1,−1, 0, 1, 1, 0, 0, 0 ],
[ −1,−1, 1, 0, 0, 0, 0, 0 ],
[ −1,−1, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, 0, 1,−1, 0,
0, 0, 1, 0, 0,
0, 1, 0,−1, 0,
0, 1, 0, 0, 0,
1, 0,−1, 0, 0,
1, 0, 0, 0, 0,
0,−1, 0, 0, 0,
0, 0, 0, 0,−1,
0, 0, 0, 0, 0,
1,−1, 0, 0,−1,
1,−1, 0, 0, 0,
1, 0,−1, 0, 0,
1, 0, 0,−1,−1,
1, 0, 0,−1, 0,
1, 0, 0, 0,−1,
1, 0, 0, 0, 0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
0,
1,
0,
0,
1,
1,
1,
0 ],
1 ],
0 ],
1 ],
0 ],
0 ],
0 ],
0 ],
1 ],
0 ],
1 ],
0 ],
0 ],
1 ],
1 ],
2]
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, 0, 1, 0,−1,
0, 0, 1, 0, 0,
0, 1, 0, 0,−1,
0, 1, 0, 0, 0,
1, 0, 0,−1, 0,
1, 0, 0, 0, 0,
0, 0,−1, 0, 0,
0, 0, 0, 0, 0,
1,−1,−1, 0, 0,
1,−1, 0, 0, 0,
1, 0,−1,−1, 0,
1, 0,−1, 0, 0,
1, 0, 0,−1, 0,
1, 0, 0, 0,−1,
1, 0, 0, 0, 0,
0,
1,
0,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0 ],
1 ],
0 ],
1 ],
0 ],
1 ],
0 ],
0 ],
0 ],
0 ],
0 ],
1 ],
0 ],
0 ],
1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, 0, 1, 0, 0,
0, 1,−1, 0, 0,
0, 1, 0, 0, 0,
1,−1, 0, 0, 0,
1, 0, 0, 0,−1,
1, 0, 0, 0, 0,
0, 0, 0,−1, 0,
0, 0, 0, 0, 0,
1,−1, 0,−1, 0,
1,−1, 0, 0, 0,
1, 0,−1, 0,−1,
1, 0,−1, 0, 0,
1, 0, 0,−1, 0,
1, 0, 0, 0,−1,
1, 0, 0, 0, 0,
0,
0,
0,
0,
0,
1,
0,
0,
0,
0,
0,
1,
0,
0,
1,
0 ],
0 ],
0 ],
0 ],
0 ],
1 ],
0 ],
1 ],
0 ],
1 ],
0 ],
1 ],
1 ],
1 ],
1 ],
1
• I≡
∗
0 D5
A2 :
2
3
4
∗
5
6





CI =



1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
7
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0

0
1
0
0
0
1
1
−1




b I =
Cox




0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
−1
















bI =
C




0
0
0
0
0
−1
−1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
0
−1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
−1

0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1





















Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 0, 0,−1,−1,−2 ],
[ −1,−1, 0, 0, 0, 0,−1,−2 ],
[ −1,−1, 0, 0, 1,−1, 0,−1 ],
[ −1,−1, 0, 0, 1, 0, 0, 0 ],
[ −1,−1, 0, 1, 0, 0, 0,−1 ],
[ −1,−1, 1, 0, 0,−1, 0,−1 ],
[ −1,−1, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ −1,−1, 0, 0, 0,−1, 0,−2 ],
[ −1,−1, 0, 0, 0, 0,−1,−1 ],
[ −1,−1, 0, 0, 1, 0,−1,−1 ],
[ −1,−1, 0, 1, 0,−1, 0,−1 ],
[ −1,−1, 0, 1, 0, 0, 0, 0 ],
[ −1,−1, 1, 0, 0, 0,−1,−1 ],
[ −1,−1, 1, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
117
[ −1,−1, 0, 0, 0,−1, 0,−1 ],
[ −1,−1, 0, 0, 0, 0, 0,−1 ],
[ −1,−1, 0, 0, 1, 0, 0,−1 ],
[ −1,−1, 0, 1, 0, 0,−1,−1 ],
[ −1,−1, 0, 1, 1, 0, 0, 0 ],
[ −1,−1, 1, 0, 0, 0, 0,−1 ],
[ −1,−1, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, 0, 0, 0,
0, 0, 0, 0,
0, 0, 0, 0,
0, 0, 0, 1,
0, 0, 1,−1,
0, 0, 1, 0,
0, 1, 0,−1,
0, 1, 0, 0,
1, 0,−1, 0,
1, 0, 0, 0,
0,−1, 0, 0,
0, 0, 0, 0,
0, 0, 0, 0,
1,−1, 0, 0,
1,−1, 0, 0,
1, 0,−1, 0,
1, 0, 0,−1,
1, 0, 0,−1,
1, 0, 0, 0,
1, 0, 0, 0,
0,−1,
0, 1,
1, 0,
0, 0,
0, 0,
0, 1,
0, 0,
0, 1,
0, 0,
0, 0,
0, 0,
0, 0,
1, 0,
0, 0,
1, 0,
0, 0,
0, 0,
1, 0,
0, 1,
1, 1,
0 ],
0 ],
0 ],
1 ],
0 ],
1 ],
0 ],
1 ],
0 ],
1 ],
0 ],
0 ],
1 ],
0 ],
1 ],
1 ],
0 ],
1 ],
2 ],
2]
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, 0, 0, 0,
0, 0, 0, 0,
0, 0, 0, 0,
0, 0, 0, 1,
0, 0, 1, 0,
0, 0, 1, 0,
0, 1, 0, 0,
0, 1, 0, 0,
1, 0, 0,−1,
1, 0, 0, 0,
0, 0,−1, 0,
0, 0, 0, 0,
1,−1,−1, 0,
1,−1, 0, 0,
1, 0,−1,−1,
1, 0,−1, 0,
1, 0, 0,−1,
1, 0, 0, 0,
1, 0, 0, 0,
0,
0,
1,
0,
0,
1,
0,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
0,−1 ],
1, 1 ],
0, 1 ],
1, 1 ],
0, 0 ],
0, 1 ],
0, 0 ],
0, 1 ],
0, 0 ],
1, 1 ],
0, 0 ],
0, 1 ],
0, 0 ],
0, 1 ],
0, 0 ],
1, 1 ],
0, 1 ],
0, 1 ],
0, 1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, 0, 0, 0,
0, 0, 0, 0,
0, 0, 0, 1,
0, 0, 0, 1,
0, 0, 1, 0,
0, 1,−1, 0,
0, 1, 0, 0,
1,−1, 0, 0,
1, 0, 0, 0,
1, 0, 0, 0,
0, 0, 0,−1,
0, 0, 0, 0,
1,−1, 0,−1,
1,−1, 0, 0,
1, 0,−1, 0,
1, 0,−1, 0,
1, 0, 0,−1,
1, 0, 0, 0,
1, 0, 0, 0,
0, 0,
1,−1,
0, 0,
1, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
1, 0,
0, 0,
0, 1,
0, 0,
0, 1,
0, 0,
1, 0,
0, 1,
0, 1,
1, 0,
1 ],
0 ],
0 ],
1 ],
1 ],
0 ],
1 ],
0 ],
0 ],
1 ],
0 ],
1 ],
0 ],
1 ],
0 ],
1 ],
1 ],
1 ],
2 ],
1
• I≡
∗
0 D4
A3 :
2
3
5





CI =



1
0
0
0
0
0
0
0
∗
4
6
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
7
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0

0
1
0
0
1
1
1
−1




b
CoxI =



0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
−1
















bI =
C




0
0
0
0
−1
−1
−1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
−1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
−1

0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1





















Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0,
[ −1,−1, 0,
[ −1,−1, 0,
[ −1,−1, 0,
[ −1,−1, 0,
[ −1,−1, 1,
[ −1,−1, 1,
[ −1, 0, 0,
[ −1, 0, 0,
[ −1, 0, 1,
[ 0,−1, 0,
[ 0,−1, 0,
[ 0, 0,−1,
[ 0, 0,−1,
0,−1,−1, 0,−2 ],
0,−1, 0, 0,−1 ],
0, 0,−1, 0,−1 ],
0, 0, 0, 0,−1 ],
1, 0, 0,−1,−1 ],
0,−1, 0, 0,−1 ],
0, 0, 0, 0,−1 ],
0,−1, 0, 0,−1 ],
0, 0, 0, 0,−1 ],
0, 0, 0, 0, 0 ],
0, 0, 0,−1,−1 ],
1, 0, 0, 0, 0 ],
0, 0,−1, 0,−1 ],
0, 0, 0, 0, 0 ],
[ −1,−1, 0,
[ −1,−1, 0,
[ −1,−1, 0,
[ −1,−1, 0,
[ −1,−1, 0,
[ −1,−1, 1,
[ −1,−1, 1,
[ −1, 0, 0,
[ −1, 0, 0,
[ 0,−1, 0,
[ 0,−1, 0,
[ 0,−1, 1,
[ 0, 0,−1,
[ 0, 0,−1,
0,−1, 0,−1,−2 ],
0, 0,−1,−1,−2 ],
0, 0, 0,−1,−2 ],
1,−1, 0, 0,−1 ],
1, 0, 0, 0,−1 ],
0, 0,−1, 0,−1 ],
0, 0, 0, 0, 0 ],
0, 0,−1, 0,−1 ],
0, 0, 0, 0, 0 ],
0,−1, 0, 0,−1 ],
0, 0, 0, 0,−1 ],
0, 0, 0, 0, 0 ],
0, 0, 0,−1,−1 ],
1, 0, 0, 0, 0 ],
118
[ −1,−1, 0, 0,−1, 0, 0,−2 ],
[ −1,−1, 0, 0, 0,−1, 0,−2 ],
[ −1,−1, 0, 0, 0, 0,−1,−1 ],
[ −1,−1, 0, 1, 0,−1, 0,−1 ],
[ −1,−1, 0, 1, 0, 0, 0, 0 ],
[ −1,−1, 1, 0, 0, 0,−1,−1 ],
[ −1,−1, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, 0,−1, 0,−1, 0,−1 ],
0, 0,−1, 0, 0, 0, 0 ],
0, 0, 0,−1, 0, 1, 0 ],
0, 0, 0, 0,−1, 0, 0 ],
0, 0, 0, 0, 0,−1, 0 ],
0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 1, 0,−1, 0 ],
0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 0, 1, 0, 1 ],
0, 1, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 1, 0, 1 ],
1, 0,−1, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 1, 1 ],
0,−1, 0, 0, 0, 0, 0 ],
0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, 1 ],
1,−1, 0, 0, 0, 0, 1 ],
1,−1, 0, 1, 0, 0, 1 ],
1, 0,−1, 0, 0, 1, 1 ],
1, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 0, 1, 0, 1 ],
1, 0, 0, 1, 0, 0, 1 ],
1, 0, 0, 1, 1, 0, 2 ]
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, 0,−1, 0, 0,−1,−1 ],
0, 0, 0,−1, 0, 0,−1 ],
0, 0, 0,−1, 1, 0, 0 ],
0, 0, 0, 0,−1, 1, 0 ],
0, 0, 0, 0, 0, 0,−1 ],
0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 1, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 1, 0, 0, 1 ],
0, 1, 0, 0, 0, 0, 1 ],
0, 1, 0, 1, 0, 0, 1 ],
1, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 1, 0, 1 ],
0, 0,−1, 0, 0, 0, 0 ],
0, 0, 0, 0, 0, 1, 1 ],
1,−1,−1, 0, 0, 0, 0 ],
1,−1, 0, 0, 0, 1, 1 ],
1, 0,−1, 0, 0, 0, 0 ],
1, 0,−1, 0, 1, 0, 1 ],
1, 0, 0, 0, 0, 1, 1 ],
1, 0, 0, 0, 1, 0, 2 ],
1, 0, 0, 1, 0, 0, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, 0,−1, 0, 0, 0,−1 ],
0, 0, 0,−1, 0, 0, 0 ],
0, 0, 0, 0,−1, 0,−1 ],
0, 0, 0, 0, 0,−1,−1 ],
0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 1,−1, 0 ],
0, 0, 0, 1,−1, 0, 0 ],
0, 0, 0, 1, 0, 0, 1 ],
0, 0, 1, 0, 0, 1, 1 ],
0, 1,−1, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 1, 1 ],
1,−1, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 0, 0, 0, 0 ],
0, 0, 0, 0, 1, 0, 1 ],
1,−1, 0, 0, 0, 0, 0 ],
1,−1, 0, 0, 1, 0, 1 ],
1, 0,−1, 0, 0, 0, 1 ],
1, 0,−1, 1, 0, 0, 1 ],
1, 0, 0, 0, 0, 1, 2 ],
1, 0, 0, 0, 1, 1, 2 ],
1, 0, 0, 1, 0, 1, 2 ],
1
• I≡
∗
0 D3
A4 :
2
4





CI =



5
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
∗
3
6
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0

0
1
0
1
1
1
1
−1




b
CoxI =



0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
−1
















b
CI =



0
0
0
−1
−1
−1
−1
1
1
1
1
0
0
0
0
−1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
−1

0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1





















Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1, 0,
[ −1, 0,
[ −1, 0,
0,−1,−1, 0, 0,−2 ],
0,−1, 0, 0, 0,−2 ],
0, 0,−1, 0,−1,−2 ],
0, 0, 0,−1,−1,−2 ],
0, 0, 0, 0,−1,−2 ],
1,−1, 0, 0, 0,−1 ],
1, 0, 0, 0,−1,−1 ],
0,−1, 0, 0, 0,−1 ],
0, 0, 0, 0,−1,−1 ],
1, 0, 0, 0, 0, 0 ],
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1, 0,
[ −1, 0,
[ 0,−1,
0,−1, 0,−1, 0,−2 ],
0,−1, 0, 0, 0,−1 ],
0, 0,−1, 0, 0,−2 ],
0, 0, 0,−1, 0,−2 ],
0, 0, 0, 0,−1,−1 ],
1, 0,−1, 0, 0,−1 ],
1, 0, 0, 0, 0,−1 ],
0, 0,−1, 0, 0,−1 ],
0, 0, 0, 0, 0,−1 ],
0,−1, 0, 0, 0,−1 ],
119
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1, 0,
[ −1, 0,
[ 0,−1,
0,−1, 0, 0,−1,−2 ],
0, 0,−1,−1, 0,−2 ],
0, 0,−1, 0, 0,−1 ],
0, 0, 0,−1, 0,−1 ],
0, 0, 0, 0, 0,−1 ],
1, 0, 0,−1, 0,−1 ],
1, 0, 0, 0, 0, 0 ],
0, 0, 0,−1, 0,−1 ],
0, 0, 0, 0, 0, 0 ],
0, 0,−1, 0, 0,−1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,−1, 0, 0, 0,−1, 0,−1 ],
0,−1, 0, 0, 0, 0, 0, 0 ],
0, 0,−1, 0,−1, 0, 0,−1 ],
0, 0,−1, 0, 0, 0, 0,−1 ],
0, 0, 0,−1, 0, 0, 0, 0 ],
0, 0, 0,−1, 1, 0, 0, 0 ],
0, 0, 0, 0,−1, 0, 1, 0 ],
0, 0, 0, 0, 0,−1, 0, 0 ],
0, 0, 0, 0, 0, 0,−1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0,−1, 0 ],
0, 0, 0, 1,−1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 1, 0, 1 ],
1, 0,−1, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 1, 1 ],
1, 0, 0, 1, 0, 0, 0, 1 ],
1, 1,−1, 0, 0, 0, 1, 1 ],
1, 1,−1, 1, 0, 0, 0, 1 ],
1, 1, 0, 0, 0, 0, 1, 2 ],
1, 1, 0, 0, 0, 1, 1, 2 ],
1, 1, 0, 0, 1, 0, 1, 2 ],
1, 1, 0, 1, 0, 0, 0, 2 ],
1, 1, 0, 1, 1, 0, 0, 2 ]
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,−1, 0, 0, 0, 0,−1,−1 ],
0,−1, 1, 0, 0, 0, 0, 0 ],
0, 0,−1, 0, 0,−1, 0,−1 ],
0, 0,−1, 0, 0, 0, 0, 0 ],
0, 0, 0,−1, 0, 0, 1, 0 ],
0, 0, 0, 0,−1, 0, 0,−1 ],
0, 0, 0, 0,−1, 1, 0, 0 ],
0, 0, 0, 0, 0,−1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0,−1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0,−1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, 0, 1, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
1, 1,−1, 0, 0, 0, 0, 0 ],
1, 1,−1, 0, 0, 1, 0, 1 ],
1, 1, 0, 0, 0, 0, 0, 1 ],
1, 1, 0, 0, 0, 1, 0, 1 ],
1, 1, 0, 0, 1, 0, 0, 1 ],
1, 1, 0, 0, 1, 1, 0, 2 ],
1, 1, 0, 1, 0, 0, 1, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,−1, 0, 0, 0, 0, 0,−1 ],
0, 0,−1,−1, 0, 0, 0,−1 ],
0, 0,−1, 0, 0, 0,−1,−1 ],
0, 0, 0,−1, 0, 0, 0,−1 ],
0, 0, 0,−1, 0, 1, 0, 0 ],
0, 0, 0, 0,−1, 0, 0, 0 ],
0, 0, 0, 0, 0,−1, 0,−1 ],
0, 0, 0, 0, 0, 0,−1,−1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1,−1, 0 ],
0, 0, 0, 0, 1,−1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0,−1, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 1, 0, 1 ],
0, 1,−1, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 1, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 0, 1, 0, 0, 1 ],
1, 1,−1, 0, 0, 0, 0, 1 ],
1, 1,−1, 0, 1, 0, 0, 1 ],
1, 1, 0, 0, 0, 0, 1, 1 ],
1, 1, 0, 0, 0, 1, 0, 2 ],
1, 1, 0, 0, 1, 0, 0, 2 ],
1, 1, 0, 1, 0, 0, 0, 1 ],
1, 1, 0, 1, 0, 1, 0, 2 ],
1
• I≡
∗
0 D2
A5 :
2
3





CI =



4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
6
0
0
1
1
1
0
0
0





b
CoxI =



0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
−1
∗
7
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
−1
















bI =
C




1
1
0
0
0
0
0
−1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
−1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1






















Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1,−1,−1, 0, 0, 0,−2 ],
[ −1,−1,−1, 0, 0, 0,−1,−2 ],
[ −1,−1, 0,−1,−1, 0, 0,−2 ],
[ −1,−1, 0,−1, 0, 0, 0,−2 ],
[ −1,−1, 0, 0,−1, 0,−1,−2 ],
[ −1,−1, 0, 0, 0,−1,−1,−2 ],
[ −1,−1,−1, 0,−1, 0,
[ −1,−1,−1, 0, 0, 0,
[ −1,−1, 0,−1, 0,−1,
[ −1,−1, 0,−1, 0, 0,
[ −1,−1, 0, 0,−1, 0,
[ −1,−1, 0, 0, 0,−1,
120
0,−2 ],
0,−2 ],
0,−2 ],
0,−1 ],
0,−2 ],
0,−2 ],
[ −1,−1,−1, 0, 0,−1, 0,−2 ],
[ −1,−1,−1, 0, 0, 0, 0,−1 ],
[ −1,−1, 0,−1, 0, 0,−1,−2 ],
[ −1,−1, 0, 0,−1,−1, 0,−2 ],
[ −1,−1, 0, 0,−1, 0, 0,−1 ],
[ −1,−1, 0, 0, 0,−1, 0,−1 ],
[ −1,−1, 0, 0, 0, 0,−1,−2 ],
[ −1, 0,−1, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, 0, 1, 2 ],
[ 1, 1, 0, 0, 0, 1, 1, 2 ],
[ 1, 1, 0, 0, 1, 0, 1, 2 ],
[ 1, 1, 0, 1, 0, 0, 0, 2 ],
[ 1, 1, 0, 1, 1, 0, 0, 2 ],
[ 1, 1, 1, 0, 0, 0, 1, 2 ],
[ 1, 1, 1, 1, 0, 0, 0, 2 ]
1
• I ≡ 1 D∗7 A0 :




CI =



[ −1,−1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 1, 1 ],
[ 1, 0, 0, 1, 0, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 1, 0, 0, 0, 1, 0, 2 ],
[ 1, 1, 0, 0, 1, 0, 0, 2 ],
[ 1, 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 1, 0, 1, 0, 1, 0, 2 ],
[ 1, 1, 1, 0, 0, 0, 0, 2 ],
[ 1, 1, 1, 0, 1, 0, 0, 2 ],
2
3

[ −1,−1, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ 0,−1,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 1, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 1, 0, 0, 1, 1, 0, 2 ],
[ 1, 1, 0, 1, 0, 0, 1, 2 ],
[ 1, 1, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 1, 0, 0, 1, 0, 2 ],
1
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
5
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
6
1
1
1
1
1
1
0
0





b
CoxI =



1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
−1
∗
7
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
















b
CI =



1
1
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
−1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1






















Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
121
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 1,−1, 0, 0, 0, 0 ],
[ −1, 1, 1, 0,−1, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1,−1, 0, 0, 0, 1,−1 ],
[ 0,−1,−1, 0, 0, 1, 0, 0 ],
[ 0,−1,−1, 0, 1, 0, 0, 0 ],
[ 0,−1,−1, 1, 0, 0, 0,−1 ],
[ 0,−1,−1, 1, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 1,−1, 0,−1, 0, 0 ],
[ 0, 1, 1,−1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 1, 0, 0, 0,−1, 1 ],
[ 1,−1,−1, 0, 0, 0, 0, 0 ],
[ 1,−1,−1, 0, 1, 0, 0, 0 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ]
1
[ −1, 1, 1, 0, 0,−1, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 0, 1 ],
[ 0,−1,−1, 0, 0, 0, 1, 0 ],
[ 0,−1,−1, 0, 0, 1, 1, 0 ],
[ 0,−1,−1, 0, 1, 0, 1, 0 ],
[ 0,−1,−1, 1, 0, 0, 0, 0 ],
[ 0,−1,−1, 1, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 1,−1, 0, 0,−1, 0 ],
[ 0, 1, 1, 0,−1,−1, 0, 0 ],
[ 0, 1, 1, 0,−1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0,−1, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 0, 1 ],
[ 1,−1,−1, 0, 0, 0, 1, 0 ],
[ 1,−1,−1, 1, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0,−1, 0 ],
[ −1, 1, 1, 0, 0, 0,−1, 0 ],
[ 0,−1,−1, 0, 0, 0, 0,−1 ],
[ 0,−1,−1, 0, 0, 1, 0,−1 ],
[ 0,−1,−1, 0, 1, 0, 0,−1 ],
[ 0,−1,−1, 0, 1, 1, 0, 0 ],
[ 0,−1,−1, 1, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0,−1, 0 ],
[ 0, 1, 1,−1,−1, 0, 0, 0 ],
[ 0, 1, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 1, 0,−1, 0,−1, 0 ],
[ 0, 1, 1, 0, 0,−1,−1, 0 ],
[ 0, 1, 1, 0, 0, 0,−1, 0 ],
[ 1,−1,−1, 0, 0, 0, 0,−1 ],
[ 1,−1,−1, 0, 0, 1, 0, 0 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
2
• I ≡ 1 D∗6 A1 :
3
4
5
∗
6
7





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0





b
CoxI =



1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
−1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
















bI =
C




1
1
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
−1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
−1
Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
122
0
0
0
1
1
1
0
0











0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1











[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0,−1, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 0, 1 ],
[ 0,−1,−1, 0, 0, 0,−1,−1 ],
[ 0,−1,−1, 0, 0, 1, 0,−1 ],
[ 0,−1,−1, 0, 1, 0, 0,−1 ],
[ 0,−1,−1, 1, 0, 0,−1,−1 ],
[ 0,−1,−1, 1, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 1,−1, 0,−1, 0, 0 ],
[ 0, 1, 1,−1, 0, 0, 1, 1 ],
[ 0, 1, 1, 0,−1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0,−1, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1, 1 ],
[ 1,−1,−1, 0, 0, 0, 0,−1 ],
[ 1,−1,−1, 0, 1, 0, 0, 0 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1, 1 ]
1
• I≡
∗
1 D5
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0,−1, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 1, 1 ],
[ 0,−1,−1, 0, 0, 0, 0,−1 ],
[ 0,−1,−1, 0, 0, 1, 0, 0 ],
[ 0,−1,−1, 0, 1, 0, 0, 0 ],
[ 0,−1,−1, 1, 0, 0, 0,−1 ],
[ 0,−1,−1, 1, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 0, 1, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 1, 0,−1,−1, 0, 0 ],
[ 0, 1, 1, 0,−1, 0, 1, 1 ],
[ 0, 1, 1, 0, 0,−1, 1, 1 ],
[ 0, 1, 1, 0, 0, 0, 1, 2 ],
[ 1,−1,−1, 0, 0, 0, 0, 0 ],
[ 1,−1,−1, 1, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
2
A2 :
3
4
∗
5
6





CI =



[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 1,−1, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1,−1, 0, 0, 0,−1,−2 ],
[ 0,−1,−1, 0, 0, 1,−1,−1 ],
[ 0,−1,−1, 0, 1, 0,−1,−1 ],
[ 0,−1,−1, 0, 1, 1, 0, 0 ],
[ 0,−1,−1, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 1,−1,−1, 0, 0, 0 ],
[ 0, 1, 1,−1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 1, 0, 0, 0, 0, 1 ],
[ 1,−1,−1, 0, 0, 0,−1,−1 ],
[ 1,−1,−1, 0, 0, 1, 0, 0 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
7
1
1
1
1
1
0
0
0





b I =
Cox




0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
−1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
















bI =
C




1
1
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
Number of sincere Tits roots of poset I sI = 0.
123
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
−1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
−1
0
0
0
1
1
0
0
0











0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1











Table of roots of qbI
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0,−1, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 1, 1 ],
[ 0,−1,−1, 0, 0,−1, 0,−2 ],
[ 0,−1,−1, 0, 0, 0,−1,−1 ],
[ 0,−1,−1, 0, 1, 0,−1,−1 ],
[ 0,−1,−1, 1, 0,−1, 0,−1 ],
[ 0,−1,−1, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 0, 1, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 1,−1, 0, 1, 0, 1 ],
[ 0, 1, 1, 0,−1, 0, 1, 1 ],
[ 0, 1, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 1, 0, 0, 1, 0, 2 ],
[ 1,−1,−1, 0, 0, 0,−1,−1 ],
[ 1,−1,−1, 0, 1, 0, 0, 0 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 0, 1 ]
1
• I≡
∗
1 D4
3
∗
4
5




CI =



[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 1,−1, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 0, 1 ],
[ 0,−1,−1, 0, 0,−1,−1,−2 ],
[ 0,−1,−1, 0, 0, 0,−1,−2 ],
[ 0,−1,−1, 0, 1,−1, 0,−1 ],
[ 0,−1,−1, 0, 1, 0, 0, 0 ],
[ 0,−1,−1, 1, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 1,−1,−1, 0, 0, 0 ],
[ 0, 1, 1,−1, 0, 0, 1, 1 ],
[ 0, 1, 1, 0,−1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 1, 0, 1 ],
[ 1,−1,−1, 0, 0,−1, 0,−1 ],
[ 1,−1,−1, 0, 0, 0, 0, 0 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1, 1 ],
2
A3 :

[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 1, 0, 1 ],
[ 0,−1,−1, 0, 0,−1, 0,−1 ],
[ 0,−1,−1, 0, 0, 0, 0,−1 ],
[ 0,−1,−1, 0, 1, 0, 0,−1 ],
[ 0,−1,−1, 1, 0, 0,−1,−1 ],
[ 0,−1,−1, 1, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 0, 1, 1,−1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 1, 0,−1, 1, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1, 2 ],
[ 0, 1, 1, 0, 0, 1, 1, 2 ],
[ 1,−1,−1, 0, 0, 0, 0,−1 ],
[ 1,−1,−1, 1, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
6
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
7
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0





b
CoxI =



0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
−1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
















bI =
C




1
1
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
Number of sincere Tits roots of poset I sI = 0.
124
1
1
1
1
0
0
0
−1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
−1
0
0
0
1
0
0
0
0











0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1











Table of roots of qbI
[ −1, 0, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 1, 0, 1 ],
[ 0,−1,−1, 0,−1, 0,−1,−2 ],
[ 0,−1,−1, 0, 0,−1,−1,−2 ],
[ 0,−1,−1, 0, 0, 0,−1,−2 ],
[ 0,−1,−1, 1,−1, 0, 0,−1 ],
[ 0,−1,−1, 1, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 0, 1, 1,−1, 0, 0, 0, 1 ],
[ 0, 1, 1,−1, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1, 2 ],
[ 0, 1, 1, 0, 0, 1, 1, 2 ],
[ 0, 1, 1, 0, 1, 0, 1, 2 ],
[ 1,−1,−1, 0, 0,−1, 0,−1 ],
[ 1,−1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 1, 0, 0, 1 ]
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 0, 1 ],
[ −1, 1, 1, 0, 1, 0, 0, 1 ],
[ 0,−1,−1, 0,−1, 0, 0,−2 ],
[ 0,−1,−1, 0, 0,−1, 0,−2 ],
[ 0,−1,−1, 0, 0, 0,−1,−1 ],
[ 0,−1,−1, 1, 0,−1, 0,−1 ],
[ 0,−1,−1, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 1,−1, 0, 0, 1, 1 ],
[ 0, 1, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 1, 1, 0, 2 ],
[ 1,−1,−1, 0, 0, 0,−1,−1 ],
[ 1,−1,−1, 1, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1, 1 ],
1
• I≡
∗
1 D3
2
A4 :
∗
3
4





CI =



5
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
6
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 1,−1, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 1, 1 ],
[ 0,−1,−1, 0,−1,−1, 0,−2 ],
[ 0,−1,−1, 0,−1, 0, 0,−1 ],
[ 0,−1,−1, 0, 0,−1, 0,−1 ],
[ 0,−1,−1, 0, 0, 0, 0,−1 ],
[ 0,−1,−1, 1, 0, 0,−1,−1 ],
[ 0,−1, 0, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 0, 1, 1,−1, 0, 0, 0, 0 ],
[ 0, 1, 1,−1, 0, 1, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 1, 0, 0, 1, 0, 2 ],
[ 0, 1, 1, 0, 1, 0, 0, 2 ],
[ 1,−1,−1, 0,−1, 0, 0,−1 ],
[ 1,−1,−1, 0, 0, 0, 0,−1 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 0, 1 ],
7
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0





b
CoxI =



0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
−1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
















bI =
C




1
1
0
0
0
0
0
0
125
1
1
1
0
0
0
0
−1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
−1
0
0
0
1
1
1
1
0











0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1











Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 0, 1 ],
[ −1, 1, 1, 0, 1, 0, 0, 1 ],
[ 0,−1,−1,−1, 0,−1, 0,−2 ],
[ 0,−1,−1,−1, 0, 0, 0,−1 ],
[ 0,−1,−1, 0,−1, 0, 0,−2 ],
[ 0,−1,−1, 0, 0,−1, 0,−2 ],
[ 0,−1,−1, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 1, 0, 0, 1, 0, 2 ],
[ 0, 1, 1, 0, 1, 0, 0, 2 ],
[ 0, 1, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 0, 1, 0, 2 ],
[ 1,−1,−1, 0,−1, 0, 0,−1 ],
[ 1,−1,−1, 0, 0, 0, 0,−1 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1, 1 ],
[ 1, 0, 0, 1, 0, 0, 0, 1 ]
1
• I ≡ 2 D∗7 A0 :
2
[ −1, 0, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 1, 1 ],
[ −1, 1, 1, 1, 0, 0, 0, 1 ],
[ 0,−1,−1,−1, 0, 0,−1,−2 ],
[ 0,−1,−1, 0,−1,−1, 0,−2 ],
[ 0,−1,−1, 0,−1, 0, 0,−1 ],
[ 0,−1,−1, 0, 0,−1, 0,−1 ],
[ 0,−1,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 1, 2 ],
[ 0, 1, 1, 0, 0, 1, 1, 2 ],
[ 0, 1, 1, 0, 1, 0, 1, 2 ],
[ 0, 1, 1, 1, 0, 0, 0, 2 ],
[ 0, 1, 1, 1, 1, 0, 0, 2 ],
[ 1,−1,−1, 0, 0,−1, 0,−1 ],
[ 1,−1,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 0, 1 ],
3
4





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 1, 0, 1 ],
[ 0,−1,−1,−1,−1, 0, 0,−2 ],
[ 0,−1,−1,−1, 0, 0, 0,−2 ],
[ 0,−1,−1, 0,−1, 0,−1,−2 ],
[ 0,−1,−1, 0, 0,−1,−1,−2 ],
[ 0,−1,−1, 0, 0, 0,−1,−2 ],
[ 0,−1, 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0, 0,−1,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 1, 1, 0, 2 ],
[ 0, 1, 1, 1, 0, 0, 1, 2 ],
[ 1,−1,−1,−1, 0, 0, 0,−1 ],
[ 1,−1,−1, 0, 0, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 1, 0, 0, 1 ],
1
1
1
0
0
0
0
0
5
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
6
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
7
1
1
1
1
1
1
1
1
∗
















b
CI =



126
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1











Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0,−1, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0, 1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 1, 1,−1, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1,−1, 0, 0, 1,−1 ],
[ 0, 0,−1,−1, 0, 1, 0, 0 ],
[ 0, 0,−1,−1, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 1, 0,−1, 0, 0 ],
[ 0, 0, 1, 1, 0, 0,−1, 1 ],
[ 0, 1,−1,−1, 0, 0, 0, 0 ],
[ 0, 1,−1,−1, 1, 0, 0, 0 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0,−1,−1, 0, 0, 0,−1 ],
[ 1, 0,−1,−1, 0, 1, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0,−1, 0 ],
[ 1, 1,−1,−1, 0, 0, 0, 0 ]
1
• I≡
∗
2 D6
2
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0,−1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 0,−1, 0, 0 ],
[ 0,−1, 1, 1, 0, 0, 0, 1 ],
[ 0, 0,−1,−1, 0, 0, 1, 0 ],
[ 0, 0,−1,−1, 0, 1, 1, 0 ],
[ 0, 0,−1,−1, 1, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 0, 1, 1,−1,−1, 0, 0 ],
[ 0, 0, 1, 1,−1, 0, 0, 1 ],
[ 0, 0, 1, 1, 0,−1, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1,−1,−1, 0, 0, 1, 0 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0,−1,−1, 0, 0, 0, 0 ],
[ 1, 0,−1,−1, 1, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 1,−1, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 0,−1, 0 ],
[ 0, 0,−1,−1, 0, 0, 0,−1 ],
[ 0, 0,−1,−1, 0, 1, 0,−1 ],
[ 0, 0,−1,−1, 1, 0, 0,−1 ],
[ 0, 0,−1,−1, 1, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1,−1, 0,−1, 0 ],
[ 0, 0, 1, 1, 0,−1,−1, 0 ],
[ 0, 0, 1, 1, 0, 0,−1, 0 ],
[ 0, 1,−1,−1, 0, 0, 0,−1 ],
[ 0, 1,−1,−1, 0, 1, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0,−1, 0 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0,−1,−1, 0, 0, 1, 0 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
3
A1 :
4
5
∗
6
7





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
















b
CI =



127
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1











0
0
0
0
0
0
1
−1





b I =
Cox




1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
−1
1
1
1
1
1
1
1
−1











Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0,−1, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 1, 1,−1, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 0, 0, 1 ],
[ 0, 0,−1,−1, 0, 0,−1,−1 ],
[ 0, 0,−1,−1, 0, 1, 0,−1 ],
[ 0, 0,−1,−1, 1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 1,−1, 0, 0, 1 ],
[ 0, 0, 1, 1, 0,−1, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, 1, 1 ],
[ 0, 1,−1,−1, 0, 0, 0,−1 ],
[ 0, 1,−1,−1, 1, 0, 0, 0 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0,−1,−1, 0, 0,−1,−1 ],
[ 1, 0,−1,−1, 0, 1, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1,−1,−1, 0, 0, 0, 0 ]
1
• I≡
∗
2 D5
2
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 0,−1, 0, 0 ],
[ 0,−1, 1, 1, 0, 0, 1, 1 ],
[ 0, 0,−1,−1, 0, 0, 0,−1 ],
[ 0, 0,−1,−1, 0, 1, 0, 0 ],
[ 0, 0,−1,−1, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1,−1,−1, 0, 0 ],
[ 0, 0, 1, 1,−1, 0, 1, 1 ],
[ 0, 0, 1, 1, 0,−1, 1, 1 ],
[ 0, 0, 1, 1, 0, 0, 1, 2 ],
[ 0, 1,−1,−1, 0, 0, 0, 0 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 0,−1,−1, 0, 0, 0,−1 ],
[ 1, 0,−1,−1, 1, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
3
A2 :
4
∗
5
6





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 1,−1, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0, 1 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1,−1, 0, 0,−1,−2 ],
[ 0, 0,−1,−1, 0, 1,−1,−1 ],
[ 0, 0,−1,−1, 1, 0,−1,−1 ],
[ 0, 0,−1,−1, 1, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 1, 0,−1, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1,−1,−1, 0, 0,−1,−1 ],
[ 0, 1,−1,−1, 0, 1, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0,−1,−1, 0, 0, 0, 0 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1, 1 ],
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
7
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
















b
CI =



128
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1











0
0
0
0
0
1
1
−1





b I =
Cox




1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
−1
0
0
0
0
0
0
1
1
1
1
1
0
0
−1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1











Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 1, 0, 1 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 1, 1,−1, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 0, 1, 1 ],
[ 0, 0,−1,−1, 0,−1, 0,−2 ],
[ 0, 0,−1,−1, 0, 0,−1,−1 ],
[ 0, 0,−1,−1, 1, 0,−1,−1 ],
[ 0, 0,−1, 0, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 1,−1, 0, 1, 1 ],
[ 0, 0, 1, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, 1, 0, 1, 0, 2 ],
[ 0, 1,−1,−1, 0, 0,−1,−1 ],
[ 0, 1,−1,−1, 1, 0, 0, 0 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 0,−1,−1, 0,−1, 0,−1 ],
[ 1, 0,−1,−1, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 1,−1,−1, 0, 0, 0, 0 ]
1
• I≡
∗
2 D4
2
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 1, 0, 1 ],
[ 0, 0,−1,−1, 0,−1, 0,−1 ],
[ 0, 0,−1,−1, 0, 0, 0,−1 ],
[ 0, 0,−1,−1, 1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 1,−1, 0, 0, 0 ],
[ 0, 0, 1, 1,−1, 1, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, 1, 2 ],
[ 0, 0, 1, 1, 0, 1, 1, 2 ],
[ 0, 1,−1,−1, 0, 0, 0,−1 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0,−1,−1, 0, 0,−1,−1 ],
[ 1, 0,−1,−1, 1, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1, 1 ],
3
A3 :
∗
4
5





CI =



6
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 1,−1, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 0, 0, 1 ],
[ 0, 0,−1,−1, 0,−1,−1,−2 ],
[ 0, 0,−1,−1, 0, 0,−1,−2 ],
[ 0, 0,−1,−1, 1,−1, 0,−1 ],
[ 0, 0,−1,−1, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 1,−1, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 1, 0, 1 ],
[ 0, 1,−1,−1, 0,−1, 0,−1 ],
[ 0, 1,−1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0,−1,−1, 0, 0, 0,−1 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 0, 1 ],
7
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
















b
CI =



129
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
0
0
1
1
1
−1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
−1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1











Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 1, 0, 1 ],
[ 0, 0,−1,−1,−1, 0,−1,−2 ],
[ 0, 0,−1,−1, 0,−1,−1,−2 ],
[ 0, 0,−1,−1, 0, 0,−1,−2 ],
[ 0, 0,−1, 0,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, 1, 2 ],
[ 0, 0, 1, 1, 0, 1, 1, 2 ],
[ 0, 0, 1, 1, 1, 0, 1, 2 ],
[ 0, 1,−1,−1, 0,−1, 0,−1 ],
[ 0, 1,−1,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0,−1,−1,−1, 0, 0,−1 ],
[ 1, 0,−1,−1, 0, 0, 0,−1 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1, 1 ],
[ 1, 1,−1,−1, 0, 0, 0, 0 ]
1
• I ≡ 3 D∗7 A0 :
2
[ −1, 0, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 0, 0, 1 ],
[ 0,−1, 1, 1, 1, 0, 0, 1 ],
[ 0, 0,−1,−1,−1, 0, 0,−2 ],
[ 0, 0,−1,−1, 0,−1, 0,−2 ],
[ 0, 0,−1,−1, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 1, 0, 2 ],
[ 0, 1,−1,−1, 0, 0,−1,−1 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 0,−1,−1, 0,−1, 0,−1 ],
[ 1, 0,−1,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 0, 1 ],
3
4
5





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 1, 0, 1 ],
[ 0,−1, 0, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 1, 0, 0, 1, 1 ],
[ 0, 0,−1,−1,−1,−1, 0,−2 ],
[ 0, 0,−1,−1,−1, 0, 0,−1 ],
[ 0, 0,−1,−1, 0,−1, 0,−1 ],
[ 0, 0,−1,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, 1, 0, 1, 0, 2 ],
[ 0, 0, 1, 1, 1, 0, 0, 2 ],
[ 0, 1,−1,−1,−1, 0, 0,−1 ],
[ 0, 1,−1,−1, 0, 0, 0,−1 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0,−1,−1, 0, 0,−1,−1 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 1, 0, 0, 1 ],
1
1
1
0
1
0
0
0
6
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
7
1
1
1
1
1
1
1
1
∗
















b
CI =



130
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1











Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0,−1, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 1, 1,−1, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 0, 1 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 1, 1, 0,−1, 0 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1,−1, 1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1,−1, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 1,−1,−1, 0, 1, 0 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0,−1,−1, 0, 0,−1 ],
[ 0, 1, 0,−1,−1, 1, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1,−1, 0, 1, 0 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0,−1,−1, 0, 0, 0 ]
1
• I≡
∗
3 D6
2
[ −1, 0,−1, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 0,−1, 0 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1,−1, 0, 1,−1 ],
[ 0, 0, 0,−1,−1, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 0, 1, 1,−1,−1, 0 ],
[ 0, 0, 0, 1, 1, 0,−1, 0 ],
[ 0, 0, 1,−1,−1, 0, 0,−1 ],
[ 0, 0, 1,−1,−1, 1, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0,−1,−1, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0,−1, 0 ],
[ 0, 1, 1,−1,−1, 0, 0, 0 ],
[ 1, 0, 0,−1,−1, 0, 0,−1 ],
[ 1, 0, 0,−1,−1, 1, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
3
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1,−1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ 0,−1,−1, 1, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 1, 1,−1, 0, 0 ],
[ 0, 0,−1, 1, 1, 0, 0, 1 ],
[ 0, 0, 0,−1,−1, 0, 1, 0 ],
[ 0, 0, 0,−1,−1, 1, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 1,−1, 0, 0 ],
[ 0, 0, 0, 1, 1, 0,−1, 1 ],
[ 0, 0, 1,−1,−1, 0, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0,−1,−1, 0, 1, 0 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1,−1, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 1,−1,−1, 0, 0, 0 ],
4
A1 :
5
∗
6
7





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
















b
CI =



131
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1











0
0
0
0
0
0
1
−1





b I =
Cox




1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
−1
0
0
0
0
0
1
1
1
1
1
1
0
−1
1
1
1
1
1
1
1
−1











Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 1, 1,−1, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 1, 1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1,−1, 0,−1,−2 ],
[ 0, 0, 0,−1,−1, 1,−1,−1 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 1,−1, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1, 2 ],
[ 0, 0, 1,−1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0,−1,−1, 0,−1,−1 ],
[ 0, 1, 0,−1,−1, 1, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1,−1, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 1, 0,−1,−1, 0, 0, 0 ]
1
• I≡
∗
3 D5
2
[ −1, 0,−1, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 1, 1, 0, 0, 1 ],
[ 0, 0, 0,−1,−1, 0,−1,−1 ],
[ 0, 0, 0,−1,−1, 1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 1,−1, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 1,−1,−1, 0,−1,−1 ],
[ 0, 0, 1,−1,−1, 1, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 0,−1,−1, 0, 0,−1 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 1,−1,−1, 0, 0, 0 ],
[ 1, 0, 0,−1,−1, 0,−1,−1 ],
[ 1, 0, 0,−1,−1, 1, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1, 1 ],
3
4
A2 :
∗
5
6





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1,−1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 1, 1 ],
[ 0,−1,−1, 1, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 0, 1 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 1, 1,−1, 0, 0 ],
[ 0, 0,−1, 1, 1, 0, 1, 1 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1,−1, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1,−1, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 1, 1 ],
[ 0, 0, 1,−1,−1, 0, 0,−1 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0,−1,−1, 0, 0, 0 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1,−1, 0, 0,−1 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1,−1,−1, 0, 0, 0 ],
7
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
















b
CI =



132
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
0
0
0
1
1
−1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
−1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1











Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 1, 0, 1 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 1, 1, 0, 0, 1 ],
[ 0, 0, 0,−1,−1,−1,−1,−2 ],
[ 0, 0, 0,−1,−1, 0,−1,−2 ],
[ 0, 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 1, 2 ],
[ 0, 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 0, 1,−1,−1, 0, 0,−1 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 0,−1,−1,−1, 0,−1 ],
[ 0, 1, 0,−1,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1,−1, 0, 0,−1 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1, 1 ],
[ 1, 1, 0,−1,−1, 0, 0, 0 ]
1
• I ≡ 4 D∗7 A0 :
2
[ −1, 0,−1, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 0, 1 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 1, 1, 0, 1, 1 ],
[ 0, 0, 0,−1,−1,−1, 0,−2 ],
[ 0, 0, 0,−1,−1, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 0, 1,−1,−1,−1, 0,−1 ],
[ 0, 0, 1,−1,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0,−1,−1, 0,−1,−1 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 1,−1,−1, 0, 0, 0 ],
[ 1, 0, 0,−1,−1,−1, 0,−1 ],
[ 1, 0, 0,−1,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 0, 1 ],
3
4
5
6





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ 0,−1,−1, 1, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 1, 1 ],
[ 0, 0,−1, 0, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 1, 1, 0, 0, 0 ],
[ 0, 0,−1, 1, 1, 1, 0, 1 ],
[ 0, 0, 0,−1,−1,−1, 0,−1 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 1, 0, 1, 1 ],
[ 0, 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 0, 1,−1,−1, 0,−1,−1 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0,−1,−1, 0, 0,−1 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1,−1, 0,−1,−1 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1,−1,−1, 0, 0, 0 ],
1
1
1
1
1
1
1
0
7
1
1
1
1
1
1
1
1
∗
















b
CI =



133
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
−1
0
0
0
0
1
1
1
1
1
1
1
−1











Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0,−1, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 1, 1,−1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 1, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 1, 1, 0, 0 ],
[ 0, 0, 0, 0,−1,−1, 1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1,−1, 1 ],
[ 0, 0, 0, 1,−1,−1, 0, 0 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0,−1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0,−1,−1, 1, 0 ],
[ 0, 1, 0, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 1,−1,−1, 0, 0 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1,−1, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 0,−1,−1, 0, 0 ]
1
• I≡
∗
4 D6
2
[ −1, 0,−1, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 1, 0, 1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 1, 0, 1 ],
[ 0, 0, 0, 0,−1,−1, 1, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1,−1,−1, 1, 0 ],
[ 0, 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0,−1,−1, 1, 0 ],
[ 0, 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 0, 1, 1,−1,−1, 0, 0 ],
[ 0, 1, 0, 0,−1,−1, 0,−1 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 0,−1,−1, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1,−1, 1, 0 ],
[ 1, 0, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 1,−1,−1, 0, 0 ],
3
4
[ −1, 0, 0,−1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 1, 1,−1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0,−1,−1, 0, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 0, 1 ],
[ 0, 0,−1,−1, 1, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 1, 1,−1, 0 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 1, 1,−1, 0 ],
[ 0, 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1,−1, 0 ],
[ 0, 0, 0, 1,−1,−1, 0,−1 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0,−1,−1, 0,−1 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0,−1,−1, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1,−1, 0,−1 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0,−1,−1, 0, 0 ],
5
A1 :
∗
6
7





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
















b
CI =



134
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
0
0
0
0
1
−1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
−1
1
1
1
1
1
1
1
−1











Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 0,−1, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 0, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 1, 1, 0, 1 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 1, 1, 0, 1 ],
[ 0, 0, 0, 0,−1,−1,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 0, 1,−1,−1, 0,−1 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, 0,−1,−1, 0,−1 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0,−1,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1,−1,−1, 0, 0 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1,−1, 0,−1 ],
[ 1, 0, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1, 1 ],
[ 1, 1, 0, 0,−1,−1, 0, 0 ]
• I ≡ D∗7 :
2
3
4
[ −1, 0,−1, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 0, 1 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 1, 1, 1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 0, 0, 1, 1, 1, 2 ],
[ 0, 0, 0, 1,−1,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0,−1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1,−1,−1, 0, 0 ],
[ 0, 1, 0, 0,−1,−1,−1,−1 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0,−1,−1, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1,−1,−1, 0, 0 ],
5
6
7
[ −1, 0, 0,−1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0,−1,−1, 0, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 1, 1 ],
[ 0, 0,−1,−1, 1, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 1, 0, 0 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 1, 0, 0 ],
[ 0, 0, 0, 0,−1,−1,−1,−2 ],
[ 0, 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1,−1,−1,−1,−1 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0,−1,−1,−1,−1 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0,−1,−1, 0,−1 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1,−1,−1,−1 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0,−1,−1, 0, 0 ],
∗
1





CI =



1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
















b
CI =



135
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
1
1
1
1
1
0
−1
1
0
0
0
0
0
0
−1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
−1
−1
−1
−1
0
0
1
1
1
1
1
1
1
1
−1











Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1,−1,−1, 0, 0, 0, 1,−1 ],
[ −1,−1, 0, 0, 0,−1, 1,−1 ],
[ −1,−1, 0, 0, 0, 0, 1, 0 ],
[ −1, 0,−1, 0, 0,−1, 1,−1 ],
[ −1, 0,−1, 0, 0, 0, 1, 0 ],
[ −1, 0, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0,−1,−1, 1,−1 ],
[ −1, 0, 0, 0,−1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0,−1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 1,−1, 0 ],
[ 1, 0, 0, 0, 1, 0,−1, 0 ],
[ 1, 0, 0, 0, 1, 1,−1, 1 ],
[ 1, 0, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 0,−1, 0 ],
[ 1, 0, 1, 0, 0, 1,−1, 1 ],
[ 1, 1, 0, 0, 0, 0,−1, 0 ],
[ 1, 1, 0, 0, 0, 1,−1, 1 ],
[ 1, 1, 1, 0, 0, 0,−1, 1 ]
b ∗ A1 :
• I≡D
6
1
2
[ −1,−1, 0,−1, 0, 0, 1,−1 ],
[ −1,−1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0,−1,−1, 0, 0, 1,−1 ],
[ −1, 0,−1, 0, 0, 0, 0,−1 ],
[ −1, 0, 0,−1,−1, 0, 1,−1 ],
[ −1, 0, 0,−1, 0, 0, 1,−1 ],
[ −1, 0, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1,−1, 1 ],
[ 1, 0, 0, 0, 1, 0,−1, 1 ],
[ 1, 0, 0, 1, 0, 0,−1, 0 ],
[ 1, 0, 0, 1, 0, 1,−1, 1 ],
[ 1, 0, 1, 0, 0, 0,−1, 1 ],
[ 1, 0, 1, 0, 1, 0,−1, 1 ],
[ 1, 1, 0, 0, 0, 0,−1, 1 ],
[ 1, 1, 0, 0, 1, 0,−1, 1 ],
3
4
5
[ −1,−1, 0, 0,−1, 0, 1,−1 ],
[ −1,−1, 0, 0, 0, 0, 1,−1 ],
[ −1, 0,−1, 0,−1, 0, 1,−1 ],
[ −1, 0,−1, 0, 0, 0, 1,−1 ],
[ −1, 0, 0,−1, 0,−1, 1,−1 ],
[ −1, 0, 0,−1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0,−1, 0, 1,−1 ],
[ −1, 0, 0, 0, 0,−1, 1,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 0, 1, 0, 0,−1, 1 ],
[ 1, 0, 0, 1, 1, 0,−1, 1 ],
[ 1, 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 1, 0, 0,−1, 1 ],
[ 1, 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 1, 0, 0,−1, 1 ],
∗
6
7





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
















b
CI =



136
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
0
0
0
0
0
−1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
−1











Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 1, 0, 0, 1, 1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 1, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 1, 1, 1 ],
[ −1, 1, 1, 0, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1,−1,−1, 0, 0, 0,−1,−1 ],
[ 1,−1, 0, 0, 0,−1,−1,−1 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0,−1, 0, 0,−1,−1,−1 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0,−1,−1 ],
[ 1, 0, 0, 0,−1,−1,−1,−1 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ]
b ∗ A2 :
• I≡D
5
1
2
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 1, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 1, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 1, 0, 1, 1 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 1,−1, 0,−1, 0, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 0,−1,−1 ],
[ 1, 0,−1,−1, 0, 0,−1,−1 ],
[ 1, 0,−1, 0, 0, 0,−1,−1 ],
[ 1, 0, 0,−1,−1, 0,−1,−1 ],
[ 1, 0, 0,−1, 0, 0,−1, 0 ],
[ 1, 0, 0, 0,−1, 0,−1,−1 ],
[ 1, 0, 0, 0, 0,−1,−1,−1 ],
[ 1, 0, 0, 0, 0, 0,−1, 0 ],
3
4
∗
5
6





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 0, 1, 0, 1, 1 ],
[ −1, 0, 0, 1, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 0, 1, 1 ],
[ −1, 0, 1, 0, 0, 0, 1, 1 ],
[ −1, 0, 1, 1, 0, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 1, 1 ],
[ −1, 1, 0, 1, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 1,−1, 0, 0,−1, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 0,−1, 0 ],
[ 1, 0,−1, 0,−1, 0,−1,−1 ],
[ 1, 0,−1, 0, 0, 0,−1, 0 ],
[ 1, 0, 0,−1, 0,−1,−1,−1 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0,−1, 0 ],
[ 1, 0, 0, 0, 0,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
7
1
1
1
1
1
1
1
1
















b
CI =



137
1
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
0
0
0
1
0
−1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
−1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
−1











Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1,−1, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 1, 1 ],
[ −1, 0, 0, 1, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 0,−1, 1, 0 ],
[ −1, 0, 1, 0, 0, 0, 1, 1 ],
[ −1, 1, 0, 0, 0,−1, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 1, 1 ],
[ −1, 1, 1, 0, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 1,−1,−1, 0, 0, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 1,−1, 0 ],
[ 1, 0,−1, 0, 0, 0,−1,−1 ],
[ 1, 0,−1, 0, 0, 1,−1, 0 ],
[ 1, 0, 0,−1, 0, 0,−1, 0 ],
[ 1, 0, 0, 0,−1, 0,−1,−1 ],
[ 1, 0, 0, 0,−1, 1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 1, 0, 1 ]
b ∗ A3 :
• I≡D
4
1
2
[ −1, 0, 0, 0, 0,−1, 1,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 0,−1, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 1, 1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 1, 1 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 1,−1, 0,−1, 0, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 0,−1, 0 ],
[ 1, 0,−1,−1, 0, 0,−1,−1 ],
[ 1, 0,−1, 0, 0, 0,−1, 0 ],
[ 1, 0, 0,−1,−1, 0,−1,−1 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 1,−1, 0 ],
3





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
∗
4
5
6
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
[ −1, 0, 0, 0, 0,−1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 1, 1 ],
[ −1, 0, 1, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 1, 0, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 1, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 1,−1, 0, 0,−1, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0,−1, 0,−1, 0,−1,−1 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0,−1,−1 ],
[ 1, 0, 0,−1, 0, 1,−1, 0 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1,−1, 1 ],
7
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
















b
CI =



138
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
0
0
1
1
0
−1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
−1
0
0
0
0
1
0
0
0
0
0
0
0
−1
0
0
1
1
1
1
1
1
1
1
−1











Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0, 0,−1,−1, 1,−1 ],
[ −1, 0, 0, 0,−1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0,−1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 0,−1, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 0,−1, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 1, 0 ],
[ −1, 1, 1, 0, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 1,−1,−1, 0, 0, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 0,−1, 0 ],
[ 1,−1, 0, 0, 1, 0,−1, 0 ],
[ 1, 0,−1, 0, 0, 0,−1, 0 ],
[ 1, 0,−1, 0, 1, 0,−1, 0 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 1,−1, 0 ],
[ 1, 0, 0, 0, 1, 0,−1, 0 ],
[ 1, 0, 0, 0, 1, 1,−1, 1 ]
b ∗ A4 :
• I≡D
3
1
2
4





CI =



1
1
0
0
0
0
0
0
6
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
[ −1, 0, 0, 0,−1, 0, 1,−1 ],
[ −1, 0, 0, 0, 0,−1, 1,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0,−1, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 1, 1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],
[ 1,−1, 0, 0, 0, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 1,−1, 0 ],
[ 1, 0,−1, 0, 0, 0,−1,−1 ],
[ 1, 0,−1, 0, 0, 1,−1, 0 ],
[ 1, 0, 0,−1, 0, 0,−1, 0 ],
[ 1, 0, 0,−1, 1, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 1, 0, 0, 1 ],
∗
3
5
1
0
0
0
0
0
0
0
[ −1, 0, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 1,−1, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 0,−1, 1, 0 ],
[ −1, 0, 1, 0, 0, 0, 1, 1 ],
[ −1, 1, 0, 0, 0,−1, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 1, 1 ],
[ 0,−1, 0, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 1,−1, 0,−1, 0, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0,−1,−1, 0, 0,−1,−1 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0,−1,−1 ],
[ 1, 0, 0,−1, 0, 1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1,−1, 1 ],
[ 1, 0, 0, 0, 1, 0,−1, 1 ],
7
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
















b
CI =



139
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
0
1
1
1
0
−1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
−1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
−1
−1
0
0
1
1
1
1
1
1
1
1
−1











Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0, 0,−1,−1, 0, 1,−1 ],
[ −1, 0, 0,−1, 0, 0, 1,−1 ],
[ −1, 0, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 1,−1, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0,−1, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 1, 1 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0,−1, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 1,−1,−1, 0, 0, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1,−1, 0, 1, 0, 0,−1, 0 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0,−1, 1, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 0, 1, 0, 0,−1, 1 ],
[ 1, 0, 0, 1, 1, 0,−1, 1 ]
b ∗ A5 :
• I≡D
2
[ −1, 0, 0,−1, 0,−1, 1,−1 ],
[ −1, 0, 0,−1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0,−1, 0, 1,−1 ],
[ −1, 0, 0, 0, 0,−1, 1,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0,−1, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 0,−1, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],
[ 1,−1, 0, 0, 0, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 1,−1, 0 ],
[ 1, 0,−1, 0, 0, 0,−1,−1 ],
[ 1, 0,−1, 0, 0, 1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 1,−1, 0 ],
[ 1, 0, 0, 0, 1, 0,−1, 0 ],
[ 1, 0, 0, 0, 1, 1,−1, 1 ],
[ 1, 0, 0, 1, 0, 0, 0, 1 ],
1
3





CI =



4
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
∗
2
5
6
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
[ −1, 0, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0,−1,−1, 1,−1 ],
[ −1, 0, 0, 0,−1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0,−1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 0,−1, 1, 0 ],
[ −1, 0, 1, 0, 0, 0, 1, 1 ],
[ −1, 1, 0, 0, 0,−1, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 1, 1 ],
[ 0,−1, 0, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0, 0,−1,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 1,−1, 0, 0, 0, 0,−1, 0 ],
[ 1,−1, 0, 0, 1, 0,−1, 0 ],
[ 1, 0,−1, 0, 0, 0,−1, 0 ],
[ 1, 0,−1, 0, 1, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1,−1, 1 ],
[ 1, 0, 0, 0, 1, 0,−1, 1 ],
[ 1, 0, 0, 1, 0, 0,−1, 0 ],
[ 1, 0, 0, 1, 0, 1,−1, 1 ],
7
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
















b
CI =



140
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
1
1
1
1
0
−1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
−1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
−1
−1
−1
0
0
1
1
1
1
1
1
1
1
−1











Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −1, 0,−1,−1, 0, 0, 1,−1 ],
[ −1, 0,−1, 0, 0, 0, 0,−1 ],
[ −1, 0, 0,−1,−1, 0, 1,−1 ],
[ −1, 0, 0,−1, 0, 0, 1,−1 ],
[ −1, 0, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 1,−1, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 0,−1, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 1, 1 ],
[ 0,−1, 0, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],
[ 1,−1, 0, 0, 0, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 1,−1, 0 ],
[ 1,−1, 1, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 0, 1, 0, 0,−1, 1 ],
[ 1, 0, 0, 1, 1, 0,−1, 1 ],
[ 1, 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 1, 0, 0,−1, 1 ]
[ −1, 0,−1, 0,−1, 0, 1,−1 ],
[ −1, 0,−1, 0, 0, 0, 1,−1 ],
[ −1, 0, 0,−1, 0,−1, 1,−1 ],
[ −1, 0, 0,−1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0,−1, 0, 1,−1 ],
[ −1, 0, 0, 0, 0,−1, 1,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0,−1, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 1,−1, 0, 0, 0, 0,−1, 0 ],
[ 1,−1, 0, 0, 1, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 1,−1, 0 ],
[ 1, 0, 0, 0, 1, 0,−1, 0 ],
[ 1, 0, 0, 0, 1, 1,−1, 1 ],
[ 1, 0, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, 0,−1, 0 ],
[ 1, 0, 1, 0, 0, 1,−1, 1 ],
141
[ −1, 0,−1, 0, 0,−1, 1,−1 ],
[ −1, 0,−1, 0, 0, 0, 1, 0 ],
[ −1, 0, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0,−1,−1, 1,−1 ],
[ −1, 0, 0, 0,−1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0,−1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, 0,−1, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 0, 1 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1,−1, 0, 1, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1,−1, 1 ],
[ 1, 0, 0, 0, 1, 0,−1, 1 ],
[ 1, 0, 0, 1, 0, 0,−1, 0 ],
[ 1, 0, 0, 1, 0, 1,−1, 1 ],
[ 1, 0, 1, 0, 0, 0,−1, 1 ],
[ 1, 0, 1, 0, 1, 0,−1, 1 ],
2.8.3
Posets of type E8
∗
7
6
• I ≡ P73 :
5
4
1
3
2





CI =








b I =
Cox




0
1
1
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
−1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
−1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1
















b
CI =



1
0
0
1
1
1
1
0
















BI =



0
1
1
1
1
1
1
0
1
0
1
2
2
1
0
1
0
0
1
1
1
1
1
0
1
1
1
2
2
1
1
0
0
0
0
1
1
1
1
0
1
0
1
2
1
1
0
0
0
0
0
0
1
1
1
0
−1
0
0
−1
−1
−1
0
0
0
0
0
0
0
1
1
0
0
0
−1
−1
−1
0
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
0
−1
0
0
0
−1











−1
0
−1
−1
−1
−1
−1
0
1
0
0
1
1
0
0
0
Number of sincere Tits roots of poset I sI = 22.
Table of roots of qbI
[ −3,−2,−2, 1, 1, 1, 1,−2 ],
[ −3,−2,−2, 1, 1, 2, 1,−1 ],
[ −3,−2,−1, 1, 1, 1, 1,−1 ],
[ −2,−2,−1, 1, 1, 1, 1,−1 ],
[ 2, 2, 1,−1,−1,−1,−1, 1 ],
[ 3, 2, 1,−1,−1,−1,−1, 1 ],
[ 3, 2, 2,−1,−1,−2,−1, 1 ],
[ 3, 2, 2,−1,−1,−1,−1, 2 ],
[ −2, −2, −1, 1, 1, 0, 1, −1 ],
[ −2, −1, −2, 0, 1, 1, 1, −1 ],
[ −2, −1, −2, 1, 1, 1, 0, −1 ],
[ −2, −1, −1, 0, 1, 0, 1, −1 ],
[ −2, −1, −1, 0, 1, 1, 1, 0 ],
[ −2, −1, −1, 1, 0, 1, 1, −1 ],
[ −2, −1, −1, 1, 1, 0, 1, −1 ],
[ −2, −1, −1, 1, 1, 1, 0, 0 ],
[ −1, −1, −1, 0, 0, 1, 0, −1 ],
[ −1, −1, −1, 0, 1, 0, 0, −1 ],
[ −1, −1, −1, 0, 1, 1, 0, −1 ],
[ −1, −1, −1, 1, 0, 0, 0, −1 ],
[ −1, −1, −1, 1, 0, 1, 0, −1 ],
[ −1, −1, −1, 1, 1, 0, 0, −1 ],
[ −3,−2,−2, 1, 1, 1, 1,−1 ],
[ −3,−2,−2, 1, 2, 1, 1,−1 ],
[ −3,−1,−2, 1, 1, 1, 1,−1 ],
[ −2,−1,−2, 1, 1, 1, 1,−1 ],
[ 2, 2, 2,−1,−1,−1,−1, 1 ],
[ 3, 2, 2,−2,−1,−1,−1, 1 ],
[ 3, 2, 2,−1,−1,−1,−2, 1 ],
[ −2, −2, −1, 0, 1, 1, 1, −1 ],
[ −2, −2, −1, 1, 1, 1, 0, −1 ],
[ −2, −1, −2, 1, 0, 1, 1, −1 ],
[ −2, −1, −2, 1, 1, 1, 1, 0 ],
[ −2, −1, −1, 0, 1, 1, 0, −1 ],
[ −2, −1, −1, 1, 0, 0, 1, −1 ],
[ −2, −1, −1, 1, 0, 1, 1, 0 ],
[ −2, −1, −1, 1, 1, 0, 1, 0 ],
[ −2, −1, −1, 1, 1, 1, 1, 0 ],
[ −1, −1, −1, 0, 0, 1, 1, −1 ],
[ −1, −1, −1, 0, 1, 0, 1, −1 ],
[ −1, −1, −1, 0, 1, 1, 0, 0 ],
[ −1, −1, −1, 1, 0, 0, 1, −1 ],
[ −1, −1, −1, 1, 0, 1, 0, 0 ],
[ −1, −1, −1, 1, 1, 0, 0, 0 ],
142
[ −3,−2,−2, 1, 1, 1, 2,−1 ],
[ −3,−2,−2, 2, 1, 1, 1,−1 ],
[ −2,−2,−2, 1, 1, 1, 1,−1 ],
[ 2, 1, 2,−1,−1,−1,−1, 1 ],
[ 3, 1, 2,−1,−1,−1,−1, 1 ],
[ 3, 2, 2,−1,−2,−1,−1, 1 ],
[ 3, 2, 2,−1,−1,−1,−1, 1 ],
[ −2, −2, −1, 1, 0, 1, 1, −1 ],
[ −2, −2, −1, 1, 1, 1, 1, 0 ],
[ −2, −1, −2, 1, 1, 0, 1, −1 ],
[ −2, −1, −1, 0, 0, 1, 1, −1 ],
[ −2, −1, −1, 0, 1, 1, 1, −1 ],
[ −2, −1, −1, 1, 0, 1, 0, −1 ],
[ −2, −1, −1, 1, 1, 0, 0, −1 ],
[ −2, −1, −1, 1, 1, 1, 0, −1 ],
[ −1, −1, −1, 0, 0, 0, 1, −1 ],
[ −1, −1, −1, 0, 0, 1, 1, 0 ],
[ −1, −1, −1, 0, 1, 0, 1, 0 ],
[ −1, −1, −1, 0, 1, 1, 1, 0 ],
[ −1, −1, −1, 1, 0, 0, 1, 0 ],
[ −1, −1, −1, 1, 0, 1, 1, 0 ],
[ −1, −1, −1, 1, 1, 0, 1, 0 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, −1, −1, 1, 1, 1, 0,
−1, −1, 0, 0, 0, 0, 1,
−1, −1, 0, 0, 0, 1, 1,
−1, −1, 0, 0, 1, 0, 1,
−1, −1, 0, 1, 0, 0, 0,
−1, −1, 0, 1, 1, 0, 0,
−1, 0, −1, 0, 0, 0, 1,
−1, 0, −1, 0, 0, 1, 1,
−1, 0, −1, 0, 1, 0, 1,
−1, 0, −1, 1, 0, 0, 0,
−1, 0, −1, 1, 1, 0, 0,
−1, 0, 0, 0, 0, 0, 1,
−1, 0, 0, 1, 0, 0, 0,
0, −1, 0, 0, 0, 0, 1,
0, −1, 0, 1, 0, 0, 0,
0, 0, −1, 0, 0, 0, 0,
0, 0, −1, 0, 1, 0, 0,
0, 0, 0, −1, 0, 0, 0,
0, 0, 0, −1, 1, 0, 0,
0, 0, 0, 0, −1, 0, 1,
0, 0, 0, 0, 0, −1, 0,
0, 0, 0, 0, 0, 0, −1,
0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, −1,
0, 0, 0, 1, −1, 0, 0,
0, 0, 0, 1, 0, 0, 0,
0, 0, 1, 0, −1, 0, 0,
0, 0, 1, 0, 0, 0, 0,
0, 1, 0, −1, 0, 0, 0,
0, 1, 0, 0, 0, 0, −1,
1, 0, 0, −1, 0, 0, 0,
1, 0, 0, 0, 0, 0, −1,
1, 0, 1, −1, −1, 0, 0,
1, 0, 1, −1, 0, 0, 0,
1, 0, 1, 0, −1, 0, −1,
1, 0, 1, 0, 0, −1, −1,
1, 0, 1, 0, 0, 0, −1,
1, 1, 0, −1, −1, 0, 0,
1, 1, 0, −1, 0, 0, 0,
1, 1, 0, 0, −1, 0, −1,
1, 1, 0, 0, 0, −1, −1,
1, 1, 0, 0, 0, 0, −1,
1, 1, 1, −1, −1, −1, 0,
1, 1, 1, −1, −1, 0, 0,
1, 1, 1, −1, 0, −1, 0,
1, 1, 1, −1, 0, 0, 0,
1, 1, 1, 0, −1, −1, 0,
1, 1, 1, 0, −1, 0, 0,
1, 1, 1, 0, 0, −1, 0,
2, 1, 1, −1, −1, −1, 0,
2, 1, 1, −1, −1, 0, −1,
2, 1, 1, −1, 0, −1, −1,
2, 1, 1, 0, −1, −1, −1,
2, 1, 1, 0, −1, 0, −1,
2, 1, 2, −1, −1, −1, 0,
2, 1, 2, 0, −1, −1, −1,
2, 2, 1, −1, −1, 0, −1,
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
0 ],
1 ],
1 ],
0 ],
1 ],
1 ],
1 ],
1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, −1, 0, 0, 0, 0, 0, −1 ],
−1, −1, 0, 0, 0, 1, 0, −1 ],
−1, −1, 0, 0, 1, 0, 0, −1 ],
−1, −1, 0, 0, 1, 1, 0, 0 ],
−1, −1, 0, 1, 0, 0, 1, 0 ],
−1, 0, −1, 0, 0, 0, 0, −1 ],
−1, 0, −1, 0, 0, 1, 0, −1 ],
−1, 0, −1, 0, 1, 0, 0, −1 ],
−1, 0, −1, 0, 1, 1, 0, 0 ],
−1, 0, −1, 1, 0, 0, 1, 0 ],
−1, 0, 0, 0, 0, 0, 0, −1 ],
−1, 0, 0, 0, 0, 1, 0, 0 ],
0, −1, 0, 0, 0, 0, 0, −1 ],
0, −1, 0, 0, 0, 1, 0, 0 ],
0, −1, 1, 0, 0, 0, 0, 0 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, −1, 1, 0, 0, 0, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, −1, 1, 0, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, −1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, −1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 1, −1, 0, −1, 0, 0 ],
1, 0, 1, −1, 0, 0, 0, 1 ],
1, 0, 1, 0, −1, 0, 0, 0 ],
1, 0, 1, 0, 0, −1, 0, 0 ],
1, 0, 1, 0, 0, 0, −1, 1 ],
1, 1, 0, −1, 0, −1, 0, 0 ],
1, 1, 0, −1, 0, 0, 0, 1 ],
1, 1, 0, 0, −1, 0, 0, 0 ],
1, 1, 0, 0, 0, −1, 0, 0 ],
1, 1, 0, 0, 0, 0, −1, 1 ],
1, 1, 1, −1, −1, 0, −1, 0 ],
1, 1, 1, −1, 0, −1, −1, 0 ],
1, 1, 1, −1, 0, 0, −1, 0 ],
1, 1, 1, 0, −1, −1, −1, 0 ],
1, 1, 1, 0, −1, 0, −1, 0 ],
1, 1, 1, 0, 0, −1, −1, 0 ],
1, 1, 1, 0, 0, 0, −1, 1 ],
2, 1, 1, −1, −1, −1, 0, 1 ],
2, 1, 1, −1, −1, 0, 0, 1 ],
2, 1, 1, −1, 0, −1, 0, 1 ],
2, 1, 1, 0, −1, −1, −1, 1 ],
2, 1, 1, 0, 0, −1, −1, 1 ],
2, 1, 2, −1, −1, 0, −1, 1 ],
2, 2, 1, −1, −1, −1, −1, 0 ],
2, 2, 1, −1, 0, −1, −1, 1 ],
143
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, −1, 0, 0, 0, 0, 1, −1 ],
−1, −1, 0, 0, 0, 1, 0, 0 ],
−1, −1, 0, 0, 1, 0, 0, 0 ],
−1, −1, 0, 1, 0, 0, 0, −1 ],
−1, −1, 0, 1, 0, 1, 0, 0 ],
−1, 0, −1, 0, 0, 0, 1, −1 ],
−1, 0, −1, 0, 0, 1, 0, 0 ],
−1, 0, −1, 0, 1, 0, 0, 0 ],
−1, 0, −1, 1, 0, 0, 0, −1 ],
−1, 0, −1, 1, 0, 1, 0, 0 ],
−1, 0, 0, 0, 0, 0, 0, 0 ],
−1, 0, 0, 0, 1, 0, 0, 0 ],
0, −1, 0, 0, 0, 0, 0, 0 ],
0, −1, 0, 0, 1, 0, 0, 0 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 1, 0, 0 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 1, 0, 0 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1, −1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 1, −1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 1, −1, 0, 0, −1, 0 ],
1, 0, 1, 0, −1, −1, 0, 0 ],
1, 0, 1, 0, −1, 0, 0, 1 ],
1, 0, 1, 0, 0, −1, 0, 1 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 1, 0, −1, 0, 0, −1, 0 ],
1, 1, 0, 0, −1, −1, 0, 0 ],
1, 1, 0, 0, −1, 0, 0, 1 ],
1, 1, 0, 0, 0, −1, 0, 1 ],
1, 1, 0, 0, 0, 0, 0, 1 ],
1, 1, 1, −1, −1, 0, 0, 0 ],
1, 1, 1, −1, 0, −1, 0, 0 ],
1, 1, 1, −1, 0, 0, −1, 1 ],
1, 1, 1, 0, −1, −1, 0, 0 ],
1, 1, 1, 0, −1, 0, −1, 1 ],
1, 1, 1, 0, 0, −1, −1, 1 ],
2, 1, 1, −1, −1, −1, −1, 0 ],
2, 1, 1, −1, −1, 0, −1, 0 ],
2, 1, 1, −1, 0, −1, −1, 0 ],
2, 1, 1, −1, 0, 0, −1, 1 ],
2, 1, 1, 0, −1, −1, 0, 1 ],
2, 1, 2, −1, −1, −1, −1, 0 ],
2, 1, 2, −1, 0, −1, −1, 1 ],
2, 2, 1, −1, −1, −1, 0, 1 ],
2, 2, 1, 0, −1, −1, −1, 1 ]
∗
7
1
6
• I ≡ P74 :
5
2
4
3





CI =








b
CoxI =



0
1
1
1
1
1
1
−1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
−1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
−1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
−1
0
−1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1
















bI =
C




1
0
0
0
0
0
0
0
















BI =



0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
−1
0
0
1
1
1
1
1
0
0
0
0
−1
−1
−1
0
−1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
−1
0
0
−1
0
0
0
0
0
1
1
0
0
−1
0
−1
−1
−1
−1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
−1
0
0
0
0
1
0
0
1
1
1
1
1
0











0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
−1
Number of sincere Tits roots of poset I sI = 28.
Table of roots of qbI
[ −2,−3,−2,−2, 1, 1, 1,−3 ],
[ −1,−3,−2,−2, 1, 1, 2,−2 ],
[ −1,−3,−2,−1, 1, 1, 1,−2 ],
[ −1,−2,−2,−1, 1, 1, 1,−2 ],
[ −1,−2,−1,−2, 1, 1, 1,−1 ],
[ 1, 2, 1, 2,−1,−1,−1, 1 ],
[ 1, 2, 2, 1,−1,−1,−1, 2 ],
[ 1, 3, 2, 1,−1,−1,−1, 2 ],
[ 1, 3, 2, 2,−1,−1,−2, 2 ],
[ 2, 3, 2, 2,−1,−1,−1, 3 ],
[ −1, −2, −2, −1, 1, 1, 0, −2 ],
[ −1, −2, −1, −2, 1, 1, 0, −2 ],
[ −1, −2, −1, −1, 0, 1, 1, −2 ],
[ −1, −2, −1, −1, 1, 0, 1, −2 ],
[ −1, −2, −1, −1, 1, 1, 0, −1 ],
[ −1, −1, −1, −1, 0, 0, 1, −1 ],
[ −1, −1, −1, −1, 0, 1, 1, −1 ],
[ −1, −1, −1, −1, 1, 0, 1, −1 ],
[ −1, −1, −1, 0, 0, 0, 0, −1 ],
[ −1, −1, −1, 0, 1, 0, 0, −1 ],
[ −1, −1, 0, −1, 0, 0, 1, −1 ],
[ −1, −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, −2, −1, −2, 1, 1, 1, −1 ],
[ 0, −2, −1, −1, 1, 1, 0, −1 ],
[ 0, −1, −1, −1, 0, 0, 1, −1 ],
[ −1,−3,−2,−2, 1, 1, 1,−3 ],
[ −1,−3,−2,−2, 1, 2, 1,−2 ],
[ −1,−3,−1,−2, 1, 1, 1,−2 ],
[ −1,−2,−2,−1, 1, 1, 1,−1 ],
[ −1,−2,−1,−1, 1, 1, 1,−1 ],
[ 1, 2, 1, 2,−1,−1,−1, 2 ],
[ 1, 2, 2, 2,−1,−1,−1, 2 ],
[ 1, 3, 2, 2,−2,−1,−1, 2 ],
[ 1, 3, 2, 2,−1,−1,−1, 2 ],
[ −1, −2, −2, −1, 0, 1, 1, −2 ],
[ −1, −2, −1, −2, 0, 1, 1, −2 ],
[ −1, −2, −1, −1, 0, 0, 1, −2 ],
[ −1, −2, −1, −1, 0, 1, 1, −1 ],
[ −1, −2, −1, −1, 1, 0, 1, −1 ],
[ −1, −1, −1, −1, 0, 0, 0, −2 ],
[ −1, −1, −1, −1, 0, 1, 0, −2 ],
[ −1, −1, −1, −1, 1, 0, 0, −2 ],
[ −1, −1, −1, −1, 1, 1, 0, −1 ],
[ −1, −1, −1, 0, 0, 0, 1, −1 ],
[ −1, −1, 0, −1, 0, 0, 0, −2 ],
[ −1, −1, 0, −1, 0, 1, 0, −1 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, −2, −1, −1, 0, 1, 1, −1 ],
[ 0, −2, −1, −1, 1, 1, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 0, −1 ],
144
[ −1,−3,−2,−2, 1, 1, 1,−2 ],
[ −1,−3,−2,−2, 2, 1, 1,−2 ],
[ −1,−2,−2,−2, 1, 1, 1,−2 ],
[ −1,−2,−1,−2, 1, 1, 1,−2 ],
[ 1, 2, 1, 1,−1,−1,−1, 1 ],
[ 1, 2, 2, 1,−1,−1,−1, 1 ],
[ 1, 3, 1, 2,−1,−1,−1, 2 ],
[ 1, 3, 2, 2,−1,−2,−1, 2 ],
[ 1, 3, 2, 2,−1,−1,−1, 3 ],
[ −1, −2, −2, −1, 1, 0, 1, −2 ],
[ −1, −2, −1, −2, 1, 0, 1, −2 ],
[ −1, −2, −1, −1, 0, 1, 0, −2 ],
[ −1, −2, −1, −1, 1, 0, 0, −2 ],
[ −1, −2, −1, −1, 1, 1, 0, −2 ],
[ −1, −1, −1, −1, 0, 0, 1, −2 ],
[ −1, −1, −1, −1, 0, 1, 0, −1 ],
[ −1, −1, −1, −1, 1, 0, 0, −1 ],
[ −1, −1, −1, 0, 0, 0, 0, −2 ],
[ −1, −1, −1, 0, 0, 1, 0, −1 ],
[ −1, −1, 0, −1, 0, 0, 0, −1 ],
[ −1, −1, 0, −1, 1, 0, 0, −1 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, −2, −2, −1, 1, 1, 1, −1 ],
[ 0, −2, −1, −1, 1, 0, 1, −1 ],
[ 0, −2, −1, −1, 1, 1, 1, 0 ],
[ 0, −1, −1, −1, 0, 1, 1, −1 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, −1, −1, 0, 1, 1, 0 ],
0, −1, −1, −1, 1, 0, 1, 0 ],
0, −1, −1, −1, 1, 1, 1, 0 ],
0, −1, −1, 0, 0, 0, 1, 0 ],
0, −1, −1, 0, 0, 1, 1, 0 ],
0, −1, −1, 0, 1, 0, 1, 0 ],
0, −1, 0, −1, 0, 0, 1, −1 ],
0, −1, 0, −1, 0, 1, 0, 0 ],
0, −1, 0, −1, 1, 0, 0, 0 ],
0, −1, 0, 0, 0, 0, 0, −1 ],
0, −1, 0, 0, 0, 1, 0, 0 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, −1, 0, 1, 0, 0, 0 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, −1, 1, 0, 0, 0 ],
0, 0, 0, 0, −1, 0, 1, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 1, −1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 0, −1, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 1, −1, 0, 0, 0 ],
0, 1, 0, 1, 0, −1, 0, 0 ],
0, 1, 0, 1, 0, 0, −1, 1 ],
0, 1, 1, 0, −1, 0, −1, 0 ],
0, 1, 1, 0, 0, −1, −1, 0 ],
0, 1, 1, 0, 0, 0, −1, 0 ],
0, 1, 1, 1, −1, −1, −1, 0 ],
0, 1, 1, 1, −1, 0, −1, 0 ],
0, 1, 1, 1, 0, −1, −1, 0 ],
0, 1, 1, 1, 0, 0, −1, 1 ],
0, 2, 1, 1, −1, −1, 0, 1 ],
0, 2, 1, 2, −1, −1, −1, 1 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 0, 1, 0, 0, 1 ],
1, 1, 0, 0, 0, 0, 0, 1 ],
1, 1, 0, 1, 0, 0, −1, 1 ],
1, 1, 1, 0, −1, 0, 0, 1 ],
1, 1, 1, 0, 0, 0, 0, 1 ],
1, 1, 1, 1, −1, 0, −1, 1 ],
1, 1, 1, 1, 0, −1, −1, 1 ],
1, 1, 1, 1, 0, 0, −1, 1 ],
1, 2, 1, 1, −1, −1, 0, 1 ],
1, 2, 1, 1, −1, 0, −1, 2 ],
1, 2, 1, 1, 0, −1, −1, 2 ],
1, 2, 1, 2, −1, −1, 0, 2 ],
1, 2, 2, 1, −1, −1, 0, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, −1, −1, 1, 0, 0, −1 ],
0, −1, −1, −1, 1, 1, 0, −1 ],
0, −1, −1, 0, 0, 0, 0, −1 ],
0, −1, −1, 0, 0, 1, 0, −1 ],
0, −1, −1, 0, 1, 0, 0, −1 ],
0, −1, −1, 0, 1, 1, 0, 0 ],
0, −1, 0, −1, 0, 0, 1, 0 ],
0, −1, 0, −1, 0, 1, 1, 0 ],
0, −1, 0, −1, 1, 0, 1, 0 ],
0, −1, 0, 0, 0, 0, 0, 0 ],
0, −1, 0, 0, 1, 0, 0, 0 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, −1, 1, 0, 0, 0, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, −1, 1, 0, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, −1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 0, 1, −1, −1, 0, 0 ],
0, 1, 0, 1, −1, 0, 0, 1 ],
0, 1, 0, 1, 0, −1, 0, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
0, 1, 1, 0, −1, 0, 0, 0 ],
0, 1, 1, 0, 0, −1, 0, 0 ],
0, 1, 1, 0, 0, 0, −1, 1 ],
0, 1, 1, 1, −1, −1, 0, 0 ],
0, 1, 1, 1, −1, 0, −1, 1 ],
0, 1, 1, 1, 0, −1, −1, 1 ],
0, 2, 1, 1, −1, −1, −1, 0 ],
0, 2, 1, 1, −1, 0, −1, 1 ],
0, 2, 2, 1, −1, −1, −1, 1 ],
1, 0, 0, 0, 0, 0, 1, 1 ],
1, 0, 0, 1, 0, 0, 0, 1 ],
1, 1, 0, 1, −1, 0, 0, 1 ],
1, 1, 0, 1, 0, 0, 0, 1 ],
1, 1, 1, 0, 0, −1, 0, 1 ],
1, 1, 1, 0, 0, 0, 0, 2 ],
1, 1, 1, 1, −1, 0, 0, 1 ],
1, 1, 1, 1, 0, −1, 0, 1 ],
1, 1, 1, 1, 0, 0, −1, 2 ],
1, 2, 1, 1, −1, −1, 0, 2 ],
1, 2, 1, 1, −1, 0, 0, 2 ],
1, 2, 1, 1, 0, −1, 0, 2 ],
1, 2, 1, 2, −1, 0, −1, 2 ],
1, 2, 2, 1, −1, 0, −1, 2 ],
∗
• I ≡ P75 :
3
7
2
6
1
5
4
145
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, −1, −1, 1, 0, 1, −1 ],
0, −1, −1, −1, 1, 1, 0, 0 ],
0, −1, −1, 0, 0, 0, 1, −1 ],
0, −1, −1, 0, 0, 1, 0, 0 ],
0, −1, −1, 0, 1, 0, 0, 0 ],
0, −1, 0, −1, 0, 0, 0, −1 ],
0, −1, 0, −1, 0, 1, 0, −1 ],
0, −1, 0, −1, 1, 0, 0, −1 ],
0, −1, 0, −1, 1, 1, 0, 0 ],
0, −1, 0, 0, 0, 0, 1, 0 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 1, 0, 0 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 1, 0, 0 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1, −1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 1, −1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 1, 0, 0, −1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 1, −1, 0, −1, 0 ],
0, 1, 0, 1, 0, −1, −1, 0 ],
0, 1, 0, 1, 0, 0, −1, 0 ],
0, 1, 1, 0, −1, −1, 0, 0 ],
0, 1, 1, 0, −1, 0, 0, 1 ],
0, 1, 1, 0, 0, −1, 0, 1 ],
0, 1, 1, 0, 0, 0, 0, 1 ],
0, 1, 1, 1, −1, −1, 0, 1 ],
0, 1, 1, 1, −1, 0, 0, 1 ],
0, 1, 1, 1, 0, −1, 0, 1 ],
0, 2, 1, 1, −1, −1, −1, 1 ],
0, 2, 1, 1, 0, −1, −1, 1 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 1, 0, 1, 0, −1, 0, 1 ],
1, 1, 0, 1, 0, 0, 0, 2 ],
1, 1, 1, 0, 0, 0, −1, 1 ],
1, 1, 1, 1, −1, −1, 0, 1 ],
1, 1, 1, 1, −1, 0, 0, 2 ],
1, 1, 1, 1, 0, −1, 0, 2 ],
1, 1, 1, 1, 0, 0, 0, 2 ],
1, 2, 1, 1, −1, 0, −1, 1 ],
1, 2, 1, 1, 0, −1, −1, 1 ],
1, 2, 1, 1, 0, 0, −1, 2 ],
1, 2, 1, 2, 0, −1, −1, 2 ],
1, 2, 2, 1, 0, −1, −1, 2 ]




CI =



1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
−1
1
1
0
1
1
0
0
−1






b I =
Cox




1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
−1
0
0
0
1
0
0
0
0
−1
−1
0
−1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
















BI =



1
1
0
0
0
0
0
0
0
0
0
0
−1
−1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
−1
0
0
0
1
1
1
1
0
1
0
0
0
−1
−1
−1
−1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
−1
0
−1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
−1
−1
−1
−1
−1
−1
−1
−1
1
−1
0
0
−1
0
0
0
1











0
0
−1
0
0
0
0
1
Number of sincere Tits roots of poset I sI = 28.
Table of roots of qbI
[ −2,−1,−3,−2,−2, 1, 1,−4 ],
[ −1,−1,−3,−2,−2, 1, 1,−3 ],
[ −1,−1,−3,−2,−1, 1, 1,−3 ],
[ −1,−1,−2,−2,−1, 1, 1,−3 ],
[ −1,−1,−2,−1,−2, 1, 1,−2 ],
[ 1, 1, 2, 1, 2,−1,−1, 2 ],
[ 1, 1, 2, 2, 1,−1,−1, 3 ],
[ 1, 1, 3, 2, 1,−1,−1, 3 ],
[ 1, 1, 3, 2, 2,−1,−1, 3 ],
[ 2, 1, 3, 2, 2,−1,−1, 4 ],
[ −1, −1, −2, −1, −2, 0, 1, −3 ],
[ −1, −1, −2, −1, −1, 0, 1, −3 ],
[ −1, −1, −2, −1, −1, 1, 0, −2 ],
[ −1, −1, −1, −1, −1, 0, 1, −2 ],
[ −1, −1, −1, 0, −1, 0, 0, −2 ],
[ −1, 0, −2, −1, −1, 0, 1, −2 ],
[ −1, 0, −2, −1, −1, 1, 1, −1 ],
[ −1, 0, −1, −1, −1, 0, 1, −1 ],
[ −1, 0, −1, −1, −1, 1, 1, −1 ],
[ −1, 0, −1, −1, 0, 0, 1, −1 ],
[ −1, 0, −1, 0, −1, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −2, −1, −2, 1, 1, −2 ],
[ 0, −1, −2, −1, −1, 1, 1, −2 ],
[ 0, −1, −1, −1, −1, 0, 1, −2 ],
[ 0, −1, −1, −1, −1, 1, 0, −1 ],
[ 0, −1, −1, −1, 0, 0, 0, −1 ],
[ 0, −1, −1, 0, −1, 0, 0, −2 ],
[ 0, −1, −1, 0, −1, 1, 0, −1 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, −1, −1, 1, 1, 0 ],
[ 0, 0, −1, −1, 0, 0, 1, 0 ],
[ 0, 0, −1, −1, 0, 1, 1, 0 ],
[ 0, 0, −1, 0, −1, 0, 1, 0 ],
[ 0, 0, −1, 0, −1, 1, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ −1,−2,−3,−2,−2, 1, 1,−4 ],
[ −1,−1,−3,−2,−2, 1, 2,−3 ],
[ −1,−1,−3,−1,−2, 1, 1,−3 ],
[ −1,−1,−2,−2,−1, 1, 1,−2 ],
[ −1,−1,−2,−1,−1, 1, 1,−2 ],
[ 1, 1, 2, 1, 2,−1,−1, 3 ],
[ 1, 1, 2, 2, 2,−1,−1, 3 ],
[ 1, 1, 3, 2, 2,−2,−1, 3 ],
[ 1, 1, 3, 2, 2,−1,−1, 4 ],
[ −1, −1, −2, −2, −1, 0, 1, −3 ],
[ −1, −1, −2, −1, −2, 1, 0, −3 ],
[ −1, −1, −2, −1, −1, 0, 1, −2 ],
[ −1, −1, −1, −1, −1, 0, 0, −3 ],
[ −1, −1, −1, −1, −1, 1, 0, −2 ],
[ −1, 0, −2, −2, −1, 1, 1, −2 ],
[ −1, 0, −2, −1, −1, 1, 0, −2 ],
[ −1, 0, −1, −1, −1, 0, 0, −2 ],
[ −1, 0, −1, −1, −1, 1, 0, −2 ],
[ −1, 0, −1, −1, 0, 0, 0, −2 ],
[ −1, 0, −1, −1, 0, 1, 0, −1 ],
[ −1, 0, −1, 0, −1, 0, 1, −1 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1, −1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −2, −1, −1, 0, 1, −2 ],
[ 0, −1, −2, −1, −1, 1, 1, −1 ],
[ 0, −1, −1, −1, −1, 0, 1, −1 ],
[ 0, −1, −1, −1, −1, 1, 1, −1 ],
[ 0, −1, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, −1, 1, 0, −1 ],
[ 0, 0, −1, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, −1, 0, 1, 0, −1 ],
[ 0, 0, −1, 0, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 1, 0 ],
146
[ −1,−1,−3,−2,−2, 1, 1,−4 ],
[ −1,−1,−3,−2,−2, 2, 1,−3 ],
[ −1,−1,−2,−2,−2, 1, 1,−3 ],
[ −1,−1,−2,−1,−2, 1, 1,−3 ],
[ 1, 1, 2, 1, 1,−1,−1, 2 ],
[ 1, 1, 2, 2, 1,−1,−1, 2 ],
[ 1, 1, 3, 1, 2,−1,−1, 3 ],
[ 1, 1, 3, 2, 2,−1,−2, 3 ],
[ 1, 2, 3, 2, 2,−1,−1, 4 ],
[ −1, −1, −2, −2, −1, 1, 0, −3 ],
[ −1, −1, −2, −1, −1, 0, 0, −3 ],
[ −1, −1, −2, −1, −1, 1, 0, −3 ],
[ −1, −1, −1, −1, −1, 0, 0, −2 ],
[ −1, −1, −1, −1, 0, 0, 0, −2 ],
[ −1, 0, −2, −1, −2, 1, 1, −2 ],
[ −1, 0, −2, −1, −1, 1, 1, −2 ],
[ −1, 0, −1, −1, −1, 0, 1, −2 ],
[ −1, 0, −1, −1, −1, 1, 0, −1 ],
[ −1, 0, −1, −1, 0, 0, 0, −1 ],
[ −1, 0, −1, 0, −1, 0, 0, −2 ],
[ −1, 0, −1, 0, −1, 1, 0, −1 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, −2, −2, −1, 1, 1, −2 ],
[ 0, −1, −2, −1, −1, 1, 0, −2 ],
[ 0, −1, −1, −1, −1, 0, 0, −2 ],
[ 0, −1, −1, −1, −1, 1, 0, −2 ],
[ 0, −1, −1, −1, 0, 0, 0, −2 ],
[ 0, −1, −1, −1, 0, 1, 0, −1 ],
[ 0, −1, −1, 0, −1, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, −2, −1, −1, 1, 1, −1 ],
[ 0, 0, −1, −1, −1, 1, 1, −1 ],
[ 0, 0, −1, −1, 0, 0, 1, −1 ],
[ 0, 0, −1, −1, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, −1, 0, 1, −1 ],
[ 0, 0, −1, 0, −1, 1, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
1
0
0
0
−1
−1
0
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
0,
0,
1,
1,
1,
1,
1,
2,
2,
0,
0,
1,
1,
1,
1,
1,
2,
2,
1,
1,
2,
2,
2,
0, 0, 0, −1,
0, 0, 0, 1,
0, 0, 1, 0,
0, 1, 0, −1,
1, −1, 0, 0,
1, 0, 0, 0,
0, 0, 0, −1,
0, 1, −1, −1,
0, 1, 0, −1,
1, 0, −1, −1,
1, 0, 0, −1,
1, 1, −1, −1,
1, 1, 0, −1,
0, 0, 0, 0,
0, 1, 0, 0,
0, 1, −1, 0,
0, 1, 0, 0,
1, 0, 0, 0,
1, 1, −1, 0,
1, 1, 0, −1,
1, 1, −1, −1,
1, 2, −1, −1,
0, 0, 0, 0,
0, 0, 1, 0,
0, 0, 0, 0,
0, 1, 0, 0,
1, 0, 0, −1,
1, 1, −1, −1,
1, 1, 0, −1,
1, 1, −1, −1,
1, 1, 0, −1,
0, 1, 0, 0,
1, 1, 0, −1,
1, 1, −1, 0,
1, 1, 0, −1,
1, 2, 0, −1,
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
1 ],
1 ],
1 ],
1 ],
2 ],
1 ],
1 ],
2 ],
2 ],
2 ],
0 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
2 ],
2 ],
2 ],
2 ],
3 ],
3 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
2,
0,
0,
1,
1,
1,
1,
1,
2,
2,
0,
0,
1,
1,
1,
1,
1,
2,
2,
1,
1,
2,
2,
2,
0,
0,
0,
0,
1,
1,
0,
0,
0,
1,
1,
1,
1,
0,
1,
0,
1,
1,
1,
1,
1,
2,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
0, 0, 0, −1 ],
0, 0, 1, 1 ],
0, 1, 0, 1 ],
1, 0, 0, 0 ],
0, −1, 0, 0 ],
0, 0, 0, 1 ],
0, 0, 0, 0 ],
1, −1, 0, 0 ],
1, 0, −1, 1 ],
0, −1, 0, 0 ],
0, 0, −1, 1 ],
1, −1, −1, 1 ],
1, −1, −1, 1 ],
0, 0, 1, 1 ],
0, 0, 0, 1 ],
1, 0, −1, 1 ],
0, −1, 0, 1 ],
0, 0, 0, 2 ],
1, −1, 0, 2 ],
1, 0, 0, 2 ],
1, −1, 0, 2 ],
1, −1, −1, 2 ],
0, 0, 0, 1 ],
1, 0, 0, 1 ],
1, −1, 0, 1 ],
1, 0, 0, 2 ],
0, 0, 0, 1 ],
1, −1, 0, 1 ],
1, 0, −1, 2 ],
1, −1, −1, 2 ],
2, −1, −1, 2 ],
0, 0, 0, 2 ],
1, 0, 0, 2 ],
1, −1, 0, 3 ],
1, 0, 0, 3 ],
1, −1, 0, 3 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
1, −1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
0,
0,
0,
0,
0,
1,
1,
1,
1,
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1,
0,
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1,
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0,
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1,
0,
1,
1,
1,
1,
1,
2,
1,
1,
1,
1,
2,
0, 0, 0,
0, 1, −1,
1, −1, 0,
1, 0, 0,
0, 0, −1,
0, −1, 0,
0, 0, 0,
1, −1, 0,
1, 0, 0,
0, −1, 0,
0, 0, 0,
1, −1, 0,
0, 0, 0,
0, 1, 0,
0, 0, 0,
1, 0, 0,
0, 0, −1,
1, −1, −1,
1, 0, −1,
1, −1, −1,
1, 0, −1,
0, 0, 0,
0, 0, 1,
0, 0, 0,
1, 0, −1,
0, −1, 0,
0, 0, 0,
1, −1, 0,
1, 0, 0,
1, −1, 0,
1, −1, −1,
1, −1, 0,
1, 0, 0,
1, 0, −1,
2, −1, 0,
1, 0, −1,
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1 ],
0 ],
0 ],
1 ],
0 ],
0 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
0 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
2 ],
0 ],
1 ],
1 ],
1 ],
1 ],
2 ],
2 ],
2 ],
2 ],
2 ],
2 ],
3 ],
2 ],
3 ],
3]
∗
• I ≡ P76 :
4
7
3
6
2
5
1




CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
−1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
−1






b
CoxI =



1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
−1
0
0
0
0
1
0
0
0
−1
−1
−1
0
−1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
















BI =



Number of sincere Tits roots of poset I sI = 28.
147
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
−1
0
0
0
0
0
−1
−1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
−1
1
1
0
1
1
0
0
−2
1
1
0
0
0
0
−1
−1
−1
−1
−1
−1
−1
−1
−1
1
1
0
0
0
1
0
0
−1











−1
−1
0
0
−1
0
0
1
1
1
0
0
1
0
−1
−2











Table of roots of qbI
[ −2,−1,−1,−3,−2,−2, 1,−5 ],
[ −1,−1,−1,−3,−2,−2, 1,−5 ],
[ −1,−1,−1,−3,−2,−1, 1,−4 ],
[ −1,−1,−1,−2,−2,−1, 1,−4 ],
[ −1,−1,−1,−2,−1,−2, 1,−3 ],
[ 1, 1, 1, 2, 1, 2,−1, 3 ],
[ 1, 1, 1, 2, 2, 1,−1, 4 ],
[ 1, 1, 1, 3, 2, 1,−1, 4 ],
[ 1, 1, 1, 3, 2, 2,−1, 5 ],
[ 2, 1, 1, 3, 2, 2,−1, 5 ],
[ −1, −1, −1, −2, −1, −1, 0, −4 ],
[ −1, −1, 0, −2, −2, −1, 1, −3 ],
[ −1, −1, 0, −2, −1, −1, 1, −3 ],
[ −1, −1, 0, −1, −1, −1, 0, −2 ],
[ −1, −1, 0, −1, 0, −1, 0, −2 ],
[ −1, 0, −1, −2, −1, −1, 0, −3 ],
[ −1, 0, −1, −1, −1, −1, 0, −3 ],
[ −1, 0, −1, −1, −1, 0, 0, −2 ],
[ −1, 0, 0, −1, −1, −1, 0, −2 ],
[ −1, 0, 0, −1, −1, 0, 0, −2 ],
[ −1, 0, 0, −1, 0, −1, 0, −2 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1, −1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −2, −1, −2, 1, −3 ],
[ 0, −1, −1, −2, −1, −1, 1, −2 ],
[ 0, −1, −1, −1, −1, −1, 1, −2 ],
[ 0, −1, 0, −2, −1, −1, 1, −2 ],
[ 0, −1, 0, −1, −1, −1, 1, −1 ],
[ 0, −1, 0, −1, −1, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, −1, 1, −1 ],
[ 0, −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, −1, −1, 0, 0, −2 ],
[ 0, 0, −1, −1, 0, −1, 0, −2 ],
[ 0, 0, −1, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, −1, −1, −1, 1, −1 ],
[ 0, 0, 0, −1, −1, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, −1, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 0, 1, 0, 1, −1, 0 ],
[ 0, 0, 0, 1, 1, 0, −1, 0 ],
[ 0, 0, 0, 1, 1, 1, −1, 1 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 1, 0, 2 ],
[ 0, 0, 1, 1, 1, 0, 0, 2 ],
[ 0, 0, 1, 1, 1, 1, 0, 2 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 1, 0, 1, −1, 1 ],
[ 0, 1, 0, 1, 1, 0, −1, 1 ],
[ 0, 1, 0, 1, 1, 1, −1, 1 ],
[ 0, 1, 0, 2, 1, 1, −1, 2 ],
[ 0, 1, 1, 1, 1, 1, −1, 2 ],
[ 0, 1, 1, 2, 1, 1, −1, 2 ],
[ 0, 1, 1, 2, 1, 2, −1, 3 ],
[ 1, 0, −1, 0, 0, 0, 0, 0 ],
[ −1,−2,−1,−3,−2,−2, 1,−5 ],
[ −1,−1,−1,−3,−2,−2, 1,−4 ],
[ −1,−1,−1,−3,−1,−2, 1,−4 ],
[ −1,−1,−1,−2,−2,−1, 1,−3 ],
[ −1,−1,−1,−2,−1,−1, 1,−3 ],
[ 1, 1, 1, 2, 1, 2,−1, 4 ],
[ 1, 1, 1, 2, 2, 2,−1, 4 ],
[ 1, 1, 1, 3, 2, 2,−2, 4 ],
[ 1, 1, 2, 3, 2, 2,−1, 5 ],
[ −1, −1, −1, −2, −2, −1, 0, −4 ],
[ −1, −1, −1, −2, −1, −1, 0, −3 ],
[ −1, −1, 0, −2, −1, −2, 1, −3 ],
[ −1, −1, 0, −2, −1, −1, 1, −2 ],
[ −1, −1, 0, −1, −1, −1, 1, −2 ],
[ −1, 0, −1, −2, −2, −1, 1, −3 ],
[ −1, 0, −1, −2, −1, −1, 1, −3 ],
[ −1, 0, −1, −1, −1, −1, 0, −2 ],
[ −1, 0, −1, −1, 0, −1, 0, −2 ],
[ −1, 0, 0, −1, −1, −1, 1, −2 ],
[ −1, 0, 0, −1, −1, 0, 0, −1 ],
[ −1, 0, 0, −1, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −2, −1, −1, 0, −3 ],
[ 0, −1, −1, −1, −1, −1, 0, −3 ],
[ 0, −1, −1, −1, −1, 0, 0, −2 ],
[ 0, −1, 0, −1, −1, −1, 0, −2 ],
[ 0, −1, 0, −1, −1, 0, 0, −2 ],
[ 0, −1, 0, −1, 0, −1, 0, −2 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, −1, −1 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, −1, −1, 1, −2 ],
[ 0, 0, −1, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, −1, 0, −1, 0, −1 ],
[ 0, 0, −1, 0, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, −1, 1 ],
[ 0, 0, 0, 1, 1, 0, −1, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 0, 1, −1, 1 ],
[ 0, 0, 1, 1, 1, 0, −1, 1 ],
[ 0, 0, 1, 1, 1, 1, −1, 1 ],
[ 0, 0, 1, 2, 1, 1, −1, 2 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 1, 1, 1, −1, 2 ],
[ 0, 1, 1, 1, 0, 1, 0, 2 ],
[ 0, 1, 1, 1, 1, 1, 0, 2 ],
[ 0, 1, 1, 2, 1, 1, −1, 3 ],
[ 0, 1, 1, 2, 2, 1, −1, 3 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
148
[ −1,−1,−2,−3,−2,−2, 1,−5 ],
[ −1,−1,−1,−3,−2,−2, 2,−4 ],
[ −1,−1,−1,−2,−2,−2, 1,−4 ],
[ −1,−1,−1,−2,−1,−2, 1,−4 ],
[ 1, 1, 1, 2, 1, 1,−1, 3 ],
[ 1, 1, 1, 2, 2, 1,−1, 3 ],
[ 1, 1, 1, 3, 1, 2,−1, 4 ],
[ 1, 1, 1, 3, 2, 2,−1, 4 ],
[ 1, 2, 1, 3, 2, 2,−1, 5 ],
[ −1, −1, −1, −2, −1, −2, 0, −4 ],
[ −1, −1, −1, −1, −1, −1, 0, −3 ],
[ −1, −1, 0, −2, −1, −1, 0, −3 ],
[ −1, −1, 0, −1, −1, −1, 0, −3 ],
[ −1, −1, 0, −1, −1, 0, 0, −2 ],
[ −1, 0, −1, −2, −1, −2, 1, −3 ],
[ −1, 0, −1, −2, −1, −1, 1, −2 ],
[ −1, 0, −1, −1, −1, −1, 1, −2 ],
[ −1, 0, 0, −2, −1, −1, 1, −2 ],
[ −1, 0, 0, −1, −1, −1, 1, −1 ],
[ −1, 0, 0, −1, −1, 0, 1, −1 ],
[ −1, 0, 0, −1, 0, −1, 1, −1 ],
[ −1, 0, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −2, −2, −1, 1, −3 ],
[ 0, −1, −1, −2, −1, −1, 1, −3 ],
[ 0, −1, −1, −1, −1, −1, 0, −2 ],
[ 0, −1, −1, −1, 0, −1, 0, −2 ],
[ 0, −1, 0, −1, −1, −1, 1, −2 ],
[ 0, −1, 0, −1, −1, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, −2, −1, −1, 1, −2 ],
[ 0, 0, −1, −1, −1, −1, 1, −1 ],
[ 0, 0, −1, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, −1, 0, −1, 1, −1 ],
[ 0, 0, −1, 0, 0, −1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, 0, 1, −1 ],
[ 0, 0, 0, −1, 0, −1, 1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 1, −1, 2 ],
[ 0, 1, −1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 1, 0, 2 ],
[ 0, 1, 0, 1, 1, 0, 0, 2 ],
[ 0, 1, 0, 1, 1, 1, 0, 2 ],
[ 0, 1, 1, 1, 1, 0, 0, 2 ],
[ 0, 1, 1, 1, 1, 1, 0, 3 ],
[ 0, 1, 1, 2, 1, 1, 0, 3 ],
[ 1, −1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
1,
1,
1,
0,
0,
0,
0,
1,
0,
1,
1,
1,
1,
1,
1,
2,
1,
1,
2,
2,
2,
0,
0,
0,
1,
1,
1,
1,
1,
0,
1,
1,
2,
1,
0, 1,
0, 0,
1, 0,
0, 0,
1, 0,
0, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, −1,
1, −1,
1, 0,
1 ],
1 ],
2 ],
2 ],
2 ],
2 ],
3 ],
3 ],
2 ],
2 ],
3 ],
3 ],
4 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
1,
1,
1,
0,
0,
0,
1,
1,
0,
1,
1,
1,
2,
1,
2,
2,
1,
1,
2,
1,
2,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1, 0,
1, −1,
0, −1,
1, −1,
1, −1,
1, −1,
1, −1,
2, −1,
0, 0,
1, 0,
1, 0,
1, 0,
2, 0,
1 ],
1 ],
1 ],
1 ],
2 ],
2 ],
2 ],
3 ],
2 ],
3 ],
3 ],
3 ],
4 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
0,
0,
0,
0,
1,
1,
1,
1,
0,
0,
0,
1,
1,
0,
1,
1,
1,
1,
1,
2,
2,
1,
2,
2,
2,
2,
1,
0,
1,
1,
0,
1,
1,
2,
1,
1,
1,
1,
2,
0, 0,
1, 0,
0, 0,
1, −1,
1, 0,
1, 0,
1, −1,
1, −1,
1, −1,
1, −1,
2, −1,
1, 0,
1, 0,
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
1
1
1
0
0
0
−1
1
1
0
0
0
0
0
−1
1 ],
1 ],
1 ],
2 ],
2 ],
2 ],
3 ],
3 ],
2 ],
2 ],
3 ],
3 ],
4]
∗
1
• I ≡ P77 :
7
3
6
2
5
4





CI =








b
CoxI =



0
1
1
1
1
1
1
−1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
−1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
−1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
−1
1
1
1
1
1
1
1
1
















bI =
C




















BI =



1
1
0
2
1
1
0
−2
1
1
1
1
1
1
0
−2
0
1
0
1
1
0
0
−1
1
0
0
1
1
0
0
−1











0
0
0
1
1
1
1
−1
2
2
1
3
2
1
0
−4
Number of sincere Tits roots of poset I sI = 28.
Table of roots of qbI
[ −3,−2,−2,−2,−1,−1,−1,−6 ],
[ −3,−2,−2,−1,−1,−1,−2,−6 ],
[ −3,−2,−1,−1,−1,−1,−1,−5 ],
[ −2,−2,−1,−1,−1,−1,−1,−5 ],
[ −2,−1,−2,−1,−1,−1,−1,−4 ],
[ 2, 1, 2, 1, 1, 1, 1, 4 ],
[ 2, 2, 1, 1, 1, 1, 1, 5 ],
[ 3, 2, 1, 1, 1, 1, 1, 5 ],
[ 3, 2, 2, 1, 1, 1, 2, 6 ],
[ 3, 2, 2, 2, 1, 1, 1, 6 ],
[ −2, −2, −1, −1, 0, −1, −1, −4 ],
[ −2, −1, −2, −1, −1, 0, −1, −4 ],
[ −2, −1, −1, −1, −1, −1, 0, −4 ],
[ −2, −1, −1, −1, −1, 0, −1, −3 ],
[ −3,−2,−2,−1,−2,−1,−1,−6 ],
[ −3,−2,−2,−1,−1,−1,−1,−6 ],
[ −3,−1,−2,−1,−1,−1,−1,−5 ],
[ −2,−2,−1,−1,−1,−1,−1,−4 ],
[ −2,−1,−1,−1,−1,−1,−1,−4 ],
[ 2, 1, 2, 1, 1, 1, 1, 5 ],
[ 2, 2, 2, 1, 1, 1, 1, 5 ],
[ 3, 2, 2, 1, 1, 1, 1, 5 ],
[ 3, 2, 2, 1, 1, 2, 1, 6 ],
[ −2, −2, −1, −1, −1, −1, 0, −4 ],
[ −2, −2, −1, 0, −1, −1, −1, −4 ],
[ −2, −1, −2, −1, 0, −1, −1, −4 ],
[ −2, −1, −1, −1, −1, −1, 0, −3 ],
[ −2, −1, −1, −1, −1, 0, 0, −3 ],
149
[ −3,−2,−2,−1,−1,−2,−1,−6 ],
[ −3,−2,−2,−1,−1,−1,−1,−5 ],
[ −2,−2,−2,−1,−1,−1,−1,−5 ],
[ −2,−1,−2,−1,−1,−1,−1,−5 ],
[ 2, 1, 1, 1, 1, 1, 1, 4 ],
[ 2, 2, 1, 1, 1, 1, 1, 4 ],
[ 3, 1, 2, 1, 1, 1, 1, 5 ],
[ 3, 2, 2, 1, 1, 1, 1, 6 ],
[ 3, 2, 2, 1, 2, 1, 1, 6 ],
[ −2, −2, −1, −1, −1, 0, −1, −4 ],
[ −2, −1, −2, −1, −1, −1, 0, −4 ],
[ −2, −1, −2, 0, −1, −1, −1, −4 ],
[ −2, −1, −1, −1, −1, 0, −1, −4 ],
[ −2, −1, −1, −1, 0, −1, −1, −4 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−2, −1, −1, −1, 0, −1, −1, −3 ],
−2, −1, −1, 0, −1, −1, −1, −4 ],
−2, −1, −1, 0, −1, 0, −1, −3 ],
−1, −1, −1, −1, −1, 0, −1, −3 ],
−1, −1, −1, −1, 0, −1, −1, −3 ],
−1, −1, −1, −1, 0, 0, −1, −3 ],
−1, −1, −1, 0, −1, −1, −1, −3 ],
−1, −1, −1, 0, −1, 0, −1, −3 ],
−1, −1, −1, 0, 0, −1, −1, −3 ],
−1, −1, −1, 0, 0, 0, −1, −2 ],
−1, −1, 0, −1, 0, 0, −1, −2 ],
−1, −1, 0, 0, −1, −1, 0, −2 ],
−1, −1, 0, 0, −1, 0, 0, −1 ],
−1, −1, 0, 0, 0, −1, 0, −1 ],
−1, −1, 0, 0, 0, 0, 0, −1 ],
−1, 0, −1, −1, 0, 0, −1, −2 ],
−1, 0, −1, 0, −1, −1, 0, −2 ],
−1, 0, −1, 0, −1, 0, 0, −1 ],
−1, 0, −1, 0, 0, −1, 0, −1 ],
−1, 0, −1, 0, 0, 0, 0, −1 ],
−1, 0, 0, 0, 0, −1, 0, −1 ],
−1, 0, 0, 0, 0, 0, 0, 0 ],
0, −1, 0, 0, 0, −1, 0, −1 ],
0, −1, 0, 0, 0, 0, 0, 0 ],
0, 0, −1, 0, −1, 0, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, −1, 1, 0, 0, 0 ],
0, 0, 0, 0, −1, 0, 1, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 1, −1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 1, 0, 1 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 0, 1, 0, 0, 1, 0, 1 ],
1, 0, 1, 0, 1, 0, 0, 1 ],
1, 0, 1, 0, 1, 1, 0, 2 ],
1, 0, 1, 1, 0, 0, 1, 2 ],
1, 1, 0, 0, 0, 0, 0, 1 ],
1, 1, 0, 0, 0, 1, 0, 1 ],
1, 1, 0, 0, 1, 0, 0, 1 ],
1, 1, 0, 0, 1, 1, 0, 2 ],
1, 1, 0, 1, 0, 0, 1, 2 ],
1, 1, 1, 0, 0, 0, 1, 2 ],
1, 1, 1, 0, 0, 1, 1, 3 ],
1, 1, 1, 0, 1, 0, 1, 3 ],
1, 1, 1, 0, 1, 1, 1, 3 ],
1, 1, 1, 1, 0, 0, 1, 3 ],
1, 1, 1, 1, 0, 1, 1, 3 ],
1, 1, 1, 1, 1, 0, 1, 3 ],
2, 1, 1, 0, 1, 0, 1, 3 ],
2, 1, 1, 0, 1, 1, 1, 4 ],
2, 1, 1, 1, 0, 1, 1, 3 ],
2, 1, 1, 1, 1, 0, 1, 3 ],
2, 1, 1, 1, 1, 1, 0, 4 ],
2, 1, 2, 1, 1, 0, 1, 4 ],
2, 2, 1, 1, 0, 1, 1, 4 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−2, −1, −1, −1, 0, −1, 0, −3 ],
−2, −1, −1, 0, −1, −1, −1, −3 ],
−2, −1, −1, 0, 0, −1, −1, −3 ],
−1, −1, −1, −1, −1, 0, 0, −3 ],
−1, −1, −1, −1, 0, −1, 0, −3 ],
−1, −1, −1, −1, 0, 0, −1, −2 ],
−1, −1, −1, 0, −1, −1, 0, −3 ],
−1, −1, −1, 0, −1, 0, −1, −2 ],
−1, −1, −1, 0, 0, −1, −1, −2 ],
−1, −1, 0, −1, −1, 0, 0, −2 ],
−1, −1, 0, −1, 0, 0, 0, −2 ],
−1, −1, 0, 0, −1, 0, −1, −2 ],
−1, −1, 0, 0, 0, −1, −1, −2 ],
−1, −1, 0, 0, 0, 0, −1, −2 ],
−1, 0, −1, −1, −1, 0, 0, −2 ],
−1, 0, −1, −1, 0, 0, 0, −2 ],
−1, 0, −1, 0, −1, 0, −1, −2 ],
−1, 0, −1, 0, 0, −1, −1, −2 ],
−1, 0, −1, 0, 0, 0, −1, −2 ],
−1, 0, 0, −1, 0, 0, 0, −1 ],
−1, 0, 0, 0, 0, 0, −1, −1 ],
0, −1, 0, −1, 0, 0, 0, −1 ],
0, −1, 0, 0, 0, 0, −1, −1 ],
0, −1, 1, 0, 0, 0, 0, 0 ],
0, 0, −1, 0, 0, −1, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, −1, 1, 0, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, 0, 1, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 0, 1, 0, 0, 1 ],
1, 0, 1, 0, 0, 0, 1, 1 ],
1, 0, 1, 0, 0, 1, 0, 2 ],
1, 0, 1, 0, 1, 0, 0, 2 ],
1, 0, 1, 1, 0, 0, 0, 1 ],
1, 0, 1, 1, 0, 1, 0, 2 ],
1, 1, 0, 0, 0, 0, 1, 1 ],
1, 1, 0, 0, 0, 1, 0, 2 ],
1, 1, 0, 0, 1, 0, 0, 2 ],
1, 1, 0, 1, 0, 0, 0, 1 ],
1, 1, 0, 1, 0, 1, 0, 2 ],
1, 1, 1, 0, 0, 1, 0, 2 ],
1, 1, 1, 0, 1, 0, 0, 2 ],
1, 1, 1, 0, 1, 1, 0, 2 ],
1, 1, 1, 1, 0, 0, 0, 2 ],
1, 1, 1, 1, 0, 1, 0, 2 ],
1, 1, 1, 1, 1, 0, 0, 2 ],
1, 1, 1, 1, 1, 1, 0, 3 ],
2, 1, 1, 0, 1, 1, 0, 3 ],
2, 1, 1, 1, 0, 0, 1, 3 ],
2, 1, 1, 1, 0, 1, 1, 4 ],
2, 1, 1, 1, 1, 0, 1, 4 ],
2, 1, 2, 0, 1, 1, 1, 4 ],
2, 1, 2, 1, 1, 1, 0, 4 ],
2, 2, 1, 1, 1, 0, 1, 4 ],
150
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−2, −1, −1, −1, 0, 0, −1, −3 ],
−2, −1, −1, 0, −1, −1, 0, −3 ],
−1, −1, −1, −1, −1, −1, 0, −3 ],
−1, −1, −1, −1, −1, 0, 0, −2 ],
−1, −1, −1, −1, 0, −1, 0, −2 ],
−1, −1, −1, −1, 0, 0, 0, −2 ],
−1, −1, −1, 0, −1, −1, 0, −2 ],
−1, −1, −1, 0, −1, 0, 0, −2 ],
−1, −1, −1, 0, 0, −1, 0, −2 ],
−1, −1, 0, −1, 0, −1, 0, −2 ],
−1, −1, 0, −1, 0, 0, 0, −1 ],
−1, −1, 0, 0, −1, 0, 0, −2 ],
−1, −1, 0, 0, 0, −1, 0, −2 ],
−1, −1, 0, 0, 0, 0, −1, −1 ],
−1, 0, −1, −1, 0, −1, 0, −2 ],
−1, 0, −1, −1, 0, 0, 0, −1 ],
−1, 0, −1, 0, −1, 0, 0, −2 ],
−1, 0, −1, 0, 0, −1, 0, −2 ],
−1, 0, −1, 0, 0, 0, −1, −1 ],
−1, 0, 0, 0, −1, 0, 0, −1 ],
−1, 0, 0, 0, 0, 0, 0, −1 ],
0, −1, 0, 0, −1, 0, 0, −1 ],
0, −1, 0, 0, 0, 0, 0, −1 ],
0, 0, −1, −1, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 0, −1, −1 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 1, 0, 0 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1, −1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 1, 0, 1 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 1, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
1, 0, 0, 0, 0, 0, 1, 1 ],
1, 0, 0, 1, 0, 0, 0, 1 ],
1, 0, 1, 0, 0, 0, 1, 2 ],
1, 0, 1, 0, 0, 1, 1, 2 ],
1, 0, 1, 0, 1, 0, 1, 2 ],
1, 0, 1, 1, 0, 0, 0, 2 ],
1, 0, 1, 1, 1, 0, 0, 2 ],
1, 1, 0, 0, 0, 0, 1, 2 ],
1, 1, 0, 0, 0, 1, 1, 2 ],
1, 1, 0, 0, 1, 0, 1, 2 ],
1, 1, 0, 1, 0, 0, 0, 2 ],
1, 1, 0, 1, 1, 0, 0, 2 ],
1, 1, 1, 0, 0, 1, 1, 2 ],
1, 1, 1, 0, 1, 0, 1, 2 ],
1, 1, 1, 0, 1, 1, 0, 3 ],
1, 1, 1, 1, 0, 0, 1, 2 ],
1, 1, 1, 1, 0, 1, 0, 3 ],
1, 1, 1, 1, 1, 0, 0, 3 ],
2, 1, 1, 0, 0, 1, 1, 3 ],
2, 1, 1, 0, 1, 1, 1, 3 ],
2, 1, 1, 1, 0, 1, 0, 3 ],
2, 1, 1, 1, 1, 0, 0, 3 ],
2, 1, 1, 1, 1, 1, 0, 3 ],
2, 1, 2, 1, 0, 1, 1, 4 ],
2, 2, 1, 0, 1, 1, 1, 4 ],
2, 2, 1, 1, 1, 1, 0, 4 ]
∗
7
2
• I ≡ P78 :
1
6
5
4
3





CI =








b
CoxI =



0
1
1
1
1
1
1
−1
1
0
1
1
1
1
0
−1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
−1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
−1
0
−1
−1
−1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
















BI =



1
0
0
0
0
0
0
0
0
0
1
0
0
0
−1
−1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
−1
−1
−2
0
0
0
1
1
1
1
0
1
0
0
0
0
0
−1
−1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
−1
0
0
0
0
0
0
1
0
0
0
0
0
−1
−1
−1
0
−1
−1
−1
−1
−1
−1
−1
1
1
0
1
0
0
0
0
−1











−1
0
−1
0
0
1
1
1
Number of sincere Tits roots of poset I sI = 28.
Table of roots of qbI
[ −2,−3,−2,−1,−1,−1, 2,−4 ],
[ −2,−3,−1,−1,−1,−2, 2,−4 ],
[ −2,−3,−1,−1,−1,−1, 2,−3 ],
[ −2,−2,−1,−1,−1,−1, 2,−3 ],
[ −1,−2,−1,−1,−1,−1, 2,−3 ],
[ 1, 2, 1, 1, 1, 1,−2, 3 ],
[ 2, 2, 1, 1, 1, 1,−2, 3 ],
[ 2, 3, 1, 1, 1, 1,−2, 3 ],
[ 2, 3, 1, 1, 1, 2,−2, 4 ],
[ 2, 3, 2, 1, 1, 1,−2, 4 ],
[ −2, −2, −1, 0, −1, −1, 1, −3 ],
[ −1, −2, −1, −1, −1, 0, 1, −2 ],
[ −1, −2, −1, −1, 0, −1, 1, −2 ],
[ −1, −2, −1, 0, −1, −1, 1, −3 ],
[ −1, −2, −1, 0, −1, 0, 1, −2 ],
[ −1, −2, 0, −1, −1, −1, 1, −2 ],
[ −1, −2, 0, −1, 0, −1, 1, −2 ],
[ −1, −1, −1, −1, 0, −1, 1, −2 ],
[ −1, −1, −1, −1, 0, 0, 1, −1 ],
[ −1, −1, −1, 0, −1, 0, 1, −2 ],
[ −1, −1, −1, 0, 0, −1, 1, −2 ],
[ −1, −1, −1, 0, 0, 0, 0, −1 ],
[ −1, −1, 0, −1, −1, 0, 0, −2 ],
[ −1, −1, 0, −1, 0, −1, 0, −2 ],
[ −1, −1, 0, −1, 0, 0, 0, −2 ],
[ −1, −1, 0, 0, −1, −1, 0, −2 ],
[ −1, −1, 0, 0, −1, 0, 0, −2 ],
[ −2,−3,−1,−2,−1,−1, 2,−4 ],
[ −2,−3,−1,−1,−1,−1, 1,−4 ],
[ −2,−2,−1,−1,−1,−1, 1,−4 ],
[ −1,−3,−1,−1,−1,−1, 2,−3 ],
[ −1,−2,−1,−1,−1,−1, 2,−2 ],
[ 1, 2, 1, 1, 1, 1,−1, 3 ],
[ 2, 2, 1, 1, 1, 1,−1, 3 ],
[ 2, 3, 1, 1, 1, 1,−2, 4 ],
[ 2, 3, 1, 1, 2, 1,−2, 4 ],
[ −2, −2, −1, −1, −1, 0, 1, −3 ],
[ −2, −2, 0, −1, −1, −1, 1, −3 ],
[ −1, −2, −1, −1, −1, 0, 2, −2 ],
[ −1, −2, −1, −1, 0, −1, 2, −2 ],
[ −1, −2, −1, 0, −1, −1, 1, −2 ],
[ −1, −2, −1, 0, 0, −1, 1, −2 ],
[ −1, −2, 0, −1, −1, −1, 2, −2 ],
[ −1, −2, 0, 0, −1, −1, 1, −2 ],
[ −1, −1, −1, −1, 0, 0, 0, −2 ],
[ −1, −1, −1, 0, −1, −1, 1, −2 ],
[ −1, −1, −1, 0, −1, 0, 1, −1 ],
[ −1, −1, −1, 0, 0, −1, 1, −1 ],
[ −1, −1, −1, 0, 0, 0, 1, −1 ],
[ −1, −1, 0, −1, −1, 0, 1, −2 ],
[ −1, −1, 0, −1, 0, −1, 1, −2 ],
[ −1, −1, 0, −1, 0, 0, 0, −1 ],
[ −1, −1, 0, 0, −1, −1, 1, −2 ],
[ −1, −1, 0, 0, −1, 0, 0, −1 ],
151
[ −2,−3,−1,−1,−2,−1, 2,−4 ],
[ −2,−3,−1,−1,−1,−1, 2,−4 ],
[ −2,−2,−1,−1,−1,−1, 1,−3 ],
[ −1,−2,−1,−1,−1,−1, 1,−3 ],
[ 1, 2, 1, 1, 1, 1,−2, 2 ],
[ 1, 3, 1, 1, 1, 1,−2, 3 ],
[ 2, 2, 1, 1, 1, 1,−1, 4 ],
[ 2, 3, 1, 1, 1, 1,−1, 4 ],
[ 2, 3, 1, 2, 1, 1,−2, 4 ],
[ −2, −2, −1, −1, 0, −1, 1, −3 ],
[ −1, −2, −1, −1, −1, 0, 1, −3 ],
[ −1, −2, −1, −1, 0, −1, 1, −3 ],
[ −1, −2, −1, −1, 0, 0, 1, −2 ],
[ −1, −2, −1, 0, −1, −1, 2, −2 ],
[ −1, −2, 0, −1, −1, −1, 1, −3 ],
[ −1, −2, 0, −1, −1, 0, 1, −2 ],
[ −1, −1, −1, −1, −1, 0, 1, −2 ],
[ −1, −1, −1, −1, 0, 0, 1, −2 ],
[ −1, −1, −1, 0, −1, 0, 0, −2 ],
[ −1, −1, −1, 0, 0, −1, 0, −2 ],
[ −1, −1, −1, 0, 0, 0, 0, −2 ],
[ −1, −1, 0, −1, −1, −1, 1, −2 ],
[ −1, −1, 0, −1, −1, 0, 1, −1 ],
[ −1, −1, 0, −1, 0, −1, 1, −1 ],
[ −1, −1, 0, −1, 0, 0, 1, −1 ],
[ −1, −1, 0, 0, −1, −1, 1, −1 ],
[ −1, −1, 0, 0, −1, 0, 1, −1 ],
1
0
1
0
0
−1
−2
−2











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, −1, 0, 0, 0, −1, 0, −2 ],
−1, −1, 0, 0, 0, 0, 0, −1 ],
−1, 0, 0, 0, −1, 0, 0, −1 ],
−1, 0, 0, 0, 0, 0, 0, −1 ],
0, −1, −1, 0, −1, 0, 1, −1 ],
0, −1, −1, 0, 0, 0, 1, −1 ],
0, −1, 0, −1, 0, −1, 1, −1 ],
0, −1, 0, −1, 0, 0, 1, 0 ],
0, −1, 0, 0, −1, 0, 1, −1 ],
0, −1, 0, 0, 0, −1, 1, −1 ],
0, −1, 0, 0, 0, 0, 0, 0 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, −1, 0, 1, 0, 0, 0 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, −1, 1, 0, 0, 0 ],
0, 0, 0, 0, −1, 0, 1, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 1, −1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 0, −1, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 1, −1, 1 ],
0, 1, 0, 0, 1, 0, −1, 1 ],
0, 1, 0, 1, 0, 0, −1, 0 ],
0, 1, 0, 1, 0, 1, −1, 1 ],
0, 1, 1, 0, 0, 0, −1, 1 ],
0, 1, 1, 0, 1, 0, −1, 1 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 0, 1, 0, 0, 1 ],
1, 1, 0, 0, 0, 0, 0, 1 ],
1, 1, 0, 0, 0, 1, 0, 2 ],
1, 1, 0, 0, 1, 0, 0, 2 ],
1, 1, 0, 0, 1, 1, 0, 2 ],
1, 1, 0, 1, 0, 0, 0, 2 ],
1, 1, 0, 1, 0, 1, 0, 2 ],
1, 1, 0, 1, 1, 0, 0, 2 ],
1, 1, 1, 0, 0, 0, 0, 1 ],
1, 1, 1, 0, 0, 1, −1, 2 ],
1, 1, 1, 0, 1, 0, −1, 2 ],
1, 1, 1, 1, 0, 0, −1, 1 ],
1, 1, 1, 1, 0, 1, −1, 2 ],
1, 2, 0, 1, 0, 1, −1, 2 ],
1, 2, 0, 1, 1, 1, −1, 2 ],
1, 2, 1, 0, 1, 0, −1, 2 ],
1, 2, 1, 0, 1, 1, −1, 3 ],
1, 2, 1, 1, 0, 1, −1, 2 ],
1, 2, 1, 1, 1, 0, −1, 2 ],
2, 2, 1, 0, 1, 1, −1, 3 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, −1, 0, 0, 0, −1, 0, −1 ],
−1, 0, −1, 0, 0, 0, 0, −1 ],
−1, 0, 0, 0, 0, −1, 0, −1 ],
−1, 0, 0, 0, 0, 0, 0, 0 ],
0, −1, −1, 0, 0, −1, 1, −1 ],
0, −1, −1, 0, 0, 0, 1, 0 ],
0, −1, 0, −1, 0, 0, 0, −1 ],
0, −1, 0, 0, −1, −1, 1, −1 ],
0, −1, 0, 0, −1, 0, 1, 0 ],
0, −1, 0, 0, 0, −1, 1, 0 ],
0, −1, 0, 0, 0, 0, 1, 0 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, −1, 1, 0, 0, 0, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, −1, 1, 0, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, −1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 0, 1, 0, 1 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
0, 1, 0, 1, 0, 0, −1, 1 ],
0, 1, 0, 1, 1, 0, −1, 1 ],
0, 1, 1, 0, 0, 0, 0, 1 ],
0, 1, 1, 1, 0, 0, −1, 1 ],
1, 0, 0, 0, 0, 0, 1, 1 ],
1, 0, 0, 1, 0, 0, 0, 1 ],
1, 1, 0, 0, 0, 1, −1, 1 ],
1, 1, 0, 0, 1, 0, −1, 1 ],
1, 1, 0, 0, 1, 1, −1, 1 ],
1, 1, 0, 1, 0, 0, −1, 1 ],
1, 1, 0, 1, 0, 1, −1, 1 ],
1, 1, 0, 1, 1, 0, −1, 1 ],
1, 1, 0, 1, 1, 1, −1, 2 ],
1, 1, 1, 0, 0, 0, 0, 2 ],
1, 1, 1, 0, 0, 1, 0, 2 ],
1, 1, 1, 0, 1, 0, 0, 2 ],
1, 1, 1, 1, 0, 0, −1, 2 ],
1, 1, 1, 1, 1, 0, −1, 2 ],
1, 2, 0, 1, 1, 0, −1, 2 ],
1, 2, 0, 1, 1, 1, −1, 3 ],
1, 2, 1, 0, 1, 1, −2, 2 ],
1, 2, 1, 1, 0, 0, −1, 2 ],
1, 2, 1, 1, 0, 1, −1, 3 ],
1, 2, 1, 1, 1, 0, −1, 3 ],
2, 2, 1, 1, 0, 1, −1, 3 ],
∗
7
6
• I ≡ P79 :
1
5
4
3
2
152
[ −1, −1, 0, 0, 0, −1, 1, −1 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, −1, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, −1, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 1, −1, 0 ],
[ 0, 1, 0, 0, 1, 0, −1, 0 ],
[ 0, 1, 0, 0, 1, 1, −1, 1 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 1, 0, 0, 1, −1, 1 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, 1, 0, 1 ],
[ 1, 1, 0, 0, 1, 0, 0, 1 ],
[ 1, 1, 0, 0, 1, 1, −1, 2 ],
[ 1, 1, 0, 1, 0, 0, 0, 1 ],
[ 1, 1, 0, 1, 0, 1, −1, 2 ],
[ 1, 1, 0, 1, 1, 0, −1, 2 ],
[ 1, 1, 1, 0, 0, 0, −1, 1 ],
[ 1, 1, 1, 0, 0, 1, −1, 1 ],
[ 1, 1, 1, 0, 1, 0, −1, 1 ],
[ 1, 1, 1, 0, 1, 1, −1, 2 ],
[ 1, 1, 1, 1, 0, 0, 0, 2 ],
[ 1, 2, 0, 0, 1, 1, −1, 2 ],
[ 1, 2, 0, 1, 1, 1, −2, 2 ],
[ 1, 2, 1, 0, 0, 1, −1, 2 ],
[ 1, 2, 1, 0, 1, 1, −1, 2 ],
[ 1, 2, 1, 1, 0, 1, −2, 2 ],
[ 1, 2, 1, 1, 1, 0, −2, 2 ],
[ 2, 2, 0, 1, 1, 1, −1, 3 ],
[ 2, 2, 1, 1, 1, 0, −1, 3 ]





CI =








b I =
Cox




0
1
1
1
1
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
−1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
−1
−1
−1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1
















bI =
C




1
0
0
0
0
1
1
0
















BI =



0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
−1
0
0
1
2
1
1
0
0
0
0
1
1
0
0
0
−1
−1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
−1
−1
−1
−1
−1
−1
−1
1
0
1
0
0
0
−1
0
−1











0
0
0
0
−1
−1
−1
−1
0
−1
0
0
1
1
0
1
Number of sincere Tits roots of poset I sI = 28.
Table of roots of qbI
[ −3,−2,−1,−1,−1, 2, 2,−2 ],
[ −3,−1,−1,−1,−2, 2, 2,−2 ],
[ −3,−1,−1,−1,−1, 2, 2,−2 ],
[ −2,−1,−1,−1,−1, 1, 2,−2 ],
[ −2,−1,−1,−1,−1, 2, 1,−1 ],
[ 2, 1, 1, 1, 1,−2,−1, 1 ],
[ 2, 1, 1, 1, 1,−1,−2, 2 ],
[ 3, 1, 1, 1, 1,−2,−2, 2 ],
[ 3, 1, 1, 1, 2,−2,−2, 2 ],
[ 3, 2, 1, 1, 1,−2,−2, 2 ],
[ −2, −1, −1, −1, 0, 1, 2, −1 ],
[ −2, −1, −1, 0, −1, 1, 1, −1 ],
[ −2, −1, −1, 0, 0, 1, 1, −1 ],
[ −2, −1, 0, −1, −1, 1, 2, −1 ],
[ −2, −1, 0, 0, −1, 1, 1, −1 ],
[ −2, 0, −1, −1, −1, 1, 2, −1 ],
[ −2, 0, −1, 0, −1, 1, 1, −1 ],
[ −1, −1, −1, 0, −1, 1, 1, −1 ],
[ −1, −1, −1, 0, 0, 1, 1, −1 ],
[ −1, −1, 0, −1, 0, 0, 1, −1 ],
[ −1, −1, 0, −1, 0, 1, 1, 0 ],
[ −1, −1, 0, 0, −1, 1, 1, −1 ],
[ −1, −1, 0, 0, 0, 0, 1, −1 ],
[ −1, −1, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, −1, −1, 0, 0, 1, −1 ],
[ −1, 0, −1, −1, 0, 1, 1, 0 ],
[ −1, 0, −1, 0, −1, 1, 1, −1 ],
[ −1, 0, −1, 0, 0, 0, 1, −1 ],
[ −1, 0, −1, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, −1, −1, 1, 0, −1 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, −1, 0, 1, 0, −1 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, −1, 1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ −3,−1,−2,−1,−1, 2, 2,−2 ],
[ −3,−1,−1,−1,−1, 1, 2,−2 ],
[ −3,−1,−1,−1,−1, 2, 2,−1 ],
[ −2,−1,−1,−1,−1, 1, 2,−1 ],
[ −2,−1,−1,−1,−1, 2, 2,−1 ],
[ 2, 1, 1, 1, 1,−2,−1, 2 ],
[ 2, 1, 1, 1, 1,−1,−1, 2 ],
[ 3, 1, 1, 1, 1,−2,−1, 2 ],
[ 3, 1, 1, 2, 1,−2,−2, 2 ],
[ −2, −1, −1, −1, 0, 1, 1, −2 ],
[ −2, −1, −1, −1, 0, 2, 1, −1 ],
[ −2, −1, −1, 0, −1, 1, 2, −1 ],
[ −2, −1, 0, −1, −1, 1, 1, −2 ],
[ −2, −1, 0, −1, −1, 2, 1, −1 ],
[ −2, 0, −1, −1, −1, 1, 1, −2 ],
[ −2, 0, −1, −1, −1, 2, 1, −1 ],
[ −2, 0, 0, −1, −1, 1, 1, −1 ],
[ −1, −1, −1, 0, 0, 0, 1, −1 ],
[ −1, −1, −1, 0, 0, 1, 1, 0 ],
[ −1, −1, 0, −1, 0, 1, 0, −1 ],
[ −1, −1, 0, 0, −1, 0, 1, −1 ],
[ −1, −1, 0, 0, −1, 1, 1, 0 ],
[ −1, −1, 0, 0, 0, 0, 1, 0 ],
[ −1, −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, −1, −1, 0, 1, 0, −1 ],
[ −1, 0, −1, 0, −1, 0, 1, −1 ],
[ −1, 0, −1, 0, −1, 1, 1, 0 ],
[ −1, 0, −1, 0, 0, 0, 1, 0 ],
[ −1, 0, −1, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, −1, −1, 1, 1, −1 ],
[ −1, 0, 0, −1, 0, 0, 1, −1 ],
[ −1, 0, 0, −1, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, −1, 0, 1, −1 ],
[ −1, 0, 0, 0, −1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
153
[ −3,−1,−1,−2,−1, 2, 2,−2 ],
[ −3,−1,−1,−1,−1, 2, 1,−2 ],
[ −2,−1,−1,−1,−1, 1, 1,−2 ],
[ −2,−1,−1,−1,−1, 2, 1,−2 ],
[ 2, 1, 1, 1, 1,−2,−2, 1 ],
[ 2, 1, 1, 1, 1,−1,−2, 1 ],
[ 3, 1, 1, 1, 1,−2,−2, 1 ],
[ 3, 1, 1, 1, 1,−1,−2, 2 ],
[ 3, 1, 2, 1, 1,−2,−2, 2 ],
[ −2, −1, −1, −1, 0, 1, 1, −1 ],
[ −2, −1, −1, 0, −1, 1, 1, −2 ],
[ −2, −1, −1, 0, −1, 2, 1, −1 ],
[ −2, −1, 0, −1, −1, 1, 1, −1 ],
[ −2, −1, 0, −1, 0, 1, 1, −1 ],
[ −2, 0, −1, −1, −1, 1, 1, −1 ],
[ −2, 0, −1, −1, 0, 1, 1, −1 ],
[ −1, −1, −1, −1, 0, 1, 1, −1 ],
[ −1, −1, −1, 0, 0, 1, 0, −1 ],
[ −1, −1, 0, −1, −1, 1, 1, −1 ],
[ −1, −1, 0, −1, 0, 1, 1, −1 ],
[ −1, −1, 0, 0, −1, 1, 0, −1 ],
[ −1, −1, 0, 0, 0, 0, 0, −1 ],
[ −1, −1, 0, 0, 0, 1, 0, −1 ],
[ −1, 0, −1, −1, −1, 1, 1, −1 ],
[ −1, 0, −1, −1, 0, 1, 1, −1 ],
[ −1, 0, −1, 0, −1, 1, 0, −1 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, 1, 0, −1 ],
[ −1, 0, 0, −1, −1, 0, 1, −1 ],
[ −1, 0, 0, −1, −1, 1, 1, 0 ],
[ −1, 0, 0, −1, 0, 0, 1, 0 ],
[ −1, 0, 0, −1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, −1, 0, 1, 0 ],
[ −1, 0, 0, 0, −1, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0, 0 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
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1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
2,
2,
2,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
0,
0,
1,
1,
1,
1,
1,
0, −1, 1, 0, 0,
0, 0, −1, 0, 1,
0, 0, 0, −1, 0,
0, 0, 0, 0, −1,
0, 0, 0, 0, 1,
0, 0, 0, 1, 0,
0, 0, 1, 0, −1,
0, 1, −1, 0, 0,
0, 1, 0, 0, 0,
1, 0, −1, 0, 0,
1, 0, 0, 0, 0,
0, −1, 0, 0, 0,
0, 0, 0, 0, −1,
0, 0, 0, −1, 0,
0, 0, 0, 0, 0,
0, 0, 1, −1, 0,
0, 0, 1, 0, 0,
0, 1, 0, −1, 0,
0, 1, 0, 0, 0,
0, 1, 1, −1, 0,
1, 0, 0, −1, 0,
1, 0, 0, 0, −1,
1, 0, 1, −1, −1,
1, 1, 0, −1, −1,
1, 1, 0, 0, −1,
0, 0, 0, −1, 0,
0, 0, 0, 0, −1,
0, 0, 1, −1, −1,
0, 1, 0, −1, −1,
0, 1, 0, 0, −1,
1, 0, 0, −1, −1,
1, 0, 1, −1, −1,
1, 0, 1, −1, −1,
1, 1, 1, −1, −2,
0, 0, 1, −1, −1,
0, 1, 1, −1, −2,
1, 0, 0, −1, −1,
1, 0, 1, −1, −1,
1, 1, 0, −1, −2,
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
0 ],
1 ],
1 ],
0 ],
1 ],
0 ],
1 ],
1 ],
0 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
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0,
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1,
1,
1,
1,
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1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
2,
2,
2,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
0,
0,
1,
1,
1,
1,
1,
0, −1, 0, 0, −1 ],
0, −1, 1, 0, 0 ],
0, 0, −1, 1, 0 ],
0, 0, 0, 0, −1 ],
0, 0, 0, 1, 1 ],
0, 0, 1, 0, 1 ],
0, 1, 0, 0, 0 ],
1, 0, −1, 0, 0 ],
1, 0, 0, 0, 1 ],
0, 0, −1, 0, 0 ],
0, 0, 0, 0, 1 ],
0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0 ],
0, 0, 0, −1, 0 ],
0, 1, −1, −1, 0 ],
0, 1, 0, −1, 0 ],
1, 0, −1, −1, 0 ],
1, 0, 0, −1, 0 ],
1, 1, −1, −1, 0 ],
1, 1, 0, −1, 1 ],
0, 0, −1, 0, 1 ],
0, 0, 0, 0, 1 ],
0, 1, −1, 0, 1 ],
1, 0, −1, −1, 1 ],
1, 1, −1, −1, 1 ],
0, 0, −1, 0, 1 ],
0, 0, 0, 0, 1 ],
0, 1, −1, 0, 1 ],
1, 0, −1, −1, 1 ],
1, 1, −1, −1, 1 ],
0, 0, −1, 0, 1 ],
1, 0, −1, −1, 1 ],
1, 0, −1, −1, 1 ],
1, 1, −1, −1, 1 ],
1, 0, −1, −1, 1 ],
1, 1, −1, −1, 1 ],
0, 1, −2, −1, 1 ],
0, 1, −1, −1, 2 ],
1, 0, −1, −1, 1 ],
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
1,
1,
1,
1,
0,
0,
1,
1,
1,
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
2,
2,
2,
2,
2,
2,
2,
0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 1, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 1 ],
0, 0, 1, 0, 0, −1, 0 ],
0, 1, −1, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, −1, 0 ],
1, −1, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 0, 0 ],
0, 0, 0, 1, −1, 0, 0 ],
0, 0, 0, 1, 0, −1, 1 ],
0, 0, 1, 0, −1, 0, 0 ],
0, 0, 1, 0, 0, −1, 1 ],
0, 0, 1, 1, −1, −1, 1 ],
0, 1, 0, 0, −1, −1, 0 ],
0, 1, 0, 0, 0, −1, 0 ],
0, 1, 0, 1, −1, −1, 0 ],
0, 1, 0, 1, 0, −1, 1 ],
0, 1, 1, 0, −1, 0, 1 ],
1, 0, 0, 0, −1, −1, 0 ],
1, 0, 0, 0, 0, −1, 0 ],
1, 0, 0, 1, −1, −1, 0 ],
1, 0, 0, 1, 0, −1, 1 ],
1, 0, 1, 0, −1, 0, 1 ],
1, 1, 0, 0, −1, −1, 0 ],
1, 1, 0, 0, 0, −1, 1 ],
0, 0, 1, 1, −1, −1, 1 ],
0, 1, 1, 1, −2, −1, 1 ],
0, 1, 1, 1, −1, −1, 2 ],
1, 0, 1, 1, −2, −1, 1 ],
1, 0, 1, 1, −1, −1, 2 ],
1, 1, 0, 1, −1, −2, 1 ],
1, 1, 1, 0, −2, −1, 1 ],
1, 1, 1, 0, −1, −1, 2 ]
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
∗
7
• I ≡ P80 :
6
2
5
1
4
3





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
















b
CI =



154
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
1
1
1
1
0
−1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
−1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
−1
0
−1
−1
−1
0
0
1
1
1
1
1
1
1
1
−1











1
 0

 0

BI = −10

 −1
 −1
−1

0
−1
1
0
0
0
−1
−1
0
0
0
0
0
0
−1
−1
0
−1
0
0
0
−1
−1
0
0
0
1
1
0
0
0
−1
0
0
0
−1
−1
−1
−1
0
0
1
−1
0
1
1
2
1
0
−1
0
0
−1
−1
−2
−1
Number of sincere Tits roots of poset I sI = 28.
Table of roots of qbI
[ −2,−2,−2,−1,−1,−1, 3,−3 ],
[ −2,−2,−1,−1,−1,−2, 3,−3 ],
[ −2,−2,−1,−1,−1,−1, 3,−2 ],
[ −2,−1,−1,−1,−1,−1, 3,−2 ],
[ −1,−2,−1,−1,−1,−1, 3,−2 ],
[ 1, 2, 1, 1, 1, 1,−3, 2 ],
[ 2, 1, 1, 1, 1, 1,−3, 2 ],
[ 2, 2, 1, 1, 1, 1,−3, 2 ],
[ 2, 2, 1, 1, 1, 2,−3, 3 ],
[ 2, 2, 2, 1, 1, 1,−3, 3 ],
[ −2, −1, −1, 0, −1, −1, 2, −2 ],
[ −1, −2, −1, −1, 0, −1, 2, −2 ],
[ −1, −1, −1, −1, −1, 0, 1, −2 ],
[ −1, −1, −1, −1, 0, −1, 1, −2 ],
[ −1, −1, −1, −1, 0, 0, 1, −2 ],
[ −1, −1, −1, 0, −1, −1, 1, −2 ],
[ −1, −1, −1, 0, −1, 0, 1, −2 ],
[ −1, −1, −1, 0, 0, −1, 1, −2 ],
[ −1, −1, −1, 0, 0, 0, 1, −1 ],
[ −1, −1, 0, −1, −1, −1, 2, −1 ],
[ −1, −1, 0, −1, −1, 0, 2, −1 ],
[ −1, −1, 0, −1, 0, −1, 2, −1 ],
[ −1, −1, 0, 0, −1, −1, 1, −1 ],
[ −1, −1, 0, 0, 0, −1, 1, −1 ],
[ −1, 0, −1, 0, 0, −1, 1, −1 ],
[ −1, 0, −1, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, −1, −1, 1, −1 ],
[ −1, 0, 0, 0, −1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, −1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, −1, 0, −1, 0, 1, −1 ],
[ 0, −1, −1, 0, 0, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, −1, 1, −1 ],
[ 0, −1, 0, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, −1, 0, 1, −1 ],
[ 0, −1, 0, 0, 0, −1, 1, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 0, 1, −1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, −1, 1 ],
[ 0, 1, 0, 0, 1, 0, −1, 1 ],
[ −2,−2,−1,−2,−1,−1, 3,−3 ],
[ −2,−2,−1,−1,−1,−1, 2,−3 ],
[ −2,−1,−1,−1,−1,−1, 2,−3 ],
[ −1,−2,−1,−1,−1,−1, 2,−3 ],
[ −1,−1,−1,−1,−1,−1, 2,−2 ],
[ 1, 2, 1, 1, 1, 1,−2, 2 ],
[ 2, 1, 1, 1, 1, 1,−2, 2 ],
[ 2, 2, 1, 1, 1, 1,−3, 3 ],
[ 2, 2, 1, 1, 2, 1,−3, 3 ],
[ −2, −1, −1, −1, −1, 0, 2, −2 ],
[ −2, −1, 0, −1, −1, −1, 2, −2 ],
[ −1, −2, −1, 0, −1, −1, 2, −2 ],
[ −1, −1, −1, −1, −1, 0, 2, −2 ],
[ −1, −1, −1, −1, 0, −1, 2, −2 ],
[ −1, −1, −1, −1, 0, 0, 1, −1 ],
[ −1, −1, −1, 0, −1, −1, 2, −2 ],
[ −1, −1, −1, 0, −1, 0, 1, −1 ],
[ −1, −1, −1, 0, 0, −1, 1, −1 ],
[ −1, −1, 0, −1, −1, −1, 1, −2 ],
[ −1, −1, 0, −1, −1, 0, 1, −2 ],
[ −1, −1, 0, −1, 0, −1, 1, −2 ],
[ −1, −1, 0, −1, 0, 0, 1, −1 ],
[ −1, −1, 0, 0, −1, −1, 2, −1 ],
[ −1, 0, −1, −1, 0, 0, 1, −1 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, −1, −1, 0, 1, −1 ],
[ −1, 0, 0, −1, 0, 0, 1, −1 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, 0, 0, −1, 1, −1 ],
[ 0, −1, −1, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, −1, −1, 1, −1 ],
[ 0, −1, 0, 0, −1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, −1, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],
155
[ −2,−2,−1,−1,−2,−1, 3,−3 ],
[ −2,−2,−1,−1,−1,−1, 3,−3 ],
[ −2,−1,−1,−1,−1,−1, 2,−2 ],
[ −1,−2,−1,−1,−1,−1, 2,−2 ],
[ 1, 1, 1, 1, 1, 1,−2, 2 ],
[ 1, 2, 1, 1, 1, 1,−2, 3 ],
[ 2, 1, 1, 1, 1, 1,−2, 3 ],
[ 2, 2, 1, 1, 1, 1,−2, 3 ],
[ 2, 2, 1, 2, 1, 1,−3, 3 ],
[ −2, −1, −1, −1, 0, −1, 2, −2 ],
[ −1, −2, −1, −1, −1, 0, 2, −2 ],
[ −1, −2, 0, −1, −1, −1, 2, −2 ],
[ −1, −1, −1, −1, −1, 0, 2, −1 ],
[ −1, −1, −1, −1, 0, −1, 2, −1 ],
[ −1, −1, −1, −1, 0, 0, 2, −1 ],
[ −1, −1, −1, 0, −1, −1, 2, −1 ],
[ −1, −1, −1, 0, −1, 0, 2, −1 ],
[ −1, −1, −1, 0, 0, −1, 2, −1 ],
[ −1, −1, 0, −1, −1, −1, 2, −2 ],
[ −1, −1, 0, −1, −1, 0, 1, −1 ],
[ −1, −1, 0, −1, 0, −1, 1, −1 ],
[ −1, −1, 0, 0, −1, −1, 1, −2 ],
[ −1, −1, 0, 0, −1, 0, 1, −1 ],
[ −1, 0, −1, 0, −1, 0, 1, −1 ],
[ −1, 0, −1, 0, 0, 0, 1, −1 ],
[ −1, 0, 0, −1, 0, −1, 1, −1 ],
[ −1, 0, 0, −1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, −1, 0, 1, −1 ],
[ −1, 0, 0, 0, 0, −1, 1, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, −1, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 1, −1, 0 ],
[ 0, 1, 0, 0, 1, 0, −1, 0 ],
[ 0, 1, 0, 0, 1, 1, −1, 1 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
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1,
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1,
1,
1,
0,
0,
0,
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1,
1,
1,
1,
0,
0,
0,
0,
1,
0,
0,
1,
1,
0,
0,
0,
0,
1,
0,
1,
1,
0,
0,
1,
1,
0,
0,
1,
0,
1,
0, −1,
1, −1,
0, −1,
0, −1,
0, −1,
1, −1,
0, −1,
1, −1,
0, 0,
0, −1,
1, −1,
1, −1,
1, −1,
1, −2,
0, −2,
1, −2,
0, −1,
1, −1,
0, −1,
1, −1,
0, −1,
1, −1,
0, −1,
1, −2,
1, −2,
0 ],
1 ],
1 ],
1 ],
0 ],
0 ],
0 ],
1 ],
1 ],
0 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
2 ],
2 ],
2 ],
2 ],
2 ],
2 ],
2 ],
2 ],
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
−1
0
−1
0
0
0
0
0
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
1,
1,
1,
1,
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1,
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2,
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1,
1,
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1, −1,
0, −1,
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1, −1,
1, −1,
0, −1,
1, −2,
1, −2,
0, −2,
1, −2,
0, −2,
1, −2,
0, −2,
1, −2,
0, −2,
1, −2,
1 ],
1 ],
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2 ],
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[
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[
[
[
[
[
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[
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[
[
[
[
[
[
[
[
[
0, 1,
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1, −1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
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1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
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1,
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1,
1,
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1
1
1
1
1
1
1
0
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1
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1
1
1
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1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
−1
1
0
1
2
1
1
0
0, 0,
0, −1,
1, −1,
0, 0,
0, 0,
1, 0,
0, 0,
0, −1,
0, −1,
0, 0,
0, −1,
1, −2,
0, −1,
1, −1,
0, −1,
1, −1,
1, −1,
0, −1,
1, −2,
0, −1,
1, −2,
0, −2,
1, −2,
1, −2,
0, −2,
1 ],
0 ],
1 ],
0 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
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2 ],
2 ],
2 ],
1 ],
1 ],
2 ],
1 ],
2 ],
2 ],
2 ],
2 ],
2]
∗
7
6
• I ≡ P81 :
5
2
4
3
1





CI =








b
CoxI =



0
0
0
0
0
0
0
−1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
















BI =



Number of sincere Tits roots of poset I sI = 22.
Table of roots of qbI
156
0
0
0
1
1
1
1
0
−1
0
0
1
1
1
0
0
−1
0
0
0
1
0
0
1
1
0
0
0
−1
0
0
0
−1
−1
−1
−1
−1
−1
−1
1
1
0
1
0
0
0
0
−1











0
0
−1
−1
−1
−1
−1
0
0
0
0
1
1
0
0
0











[ −2, 3, 2, 2,−1,−1,−1, 1 ],
[ −1, 2, 2, 2,−1,−1,−1, 1 ],
[ −1, 3, 2, 2,−2,−1,−1, 1 ],
[ −1, 3, 2, 2,−1,−1,−1, 1 ],
[ 1,−3,−2,−2, 1, 1, 1,−1 ],
[ 1,−3,−2,−2, 2, 1, 1,−1 ],
[ 1,−2,−2,−2, 1, 1, 1,−1 ],
[ 2,−3,−2,−2, 1, 1, 1,−1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, −1, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, −1, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 0, 1 ],
[ −1, 1, 1, 1, −1, 0, 0, 0 ],
[ −1, 1, 1, 1, 0, −1, 0, 0 ],
[ −1, 1, 1, 1, 0, 0, −1, 1 ],
[ −1, 2, 1, 1, −1, −1, 0, 0 ],
[ −1, 2, 1, 1, −1, 0, −1, 1 ],
[ −1, 2, 1, 1, 0, −1, −1, 1 ],
[ −1, 2, 1, 2, −1, −1, −1, 0 ],
[ −1, 2, 1, 2, 0, −1, −1, 1 ],
[ −1, 2, 2, 1, −1, 0, −1, 1 ],
[ 0, −2, −1, −2, 1, 1, 1, −1 ],
[ 0, −2, −1, −1, 1, 1, 0, −1 ],
[ 0, −1, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 1, 0 ],
[ 0, −1, −1, −1, 1, 0, 1, 0 ],
[ 0, −1, −1, −1, 1, 1, 1, 0 ],
[ 0, −1, −1, 0, 0, 0, 1, 0 ],
[ 0, −1, −1, 0, 0, 1, 1, 0 ],
[ 0, −1, −1, 0, 1, 0, 1, 0 ],
[ 0, −1, 0, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 1, 0, 0 ],
[ 0, −1, 0, −1, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 0, 1, −1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, −1, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, −1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, −1, 1 ],
[ 0, 1, 1, 0, −1, 0, −1, 0 ],
[ 0, 1, 1, 0, 0, −1, −1, 0 ],
[ 0, 1, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 1, 1, −1, −1, −1, 0 ],
[ 0, 1, 1, 1, −1, 0, −1, 0 ],
[ 0, 1, 1, 1, 0, −1, −1, 0 ],
[ 0, 1, 1, 1, 0, 0, −1, 1 ],
[ 0, 2, 1, 1, −1, −1, 0, 1 ],
[ 0, 2, 1, 2, −1, −1, −1, 1 ],
[ 1, −2, −2, −1, 1, 0, 1, −1 ],
[ 1, −2, −1, −2, 0, 1, 1, −1 ],
[ 1, −2, −1, −2, 1, 1, 1, 0 ],
[ 1, −2, −1, −1, 0, 1, 1, −1 ],
[ 1, −2, −1, −1, 1, 0, 1, −1 ],
[ 1, −2, −1, −1, 1, 1, 0, 0 ],
[ 1, −1, −1, −1, 0, 0, 1, −1 ],
[ −1, 2, 1, 2,−1,−1,−1, 1 ],
[ −1, 3, 1, 2,−1,−1,−1, 1 ],
[ −1, 3, 2, 2,−1,−2,−1, 1 ],
[ −1, 3, 2, 2,−1,−1,−1, 2 ],
[ 1,−3,−2,−2, 1, 1, 2,−1 ],
[ 1,−3,−2,−1, 1, 1, 1,−1 ],
[ 1,−2,−2,−1, 1, 1, 1,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, −1, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 0, 1 ],
[ −1, 1, 1, 0, 0, 0, −1, 0 ],
[ −1, 1, 1, 1, −1, −1, 0, 0 ],
[ −1, 1, 1, 1, −1, 0, 0, 1 ],
[ −1, 1, 1, 1, 0, −1, 0, 1 ],
[ −1, 1, 1, 1, 0, 0, 0, 1 ],
[ −1, 2, 1, 1, −1, −1, 0, 1 ],
[ −1, 2, 1, 1, −1, 0, 0, 1 ],
[ −1, 2, 1, 1, 0, −1, 0, 1 ],
[ −1, 2, 1, 2, −1, −1, 0, 1 ],
[ −1, 2, 2, 1, −1, −1, −1, 0 ],
[ −1, 2, 2, 1, 0, −1, −1, 1 ],
[ 0, −2, −1, −1, 0, 1, 1, −1 ],
[ 0, −2, −1, −1, 1, 1, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 0, −1 ],
[ 0, −1, −1, −1, 1, 0, 0, −1 ],
[ 0, −1, −1, −1, 1, 1, 0, −1 ],
[ 0, −1, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, −1, 0, 0, 1, 0, −1 ],
[ 0, −1, −1, 0, 1, 0, 0, −1 ],
[ 0, −1, −1, 0, 1, 1, 0, 0 ],
[ 0, −1, 0, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, −1, 1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 1, −1, −1, 0, 0 ],
[ 0, 1, 0, 1, −1, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, −1, 0, 1 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, −1, 0, 0, 0 ],
[ 0, 1, 1, 0, 0, −1, 0, 0 ],
[ 0, 1, 1, 0, 0, 0, −1, 1 ],
[ 0, 1, 1, 1, −1, −1, 0, 0 ],
[ 0, 1, 1, 1, −1, 0, −1, 1 ],
[ 0, 1, 1, 1, 0, −1, −1, 1 ],
[ 0, 2, 1, 1, −1, −1, −1, 0 ],
[ 0, 2, 1, 1, −1, 0, −1, 1 ],
[ 0, 2, 2, 1, −1, −1, −1, 1 ],
[ 1, −2, −2, −1, 1, 1, 0, −1 ],
[ 1, −2, −1, −2, 1, 0, 1, −1 ],
[ 1, −2, −1, −1, 0, 0, 1, −1 ],
[ 1, −2, −1, −1, 0, 1, 1, 0 ],
[ 1, −2, −1, −1, 1, 0, 1, 0 ],
[ 1, −2, −1, −1, 1, 1, 1, 0 ],
[ 1, −1, −1, −1, 0, 0, 1, 0 ],
157
[ −1, 2, 2, 1,−1,−1,−1, 1 ],
[ −1, 3, 2, 1,−1,−1,−1, 1 ],
[ −1, 3, 2, 2,−1,−1,−2, 1 ],
[ 1,−3,−2,−2, 1, 1, 1,−2 ],
[ 1,−3,−2,−2, 1, 2, 1,−1 ],
[ 1,−3,−1,−2, 1, 1, 1,−1 ],
[ 1,−2,−1,−2, 1, 1, 1,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, −1, 0 ],
[ −1, 1, 1, 0, −1, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 1, −1, 0, −1, 0 ],
[ −1, 1, 1, 1, 0, −1, −1, 0 ],
[ −1, 1, 1, 1, 0, 0, −1, 0 ],
[ −1, 2, 1, 1, −1, −1, −1, 0 ],
[ −1, 2, 1, 1, −1, 0, −1, 0 ],
[ −1, 2, 1, 1, 0, −1, −1, 0 ],
[ −1, 2, 1, 1, 0, 0, −1, 1 ],
[ −1, 2, 1, 2, −1, 0, −1, 1 ],
[ −1, 2, 2, 1, −1, −1, 0, 1 ],
[ 0, −2, −2, −1, 1, 1, 1, −1 ],
[ 0, −2, −1, −1, 1, 0, 1, −1 ],
[ 0, −2, −1, −1, 1, 1, 1, 0 ],
[ 0, −1, −1, −1, 0, 1, 1, −1 ],
[ 0, −1, −1, −1, 1, 0, 1, −1 ],
[ 0, −1, −1, −1, 1, 1, 0, 0 ],
[ 0, −1, −1, 0, 0, 0, 1, −1 ],
[ 0, −1, −1, 0, 0, 1, 0, 0 ],
[ 0, −1, −1, 0, 1, 0, 0, 0 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 1, 0, −1 ],
[ 0, −1, 0, −1, 1, 0, 0, −1 ],
[ 0, −1, 0, −1, 1, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, −1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, −1, 0, −1, 0 ],
[ 0, 1, 0, 1, 0, −1, −1, 0 ],
[ 0, 1, 0, 1, 0, 0, −1, 0 ],
[ 0, 1, 1, 0, −1, −1, 0, 0 ],
[ 0, 1, 1, 0, −1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, −1, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, −1, −1, 0, 1 ],
[ 0, 1, 1, 1, −1, 0, 0, 1 ],
[ 0, 1, 1, 1, 0, −1, 0, 1 ],
[ 0, 2, 1, 1, −1, −1, −1, 1 ],
[ 0, 2, 1, 1, 0, −1, −1, 1 ],
[ 1, −2, −2, −1, 0, 1, 1, −1 ],
[ 1, −2, −2, −1, 1, 1, 1, 0 ],
[ 1, −2, −1, −2, 1, 1, 0, −1 ],
[ 1, −2, −1, −1, 0, 1, 0, −1 ],
[ 1, −2, −1, −1, 1, 0, 0, −1 ],
[ 1, −2, −1, −1, 1, 1, 0, −1 ],
[ 1, −1, −1, −1, 0, 0, 0, −1 ],
[ 1, −1, −1, −1, 0, 1, 0, −1 ],
[
[
[
[
[
[
[
[
1, −1, −1, −1,
1, −1, −1, −1,
1, −1, −1, 0,
1, −1, −1, 0,
1, −1, 0, −1,
1, −1, 0, −1,
1, 0, 0, −1,
1, 0, 0, 0,
0,
1,
0,
0,
0,
1,
0,
0,
1, 0, 0 ],
0, 0, 0 ],
0, 0, −1 ],
1, 0, 0 ],
0, 0, 0 ],
0, 0, 0 ],
0, 0, 0 ],
0, −1, 0 ],
[
[
[
[
[
[
[
[
1, −1, −1, −1, 0,
1, −1, −1, −1, 1,
1, −1, −1, 0, 0,
1, −1, −1, 0, 1,
1, −1, 0, −1, 0,
1, −1, 0, 0, 0,
1, 0, 0, 0, −1,
1, 0, 0, 0, 0,
1,
0,
0,
0,
0,
0,
0,
0,
1,
1,
0,
0,
1,
0,
0,
0,
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
[
[
[
[
[
[
[
[
1, −1, −1, −1,
1, −1, −1, −1,
1, −1, −1, 0,
1, −1, 0, −1,
1, −1, 0, −1,
1, 0, −1, 0,
1, 0, 0, 0,
1, 0, 0, 0,
1, 0,
1, 1,
0, 0,
0, 0,
0, 1,
0, 0,
0, −1,
0, 0,
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0, −1 ],
0, 0 ],
1, 0 ],
0, −1 ],
0, 0 ],
0, 0 ],
0, 0 ],
0, 1 ]
∗
7
1
6
• I ≡ P82 :
3
5
4
2




CI =



1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
−1
1
0
0
0
0
0
0
−1






b I =
Cox




0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
−1
0
−1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
















b
CI =



1
1
1
1
1
1
1
−1
















BI =



1
0
0
0
0
0
0
−1
0
1
1
1
1
1
1
−1
0
0
0
1
1
1
1
0
0
0
−1
0
−1
−1
−1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
−1
−1
−1
−1
0
0
0
−1
0
0
−1
0
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
1
0
0
1
1
0











0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
−1
Number of sincere Tits roots of poset I sI = 28.
Table of roots of qbI
[ −2, 1,−3,−2,−2, 1, 1,−3 ],
[ −1, 1,−3,−2,−2, 1, 2,−2 ],
[ −1, 1,−3,−1,−2, 1, 1,−2 ],
[ −1, 1,−2,−2,−1, 1, 1,−1 ],
[ −1, 1,−2,−1,−1, 1, 1,−1 ],
[ 1,−1, 2, 1, 1,−1,−1, 1 ],
[ 1,−1, 2, 2, 1,−1,−1, 1 ],
[ 1,−1, 3, 1, 2,−1,−1, 2 ],
[ 1,−1, 3, 2, 2,−1,−2, 2 ],
[ 2,−1, 3, 2, 2,−1,−1, 3 ],
[ −1, 0, −2, −1, −2, 1, 1, −2 ],
[ −1, 0, −2, −1, −1, 1, 1, −2 ],
[ −1, 0, −1, −1, −1, 0, 1, −2 ],
[ −1, 0, −1, −1, −1, 1, 0, −1 ],
[ −1, 0, −1, −1, 0, 0, 0, −1 ],
[ −1, 0, −1, 0, −1, 0, 0, −2 ],
[ −1, 0, −1, 0, −1, 1, 0, −1 ],
[ −1, 1,−3,−2,−2, 1, 1,−3 ],
[ −1, 1,−3,−2,−2, 2, 1,−2 ],
[ −1, 1,−2,−2,−2, 1, 1,−2 ],
[ −1, 1,−2,−1,−2, 1, 1,−2 ],
[ −1, 2,−3,−2,−2, 1, 1,−2 ],
[ 1,−1, 2, 1, 2,−1,−1, 1 ],
[ 1,−1, 2, 2, 1,−1,−1, 2 ],
[ 1,−1, 3, 2, 1,−1,−1, 2 ],
[ 1,−1, 3, 2, 2,−1,−1, 2 ],
[ −1, −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, −2, −1, −1, 0, 1, −2 ],
[ −1, 0, −2, −1, −1, 1, 1, −1 ],
[ −1, 0, −1, −1, −1, 0, 1, −1 ],
[ −1, 0, −1, −1, −1, 1, 1, −1 ],
[ −1, 0, −1, −1, 0, 0, 1, −1 ],
[ −1, 0, −1, 0, −1, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
158
[ −1, 1,−3,−2,−2, 1, 1,−2 ],
[ −1, 1,−3,−2,−1, 1, 1,−2 ],
[ −1, 1,−2,−2,−1, 1, 1,−2 ],
[ −1, 1,−2,−1,−2, 1, 1,−1 ],
[ 1,−2, 3, 2, 2,−1,−1, 2 ],
[ 1,−1, 2, 1, 2,−1,−1, 2 ],
[ 1,−1, 2, 2, 2,−1,−1, 2 ],
[ 1,−1, 3, 2, 2,−2,−1, 2 ],
[ 1,−1, 3, 2, 2,−1,−1, 3 ],
[ −1, 0, −2, −2, −1, 1, 1, −2 ],
[ −1, 0, −2, −1, −1, 1, 0, −2 ],
[ −1, 0, −1, −1, −1, 0, 0, −2 ],
[ −1, 0, −1, −1, −1, 1, 0, −2 ],
[ −1, 0, −1, −1, 0, 0, 0, −2 ],
[ −1, 0, −1, −1, 0, 1, 0, −1 ],
[ −1, 0, −1, 0, −1, 0, 1, −1 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, 0, 0, −1, 0, 0, −1 ],
−1, 0, 0, 0, 0, 0, 0, −1 ],
−1, 1, −2, −2, −1, 1, 0, −2 ],
−1, 1, −2, −1, −1, 0, 0, −2 ],
−1, 1, −2, −1, −1, 1, 0, −2 ],
−1, 1, −1, −1, −1, 0, 0, −1 ],
−1, 1, −1, −1, 0, 0, 0, −1 ],
0, −1, 0, 0, 0, 0, 0, 0 ],
0, −1, 0, 0, 1, 0, 0, 0 ],
0, −1, 1, 0, 1, −1, 0, 0 ],
0, −1, 1, 0, 1, 0, 0, 1 ],
0, −1, 1, 1, 0, 0, 0, 0 ],
0, −1, 1, 1, 1, −1, 0, 0 ],
0, −1, 1, 1, 1, 0, −1, 1 ],
0, −1, 2, 1, 1, −1, −1, 1 ],
0, −1, 2, 1, 2, −1, −1, 1 ],
0, 0, −1, −1, −1, 0, 1, −1 ],
0, 0, −1, −1, −1, 1, 1, 0 ],
0, 0, −1, −1, 0, 0, 1, 0 ],
0, 0, −1, −1, 0, 1, 1, 0 ],
0, 0, −1, 0, −1, 0, 1, 0 ],
0, 0, −1, 0, −1, 1, 1, 0 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, −1, 1, 0, 0, 0 ],
0, 0, 0, 0, −1, 0, 1, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 1, −1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 0, 1, 0, 1, −1, −1, 0 ],
0, 0, 1, 0, 1, 0, −1, 0 ],
0, 0, 1, 1, 0, −1, −1, 0 ],
0, 0, 1, 1, 0, 0, −1, 0 ],
0, 0, 1, 1, 1, −1, −1, 0 ],
0, 0, 1, 1, 1, 0, −1, 1 ],
0, 1, −2, −1, −2, 1, 1, −1 ],
0, 1, −2, −1, −1, 1, 1, −1 ],
0, 1, −1, −1, −1, 0, 1, −1 ],
0, 1, −1, −1, −1, 1, 0, 0 ],
0, 1, −1, −1, 0, 0, 0, 0 ],
0, 1, −1, 0, −1, 0, 0, −1 ],
0, 1, −1, 0, −1, 1, 0, 0 ],
0, 1, 0, 0, −1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
1, −1, 1, 1, 0, 0, 0, 1 ],
1, −1, 1, 1, 1, 0, 0, 1 ],
1, −1, 2, 1, 1, −1, 0, 2 ],
1, −1, 2, 1, 1, 0, 0, 2 ],
1, −1, 2, 2, 1, −1, 0, 2 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 0, 1, 0, 0, 1 ],
1, 0, 1, 0, 1, −1, 0, 1 ],
1, 0, 1, 0, 1, 0, 0, 2 ],
1, 0, 1, 1, 0, 0, 0, 1 ],
1, 0, 1, 1, 1, −1, 0, 1 ],
1, 0, 1, 1, 1, 0, −1, 2 ],
1, 0, 2, 1, 1, −1, −1, 2 ],
1, 0, 2, 1, 2, −1, −1, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, 0, 0, 0, −1, 0, −1 ],
−1, 0, 0, 0, 0, 0, 0, 0 ],
−1, 1, −2, −1, −2, 0, 1, −2 ],
−1, 1, −2, −1, −1, 0, 1, −2 ],
−1, 1, −2, −1, −1, 1, 0, −1 ],
−1, 1, −1, −1, −1, 0, 1, −1 ],
−1, 1, −1, 0, −1, 0, 0, −1 ],
0, −1, 0, 0, 0, 0, 1, 0 ],
0, −1, 0, 1, 0, 0, 0, 0 ],
0, −1, 1, 0, 1, 0, −1, 0 ],
0, −1, 1, 1, 0, −1, 0, 0 ],
0, −1, 1, 1, 0, 0, 0, 1 ],
0, −1, 1, 1, 1, −1, 0, 1 ],
0, −1, 1, 1, 1, 0, 0, 1 ],
0, −1, 2, 1, 1, −1, 0, 1 ],
0, −1, 2, 2, 1, −1, −1, 1 ],
0, 0, −1, −1, −1, 1, 0, −1 ],
0, 0, −1, −1, 0, 0, 0, −1 ],
0, 0, −1, −1, 0, 1, 0, −1 ],
0, 0, −1, 0, −1, 0, 0, −1 ],
0, 0, −1, 0, −1, 1, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 1, 0, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, −1, 1, 0, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 1, −1, 0, 0 ],
0, 0, 1, 0, 1, 0, −1, 1 ],
0, 0, 1, 1, 0, −1, 0, 0 ],
0, 0, 1, 1, 0, 0, −1, 1 ],
0, 0, 1, 1, 1, −1, −1, 1 ],
0, 0, 2, 1, 1, −1, −1, 1 ],
0, 1, −2, −1, −1, 0, 1, −1 ],
0, 1, −2, −1, −1, 1, 1, 0 ],
0, 1, −1, −1, −1, 0, 1, 0 ],
0, 1, −1, −1, −1, 1, 1, 0 ],
0, 1, −1, −1, 0, 0, 1, 0 ],
0, 1, −1, 0, −1, 0, 0, 0 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
1, −1, 1, 1, 1, −1, 0, 1 ],
1, −1, 1, 1, 1, 0, 0, 2 ],
1, −1, 2, 1, 1, 0, −1, 1 ],
1, −1, 2, 1, 2, −1, 0, 2 ],
1, −1, 2, 2, 1, 0, −1, 2 ],
1, 0, 0, 0, 0, 0, 1, 1 ],
1, 0, 0, 1, 0, 0, 0, 1 ],
1, 0, 1, 0, 1, 0, −1, 1 ],
1, 0, 1, 1, 0, −1, 0, 1 ],
1, 0, 1, 1, 0, 0, 0, 2 ],
1, 0, 1, 1, 1, −1, 0, 2 ],
1, 0, 1, 1, 1, 0, 0, 2 ],
1, 0, 2, 1, 1, −1, 0, 2 ],
1, 0, 2, 2, 1, −1, −1, 2 ],
159
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, 0, 0, 0, 0, −1, −1 ],
−1, 1, −2, −2, −1, 0, 1, −2 ],
−1, 1, −2, −1, −2, 1, 0, −2 ],
−1, 1, −2, −1, −1, 0, 1, −1 ],
−1, 1, −1, −1, −1, 0, 0, −2 ],
−1, 1, −1, −1, −1, 1, 0, −1 ],
0, −1, 0, 0, 0, 0, 0, −1 ],
0, −1, 0, 0, 0, 1, 0, 0 ],
0, −1, 1, 0, 0, 0, 0, 0 ],
0, −1, 1, 0, 1, 0, 0, 0 ],
0, −1, 1, 1, 0, 0, −1, 0 ],
0, −1, 1, 1, 1, −1, −1, 0 ],
0, −1, 1, 1, 1, 0, −1, 0 ],
0, −1, 2, 1, 1, −1, −1, 0 ],
0, −1, 2, 1, 1, 0, −1, 1 ],
0, 0, −2, −1, −1, 1, 1, −1 ],
0, 0, −1, −1, −1, 1, 1, −1 ],
0, 0, −1, −1, 0, 0, 1, −1 ],
0, 0, −1, −1, 0, 1, 0, 0 ],
0, 0, −1, 0, −1, 0, 1, −1 ],
0, 0, −1, 0, −1, 1, 0, 0 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 1, 0, 0 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1, −1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 1, 0, 0, −1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 1, −1, 0, 1 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 0, 1, 1, 0, −1, 0, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 0, 1, 1, 1, −1, 0, 1 ],
0, 1, −2, −2, −1, 1, 1, −1 ],
0, 1, −2, −1, −1, 1, 0, −1 ],
0, 1, −1, −1, −1, 0, 0, −1 ],
0, 1, −1, −1, −1, 1, 0, −1 ],
0, 1, −1, −1, 0, 0, 0, −1 ],
0, 1, −1, −1, 0, 1, 0, 0 ],
0, 1, −1, 0, −1, 0, 1, 0 ],
0, 1, 0, −1, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
1, −1, 1, 0, 1, 0, 0, 1 ],
1, −1, 1, 1, 1, 0, −1, 1 ],
1, −1, 2, 1, 1, −1, 0, 1 ],
1, −1, 2, 1, 1, 0, −1, 2 ],
1, −1, 2, 1, 2, 0, −1, 2 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 0, 1, 0, 1, 0, 0, 1 ],
1, 0, 1, 1, 0, 0, −1, 1 ],
1, 0, 1, 1, 1, −1, −1, 1 ],
1, 0, 1, 1, 1, 0, −1, 1 ],
1, 0, 2, 1, 1, −1, −1, 1 ],
1, 0, 2, 1, 1, 0, −1, 2 ],
1, 1, 0, 0, 0, 0, 0, 1 ]
∗
• I ≡ P83 :
4
7
2
6
1
5
3





CI =








b I =
Cox




0
0
1
1
1
1
1
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
−1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
−1
0
−1
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
















b
CI =



1
1
1
1
1
1
1
−1
















BI =



1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
−1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
−1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
−1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
0
−1
0
0
−1
0











0
0
−1
0
−1
−1
0
1
1
0
1
0
0
0
0
−1
Number of sincere Tits roots of poset I sI = 28.
Table of roots of qbI
[ −2,−1, 1,−3,−2,−2, 1,−4 ],
[ −1,−1, 1,−3,−2,−2, 1,−3 ],
[ −1,−1, 1,−3,−1,−2, 1,−3 ],
[ −1,−1, 1,−2,−2,−1, 1,−2 ],
[ −1,−1, 1,−2,−1,−1, 1,−2 ],
[ 1, 1,−1, 2, 1, 1,−1, 2 ],
[ 1, 1,−1, 2, 2, 1,−1, 2 ],
[ 1, 1,−1, 3, 1, 2,−1, 3 ],
[ 1, 1,−1, 3, 2, 2,−1, 3 ],
[ 2, 1,−1, 3, 2, 2,−1, 4 ],
[ −1, −1, 0, −2, −1, −1, 0, −3 ],
[ −1, −1, 0, −1, −1, −1, 0, −3 ],
[ −1, −1, 0, −1, −1, 0, 0, −2 ],
[ −1, −1, 1, −2, −1, −2, 0, −3 ],
[ −1, −1, 1, −1, −1, −1, 0, −2 ],
[ −1, 0, 0, −1, −1, −1, 0, −2 ],
[ −1, 0, 0, −1, −1, 0, 0, −2 ],
[ −1, 0, 0, −1, 0, −1, 0, −2 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1, −1 ],
[ −1, 0, 1, −2, −2, −1, 1, −2 ],
[ −1, 0, 1, −2, −1, −1, 1, −2 ],
[ −1, 0, 1, −1, −1, −1, 0, −1 ],
[ −1, 0, 1, −1, 0, −1, 0, −1 ],
[ 0, −1, 0, −2, −1, −1, 1, −2 ],
[ 0, −1, 0, −1, −1, −1, 1, −1 ],
[ 0, −1, 0, −1, −1, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, −1, 1, −1 ],
[ 0, −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ −1,−2, 1,−3,−2,−2, 1,−4 ],
[ −1,−1, 1,−3,−2,−2, 2,−3 ],
[ −1,−1, 1,−2,−2,−2, 1,−3 ],
[ −1,−1, 1,−2,−1,−2, 1,−3 ],
[ −1,−1, 2,−3,−2,−2, 1,−3 ],
[ 1, 1,−1, 2, 1, 2,−1, 2 ],
[ 1, 1,−1, 2, 2, 1,−1, 3 ],
[ 1, 1,−1, 3, 2, 1,−1, 3 ],
[ 1, 1,−1, 3, 2, 2,−1, 4 ],
[ −1, −1, 0, −2, −2, −1, 1, −3 ],
[ −1, −1, 0, −2, −1, −1, 1, −3 ],
[ −1, −1, 0, −1, −1, −1, 0, −2 ],
[ −1, −1, 0, −1, 0, −1, 0, −2 ],
[ −1, −1, 1, −2, −1, −1, 0, −3 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, −1, −1, −1, 1, −2 ],
[ −1, 0, 0, −1, −1, 0, 0, −1 ],
[ −1, 0, 0, −1, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 1, −2, −1, −2, 1, −2 ],
[ −1, 0, 1, −2, −1, −1, 1, −1 ],
[ −1, 0, 1, −1, −1, −1, 1, −1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, −1, −1, −1, 0, −2 ],
[ 0, −1, 0, −1, −1, 0, 0, −2 ],
[ 0, −1, 0, −1, 0, −1, 0, −2 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, −1, −1 ],
[ 0, −1, 1, −2, −2, −1, 1, −2 ],
160
[ −1,−1, 1,−3,−2,−2, 1,−4 ],
[ −1,−1, 1,−3,−2,−1, 1,−3 ],
[ −1,−1, 1,−2,−2,−1, 1,−3 ],
[ −1,−1, 1,−2,−1,−2, 1,−2 ],
[ 1, 1,−2, 3, 2, 2,−1, 3 ],
[ 1, 1,−1, 2, 1, 2,−1, 3 ],
[ 1, 1,−1, 2, 2, 2,−1, 3 ],
[ 1, 1,−1, 3, 2, 2,−2, 3 ],
[ 1, 2,−1, 3, 2, 2,−1, 4 ],
[ −1, −1, 0, −2, −1, −2, 1, −3 ],
[ −1, −1, 0, −2, −1, −1, 1, −2 ],
[ −1, −1, 0, −1, −1, −1, 1, −2 ],
[ −1, −1, 1, −2, −2, −1, 0, −3 ],
[ −1, −1, 1, −2, −1, −1, 0, −2 ],
[ −1, 0, 0, −2, −1, −1, 1, −2 ],
[ −1, 0, 0, −1, −1, −1, 1, −1 ],
[ −1, 0, 0, −1, −1, 0, 1, −1 ],
[ −1, 0, 0, −1, 0, −1, 1, −1 ],
[ −1, 0, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, −2, −1, −1, 0, −2 ],
[ −1, 0, 1, −1, −1, −1, 0, −2 ],
[ −1, 0, 1, −1, −1, 0, 0, −1 ],
[ 0, −1, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, −1, −1, 1, −2 ],
[ 0, −1, 0, −1, −1, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 1, −2, −1, −2, 1, −2 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 1, −2, −1, −1, 0, −2 ],
0, −1, 1, −1, −1, −1, 0, −2 ],
0, −1, 1, −1, −1, 0, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, −1, 0, 1, 0, 0, 0 ],
0, 0, −1, 1, 0, 1, 0, 0 ],
0, 0, −1, 1, 1, 0, 0, 0 ],
0, 0, −1, 1, 1, 1, −1, 1 ],
0, 0, 0, −1, −1, −1, 1, −1 ],
0, 0, 0, −1, −1, 0, 1, 0 ],
0, 0, 0, −1, 0, −1, 1, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, 0, 1, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 0, 1, 0, 1, −1, 0 ],
0, 0, 0, 1, 1, 0, −1, 0 ],
0, 0, 0, 1, 1, 1, −1, 1 ],
0, 0, 1, −1, −1, −1, 1, −1 ],
0, 0, 1, −1, −1, 0, 0, 0 ],
0, 0, 1, −1, 0, −1, 0, 0 ],
0, 0, 1, 0, −1, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 1, −1, 1, 1, 0, 0, 1 ],
0, 1, −1, 1, 1, 1, 0, 2 ],
0, 1, −1, 2, 1, 1, 0, 2 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 1, 0, 1 ],
0, 1, 0, 1, 0, 1, −1, 1 ],
0, 1, 0, 1, 1, 0, −1, 1 ],
0, 1, 0, 1, 1, 1, −1, 1 ],
0, 1, 0, 2, 1, 1, −1, 2 ],
1, 0, −1, 1, 0, 1, 0, 1 ],
1, 0, −1, 1, 1, 1, 0, 1 ],
1, 0, −1, 2, 1, 1, −1, 2 ],
1, 0, −1, 2, 2, 1, −1, 2 ],
1, 0, 0, 0, 0, 0, 1, 1 ],
1, 0, 0, 1, 0, 0, 0, 1 ],
1, 0, 0, 1, 0, 1, 0, 2 ],
1, 0, 0, 1, 1, 0, 0, 2 ],
1, 0, 0, 1, 1, 1, 0, 2 ],
1, 1, −1, 1, 1, 1, 0, 2 ],
1, 1, −1, 2, 1, 2, 0, 3 ],
1, 1, 0, 1, 1, 0, 0, 2 ],
1, 1, 0, 1, 1, 1, 0, 3 ],
1, 1, 0, 2, 1, 1, 0, 3 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 1, −2, −1, −1, 1, −2 ],
0, −1, 1, −1, −1, −1, 0, −1 ],
0, −1, 1, −1, 0, −1, 0, −1 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, −1, 1, 0, 0, 0, 0 ],
0, 0, −1, 1, 0, 1, 0, 1 ],
0, 0, −1, 1, 1, 0, 0, 1 ],
0, 0, −1, 1, 1, 1, 0, 1 ],
0, 0, 0, −1, −1, 0, 0, −1 ],
0, 0, 0, −1, 0, −1, 0, −1 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, −1, 1, 0, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 0, 1, 0, 1, −1, 1 ],
0, 0, 0, 1, 1, 0, −1, 1 ],
0, 0, 1, −2, −1, −1, 1, −1 ],
0, 0, 1, −1, −1, −1, 1, 0 ],
0, 0, 1, −1, −1, 0, 1, 0 ],
0, 0, 1, −1, 0, −1, 1, 0 ],
0, 0, 1, 0, 0, −1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 1, −1, 1, 1, 1, −1, 1 ],
0, 1, −1, 2, 1, 1, −1, 1 ],
0, 1, −1, 2, 1, 2, −1, 2 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
0, 1, 0, 1, 0, 1, 0, 1 ],
0, 1, 0, 1, 1, 0, 0, 1 ],
0, 1, 0, 1, 1, 1, −1, 2 ],
0, 1, 1, 0, 0, 0, 0, 1 ],
1, 0, −1, 1, 1, 0, 0, 1 ],
1, 0, −1, 1, 1, 1, 0, 2 ],
1, 0, −1, 2, 1, 1, 0, 2 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
1, 0, 0, 1, 0, 1, −1, 1 ],
1, 0, 0, 1, 1, 0, −1, 1 ],
1, 0, 0, 1, 1, 1, −1, 1 ],
1, 0, 0, 2, 1, 1, −1, 2 ],
1, 1, −1, 2, 1, 1, 0, 2 ],
1, 1, −1, 2, 2, 1, 0, 3 ],
1, 1, 0, 1, 1, 1, −1, 2 ],
1, 1, 0, 2, 1, 1, −1, 2 ],
1, 1, 0, 2, 1, 2, −1, 3 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 1, −2, −1, −1, 1, −1 ],
0, −1, 1, −1, −1, −1, 1, −1 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 1, 0, 0 ],
0, 0, −1, 1, 0, 1, −1, 0 ],
0, 0, −1, 1, 1, 0, −1, 0 ],
0, 0, −1, 1, 1, 1, −1, 0 ],
0, 0, −1, 2, 1, 1, −1, 1 ],
0, 0, 0, −1, −1, 0, 1, −1 ],
0, 0, 0, −1, 0, −1, 1, −1 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1, −1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 0, 1, 0, 1 ],
0, 0, 0, 1, 1, 0, 0, 1 ],
0, 0, 1, −1, −1, −1, 0, −1 ],
0, 0, 1, −1, −1, 0, 0, −1 ],
0, 0, 1, −1, 0, −1, 0, −1 ],
0, 0, 1, −1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 1, −1, 1, 0, 1, 0, 1 ],
0, 1, −1, 1, 1, 1, 0, 1 ],
0, 1, −1, 2, 1, 1, −1, 2 ],
0, 1, −1, 2, 2, 1, −1, 2 ],
0, 1, 0, 0, 0, 0, 1, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
0, 1, 0, 1, 0, 1, 0, 2 ],
0, 1, 0, 1, 1, 0, 0, 2 ],
0, 1, 0, 1, 1, 1, 0, 2 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, −1, 1, 1, 1, −1, 1 ],
1, 0, −1, 2, 1, 1, −1, 1 ],
1, 0, −1, 2, 1, 2, −1, 2 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 0, 1, 0, 0, 1 ],
1, 0, 0, 1, 0, 1, 0, 1 ],
1, 0, 0, 1, 1, 0, 0, 1 ],
1, 0, 0, 1, 1, 1, −1, 2 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 1, −1, 2, 1, 1, 0, 3 ],
1, 1, 0, 1, 0, 1, 0, 2 ],
1, 1, 0, 1, 1, 1, 0, 2 ],
1, 1, 0, 2, 1, 1, −1, 3 ],
1, 1, 0, 2, 2, 1, −1, 3 ]
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
∗
5
• I ≡ P84 :
6
7
3
4
1
2





CI =



1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
















b
CI =



161
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
1
0
1
0
0
1
−1
1
0
1
0
1
1
0
−1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
−1
















BI =



0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
−1
1
1
0
0
1
0
0
−1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
−1
1
0
1
0
0
1
0
−1
0
1
0
1
0
0
1
−1
2
1
1
1
1
0
0
−2
Number of sincere Tits roots of poset I sI = 28.
Table of roots of qbI
[ −2, 1, 2, 1, 3, 2, 1, 4 ],
[ −1, 1, 1, 1, 2, 2, 1, 4 ],
[ −1, 1, 2, 1, 2, 1, 1, 4 ],
[ −1, 1, 2, 1, 3, 2, 1, 4 ],
[ −1, 1, 2, 2, 3, 2, 1, 5 ],
[ 1,−1,−2,−2,−3,−2,−1,−5 ],
[ 1,−1,−2,−1,−3,−2,−1,−4 ],
[ 1,−1,−2,−1,−2,−1,−1,−4 ],
[ 1,−1,−1,−1,−2,−2,−1,−4 ],
[ 2,−1,−2,−1,−3,−2,−1,−4 ],
[ −1, 0, 0, 0, 0, 0, −1, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 1, 1 ],
[ −1, 0, 1, 0, 1, 1, 1, 2 ],
[ −1, 0, 1, 1, 1, 1, 0, 1 ],
[ −1, 0, 1, 1, 2, 1, 0, 2 ],
[ −1, 0, 1, 1, 2, 2, 1, 3 ],
[ −1, 1, 1, 0, 1, 0, 0, 1 ],
[ −1, 1, 1, 0, 1, 1, 1, 2 ],
[ −1, 1, 1, 0, 2, 1, 1, 3 ],
[ −1, 1, 1, 1, 2, 1, 0, 2 ],
[ −1, 1, 2, 0, 2, 1, 1, 3 ],
[ 0, −1, −1, −1, −2, −2, −1, −4 ],
[ 0, −1, −1, −1, −2, −1, 0, −3 ],
[ 0, −1, −1, −1, −1, −1, 0, −2 ],
[ 0, −1, −1, 0, −1, −1, −1, −3 ],
[ 0, −1, −1, 0, −1, 0, −1, −2 ],
[ 0, −1, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, −1, −1, 0, −2 ],
[ 0, −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, −1, −1, −1, −1, −3 ],
[ 0, 0, −1, −1, −1, 0, −1, −2 ],
[ 0, 0, −1, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 0, −1, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, −1, −1, −1, −2 ],
[ 0, 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, −1, −1, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ −1, 1, 1, 1, 2, 1, 1, 3 ],
[ −1, 1, 1, 1, 3, 2, 1, 4 ],
[ −1, 1, 2, 1, 2, 2, 1, 4 ],
[ −1, 1, 2, 1, 3, 2, 1, 5 ],
[ −1, 2, 2, 1, 3, 2, 1, 5 ],
[ 1,−1,−2,−1,−3,−2,−2,−5 ],
[ 1,−1,−2,−1,−3,−1,−1,−4 ],
[ 1,−1,−2,−1,−2,−1,−1,−3 ],
[ 1,−1,−1,−1,−2,−2,−1,−3 ],
[ −1, −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 0, 2, 1, 1, 2 ],
[ −1, 0, 1, 1, 1, 1, 0, 2 ],
[ −1, 0, 1, 1, 2, 1, 1, 2 ],
[ −1, 0, 2, 1, 2, 1, 1, 3 ],
[ −1, 1, 1, 0, 1, 1, 0, 1 ],
[ −1, 1, 1, 0, 2, 1, 0, 2 ],
[ −1, 1, 1, 0, 2, 2, 1, 3 ],
[ −1, 1, 1, 1, 2, 1, 0, 3 ],
[ −1, 1, 2, 1, 2, 1, 0, 3 ],
[ 0, −1, −1, −1, −2, −1, −1, −4 ],
[ 0, −1, −1, −1, −1, −1, −1, −3 ],
[ 0, −1, −1, −1, −1, 0, 0, −2 ],
[ 0, −1, −1, 0, −1, −1, −1, −2 ],
[ 0, −1, −1, 0, −1, 0, 0, −2 ],
[ 0, −1, 0, −1, −1, −1, 0, −2 ],
[ 0, −1, 0, 0, −1, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, −1, −1, −1, −2 ],
[ 0, 0, −1, −1, −1, 0, 0, −2 ],
[ 0, 0, −1, 0, −1, −1, −1, −2 ],
[ 0, 0, −1, 0, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, −1, 0, −2 ],
[ 0, 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 0, 0, 1, 1, 1, 2 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 1, 0, 1, 2 ],
[ 0, 0, 1, 1, 1, 0, 0, 1 ],
162
[ −1, 1, 1, 1, 2, 2, 1, 3 ],
[ −1, 1, 2, 1, 2, 1, 1, 3 ],
[ −1, 1, 2, 1, 3, 1, 1, 4 ],
[ −1, 1, 2, 1, 3, 2, 2, 5 ],
[ 1,−2,−2,−1,−3,−2,−1,−5 ],
[ 1,−1,−2,−1,−3,−2,−1,−5 ],
[ 1,−1,−2,−1,−2,−2,−1,−4 ],
[ 1,−1,−1,−1,−3,−2,−1,−4 ],
[ 1,−1,−1,−1,−2,−1,−1,−3 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 1, 0, 1, 0, 0, 1 ],
[ −1, 0, 1, 0, 1, 1, 1, 1 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 1, 2 ],
[ −1, 0, 1, 1, 2, 1, 1, 3 ],
[ −1, 1, 0, 0, 1, 1, 0, 1 ],
[ −1, 1, 1, 0, 1, 1, 0, 2 ],
[ −1, 1, 1, 0, 2, 1, 1, 2 ],
[ −1, 1, 1, 1, 1, 1, 0, 2 ],
[ −1, 1, 1, 1, 2, 2, 0, 3 ],
[ 0, −1, −2, −1, −2, −1, −1, −4 ],
[ 0, −1, −1, −1, −2, −1, −1, −3 ],
[ 0, −1, −1, −1, −1, −1, 0, −3 ],
[ 0, −1, −1, 0, −2, −1, −1, −3 ],
[ 0, −1, −1, 0, −1, −1, 0, −2 ],
[ 0, −1, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, −1, −1, −1, −2 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, −2, −1, −1, −3 ],
[ 0, 0, −1, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 0, −1, −2 ],
[ 0, 0, −1, 0, 0, 0, −1, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, −1, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1, −2 ],
[ 0, 0, 0, 0, −1, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 1, 1, 2 ],
[ 0, 0, 1, 1, 1, 0, 0, 2 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 1, 1, 1, 0, 1, 2 ],
0, 0, 1, 1, 1, 1, 1, 3 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 0, 0, 0, 1, 0, 1 ],
0, 1, 0, 0, 1, 1, 0, 2 ],
0, 1, 1, 0, 0, 0, 0, 1 ],
0, 1, 1, 0, 1, 0, 1, 2 ],
0, 1, 1, 0, 1, 1, 1, 3 ],
0, 1, 1, 1, 1, 1, 0, 2 ],
0, 1, 1, 1, 2, 1, 0, 3 ],
0, 1, 1, 1, 2, 2, 1, 4 ],
1, −1, −2, 0, −2, −1, −1, −3 ],
1, −1, −1, −1, −2, −1, 0, −2 ],
1, −1, −1, 0, −2, −1, −1, −3 ],
1, −1, −1, 0, −1, −1, −1, −2 ],
1, −1, −1, 0, −1, 0, 0, −1 ],
1, 0, −1, −1, −2, −2, −1, −3 ],
1, 0, −1, −1, −2, −1, 0, −2 ],
1, 0, −1, −1, −1, −1, 0, −1 ],
1, 0, −1, 0, −1, −1, −1, −2 ],
1, 0, −1, 0, −1, 0, −1, −1 ],
1, 0, −1, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, −1, −1, 0, −1 ],
1, 0, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 1, 1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 1, 1, 1, 1, 0, 2 ],
0, 0, 1, 1, 2, 1, 1, 3 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
0, 1, 0, 0, 1, 1, 1, 2 ],
0, 1, 1, 0, 1, 0, 0, 1 ],
0, 1, 1, 0, 1, 1, 0, 2 ],
0, 1, 1, 0, 2, 1, 1, 3 ],
0, 1, 1, 1, 1, 1, 0, 3 ],
0, 1, 1, 1, 2, 1, 1, 3 ],
0, 1, 2, 1, 2, 1, 1, 4 ],
1, −1, −1, −1, −2, −2, 0, −3 ],
1, −1, −1, −1, −1, −1, 0, −2 ],
1, −1, −1, 0, −2, −1, −1, −2 ],
1, −1, −1, 0, −1, −1, 0, −2 ],
1, −1, 0, 0, −1, −1, 0, −1 ],
1, 0, −1, −1, −2, −1, −1, −3 ],
1, 0, −1, −1, −1, −1, −1, −2 ],
1, 0, −1, −1, −1, 0, 0, −1 ],
1, 0, −1, 0, −1, −1, −1, −1 ],
1, 0, −1, 0, −1, 0, 0, −1 ],
1, 0, 0, −1, −1, −1, 0, −1 ],
1, 0, 0, 0, −1, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 1, 0, 0, 0, 1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 1, 1, 1, 1, 1, 2 ],
0, 1, 0, −1, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 1, 1, 0, 1 ],
0, 1, 0, 1, 1, 1, 0, 2 ],
0, 1, 1, 0, 1, 0, 0, 2 ],
0, 1, 1, 0, 1, 1, 1, 2 ],
0, 1, 1, 1, 1, 0, 0, 2 ],
0, 1, 1, 1, 1, 1, 1, 3 ],
0, 1, 1, 1, 2, 1, 1, 4 ],
1, −1, −2, −1, −2, −1, 0, −3 ],
1, −1, −1, −1, −2, −1, 0, −3 ],
1, −1, −1, 0, −2, −2, −1, −3 ],
1, −1, −1, 0, −2, −1, 0, −2 ],
1, −1, −1, 0, −1, −1, 0, −1 ],
1, 0, −2, −1, −2, −1, −1, −3 ],
1, 0, −1, −1, −2, −1, −1, −2 ],
1, 0, −1, −1, −1, −1, 0, −2 ],
1, 0, −1, 0, −2, −1, −1, −2 ],
1, 0, −1, 0, −1, −1, 0, −1 ],
1, 0, −1, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, −1, −1, −1, −1 ],
1, 0, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 1, 0, 0, 0, 0, 0, 1 ]
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
∗
7
2
6
• I ≡ P85 :
5
4
3
1





CI =








b
CoxI =



0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
−1
0
−1
−1
−1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
−1
1
1
1
1
1
1
1
1
















bI =
C




















BI =



1
1
1
1
1
1
1
0
−1
0
0
0
0
1
1
0
2
1
1
0
0
−1
−1
−1
Number of sincere Tits roots of poset I sI = 28.
Table of roots of qbI
163
0
0
0
1
1
1
1
0
1
0
0
0
0
0
−1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
−1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
−1
−1
−1
0
−1
−1
−1
−1
−1
−1
−1
1

1
0
1
0
0
0
0
0
−1
0
−1
0
0
1
1
0










1
0
1
0
0
0
−1
−1











[ −2, 2, 1, 1, 1, 1,−2, 1 ],
[ −2, 3, 1, 1, 1, 1,−2, 1 ],
[ −2, 3, 1, 1, 1, 2,−2, 2 ],
[ −2, 3, 2, 1, 1, 1,−2, 2 ],
[ −1, 2, 1, 1, 1, 1,−1, 2 ],
[ 1,−2,−1,−1,−1,−1, 1,−2 ],
[ 2,−3,−2,−1,−1,−1, 2,−2 ],
[ 2,−3,−1,−1,−1,−2, 2,−2 ],
[ 2,−3,−1,−1,−1,−1, 2,−1 ],
[ 2,−2,−1,−1,−1,−1, 2,−1 ],
[ −2, 2, 1, 1, 0, 1, −1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 1, 0, 1 ],
[ −1, 1, 0, 0, 1, 0, 0, 1 ],
[ −1, 1, 0, 0, 1, 1, 0, 1 ],
[ −1, 1, 0, 1, 0, 0, 0, 1 ],
[ −1, 1, 0, 1, 0, 1, 0, 1 ],
[ −1, 1, 0, 1, 1, 0, 0, 1 ],
[ −1, 1, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 1, 0, 0, 1, −1, 1 ],
[ −1, 1, 1, 0, 1, 0, −1, 1 ],
[ −1, 1, 1, 1, 0, 0, −1, 0 ],
[ −1, 1, 1, 1, 0, 1, −1, 1 ],
[ −1, 2, 0, 1, 0, 1, −1, 1 ],
[ −1, 2, 0, 1, 1, 1, −1, 1 ],
[ −1, 2, 1, 0, 1, 0, −1, 1 ],
[ −1, 2, 1, 0, 1, 1, −1, 2 ],
[ −1, 2, 1, 1, 0, 1, −1, 1 ],
[ −1, 2, 1, 1, 1, 0, −1, 1 ],
[ 0, −1, −1, 0, −1, 0, 1, −1 ],
[ 0, −1, −1, 0, 0, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, −1, 1, −1 ],
[ 0, −1, 0, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, −1, 0, 1, −1 ],
[ 0, −1, 0, 0, 0, −1, 1, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 0, 1, −1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, −1, 1 ],
[ 0, 1, 0, 0, 1, 0, −1, 1 ],
[ 0, 1, 0, 1, 0, 0, −1, 0 ],
[ 0, 1, 0, 1, 0, 1, −1, 1 ],
[ 0, 1, 1, 0, 0, 0, −1, 1 ],
[ 0, 1, 1, 0, 1, 0, −1, 1 ],
[ 1, −2, −1, −1, −1, 0, 1, −1 ],
[ 1, −2, −1, −1, 0, −1, 1, −1 ],
[ 1, −2, −1, 0, −1, −1, 1, −2 ],
[ 1, −2, −1, 0, −1, 0, 1, −1 ],
[ 1, −2, 0, −1, −1, −1, 1, −1 ],
[ 1, −2, 0, −1, 0, −1, 1, −1 ],
[ 1, −1, −1, −1, 0, −1, 1, −1 ],
[ 1, −1, −1, −1, 0, 0, 1, 0 ],
[ 1, −1, −1, 0, −1, 0, 1, −1 ],
[ 1, −1, −1, 0, 0, −1, 1, −1 ],
[ 1, −1, −1, 0, 0, 0, 0, 0 ],
[ 1, −1, 0, −1, −1, 0, 0, −1 ],
[ 1, −1, 0, −1, 0, −1, 0, −1 ],
[ −2, 2, 1, 1, 1, 1,−1, 1 ],
[ −2, 3, 1, 1, 1, 1,−2, 2 ],
[ −2, 3, 1, 1, 2, 1,−2, 2 ],
[ −1, 2, 1, 1, 1, 1,−2, 1 ],
[ −1, 3, 1, 1, 1, 1,−2, 2 ],
[ 1,−2,−1,−1,−1,−1, 2,−2 ],
[ 2,−3,−1,−2,−1,−1, 2,−2 ],
[ 2,−3,−1,−1,−1,−1, 1,−2 ],
[ 2,−2,−1,−1,−1,−1, 1,−2 ],
[ −2, 2, 0, 1, 1, 1, −1, 1 ],
[ −2, 2, 1, 1, 1, 0, −1, 1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 1, −1, 0 ],
[ −1, 1, 0, 0, 1, 0, −1, 0 ],
[ −1, 1, 0, 0, 1, 1, −1, 0 ],
[ −1, 1, 0, 1, 0, 0, −1, 0 ],
[ −1, 1, 0, 1, 0, 1, −1, 0 ],
[ −1, 1, 0, 1, 1, 0, −1, 0 ],
[ −1, 1, 0, 1, 1, 1, −1, 1 ],
[ −1, 1, 1, 0, 0, 0, 0, 1 ],
[ −1, 1, 1, 0, 0, 1, 0, 1 ],
[ −1, 1, 1, 0, 1, 0, 0, 1 ],
[ −1, 1, 1, 1, 0, 0, −1, 1 ],
[ −1, 1, 1, 1, 1, 0, −1, 1 ],
[ −1, 2, 0, 1, 1, 0, −1, 1 ],
[ −1, 2, 0, 1, 1, 1, −1, 2 ],
[ −1, 2, 1, 0, 1, 1, −2, 1 ],
[ −1, 2, 1, 1, 0, 0, −1, 1 ],
[ −1, 2, 1, 1, 0, 1, −1, 2 ],
[ −1, 2, 1, 1, 1, 0, −1, 2 ],
[ 0, −1, −1, 0, 0, −1, 1, −1 ],
[ 0, −1, −1, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, −1, −1, 1, −1 ],
[ 0, −1, 0, 0, −1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, −1, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 0, −1, 1 ],
[ 0, 1, 0, 1, 1, 0, −1, 1 ],
[ 0, 1, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 0, 0, −1, 1 ],
[ 1, −2, −1, −1, −1, 0, 2, −1 ],
[ 1, −2, −1, −1, 0, −1, 2, −1 ],
[ 1, −2, −1, 0, −1, −1, 1, −1 ],
[ 1, −2, −1, 0, 0, −1, 1, −1 ],
[ 1, −2, 0, −1, −1, −1, 2, −1 ],
[ 1, −2, 0, 0, −1, −1, 1, −1 ],
[ 1, −1, −1, −1, 0, 0, 0, −1 ],
[ 1, −1, −1, 0, −1, −1, 1, −1 ],
[ 1, −1, −1, 0, −1, 0, 1, 0 ],
[ 1, −1, −1, 0, 0, −1, 1, 0 ],
[ 1, −1, −1, 0, 0, 0, 1, 0 ],
[ 1, −1, 0, −1, −1, 0, 1, −1 ],
[ 1, −1, 0, −1, 0, −1, 1, −1 ],
164
[ −2, 2, 1, 1, 1, 1,−1, 2 ],
[ −2, 3, 1, 1, 1, 1,−1, 2 ],
[ −2, 3, 1, 2, 1, 1,−2, 2 ],
[ −1, 2, 1, 1, 1, 1,−2, 2 ],
[ 1,−3,−1,−1,−1,−1, 2,−2 ],
[ 1,−2,−1,−1,−1,−1, 2,−1 ],
[ 2,−3,−1,−1,−2,−1, 2,−2 ],
[ 2,−3,−1,−1,−1,−1, 2,−2 ],
[ 2,−2,−1,−1,−1,−1, 1,−1 ],
[ −2, 2, 1, 0, 1, 1, −1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 1, 1, −1, 1 ],
[ −1, 1, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 1, −1, 1 ],
[ −1, 1, 0, 1, 1, 0, −1, 1 ],
[ −1, 1, 1, 0, 0, 0, −1, 0 ],
[ −1, 1, 1, 0, 0, 1, −1, 0 ],
[ −1, 1, 1, 0, 1, 0, −1, 0 ],
[ −1, 1, 1, 0, 1, 1, −1, 1 ],
[ −1, 1, 1, 1, 0, 0, 0, 1 ],
[ −1, 2, 0, 0, 1, 1, −1, 1 ],
[ −1, 2, 0, 1, 1, 1, −2, 1 ],
[ −1, 2, 1, 0, 0, 1, −1, 1 ],
[ −1, 2, 1, 0, 1, 1, −1, 1 ],
[ −1, 2, 1, 1, 0, 1, −2, 1 ],
[ −1, 2, 1, 1, 1, 0, −2, 1 ],
[ 0, −1, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, −1, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 1, −1, 0 ],
[ 0, 1, 0, 0, 1, 0, −1, 0 ],
[ 0, 1, 0, 0, 1, 1, −1, 1 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 1, 0, 0, 1, −1, 1 ],
[ 1, −2, −1, −1, −1, 0, 1, −2 ],
[ 1, −2, −1, −1, 0, −1, 1, −2 ],
[ 1, −2, −1, −1, 0, 0, 1, −1 ],
[ 1, −2, −1, 0, −1, −1, 2, −1 ],
[ 1, −2, 0, −1, −1, −1, 1, −2 ],
[ 1, −2, 0, −1, −1, 0, 1, −1 ],
[ 1, −1, −1, −1, −1, 0, 1, −1 ],
[ 1, −1, −1, −1, 0, 0, 1, −1 ],
[ 1, −1, −1, 0, −1, 0, 0, −1 ],
[ 1, −1, −1, 0, 0, −1, 0, −1 ],
[ 1, −1, −1, 0, 0, 0, 0, −1 ],
[ 1, −1, 0, −1, −1, −1, 1, −1 ],
[ 1, −1, 0, −1, −1, 0, 1, 0 ],
[ 1, −1, 0, −1, 0, −1, 1, 0 ],
[
[
[
[
[
[
[
[
1, −1, 0, −1, 0, 0,
1, −1, 0, 0, −1, −1,
1, −1, 0, 0, −1, 0,
1, −1, 0, 0, 0, −1,
1, −1, 0, 0, 0, 0,
1, 0, 0, 0, −1, 0,
1, 0, 0, 0, 0, 0,
2, −2, −1, −1, 0, −1,
0, −1 ],
0, −1 ],
0, −1 ],
0, −1 ],
0, 0 ],
0, 0 ],
0, 0 ],
1, −1 ],
[
[
[
[
[
[
[
[
1, −1, 0, −1, 0, 0,
1, −1, 0, 0, −1, −1,
1, −1, 0, 0, −1, 0,
1, −1, 0, 0, 0, −1,
1, 0, −1, 0, 0, 0,
1, 0, 0, 0, 0, −1,
1, 0, 0, 0, 0, 0,
2, −2, −1, 0, −1, −1,
0, 0 ],
1, −1 ],
0, 0 ],
0, 0 ],
0, 0 ],
0, 0 ],
0, 1 ],
1, −1 ],
[
[
[
[
[
[
[
[
1, −1, 0, −1, 0, 0, 1, 0 ],
1, −1, 0, 0, −1, −1, 1, 0 ],
1, −1, 0, 0, −1, 0, 1, 0 ],
1, −1, 0, 0, 0, −1, 1, 0 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, −1, 0 ],
2, −2, −1, −1, −1, 0, 1, −1 ],
2, −2, 0, −1, −1, −1, 1, −1 ]
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
∗
6
7
5
4
• I ≡ P86 :
3
2
1





CI =








b I =
Cox




0
0
0
0
1
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
−1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
−1
1
1
1
1
1
1
1
1
















b
CI =



















BI =



1
1
1
1
0
1
1
0
−1
−1
0
0
0
−1
0
1
1
1
1
0
0
1
0
−1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
−1
0
0
0
0
0
1
0
0
2
1
1
1
0
1
0
−1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
2
2
1
1
1
1
0
−2











1
1
1
1
0
0
1
−1
3
2
2
1
1
1
0
−2
Number of sincere Tits roots of poset I sI = 28.
Table of roots of qbI
[ −2, 1, 1, 1, 1, 2, 1, 2 ],
[ −2, 1, 1, 1, 2, 2, 1, 3 ],
[ −2, 1, 1, 1, 2, 3, 2, 4 ],
[ −2, 2, 1, 1, 2, 3, 1, 4 ],
[ −1, 1, 1, 1, 2, 2, 1, 4 ],
[ 1,−1,−1,−1,−2,−2,−1,−4 ],
[ 2,−2,−1,−1,−2,−3,−1,−4 ],
[ 2,−1,−1,−1,−2,−3,−2,−4 ],
[ 2,−1,−1,−1,−2,−2,−1,−3 ],
[ 2,−1,−1,−1,−1,−2,−1,−2 ],
[ −2, 1, 1, 0, 1, 2, 1, 2 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 1, 0, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −2, 1, 1, 1, 1, 2, 1, 3 ],
[ −2, 1, 1, 1, 2, 3, 1, 3 ],
[ −2, 1, 1, 2, 2, 3, 1, 4 ],
[ −1, 1, 1, 1, 1, 2, 1, 3 ],
[ −1, 1, 1, 1, 2, 3, 1, 4 ],
[ 1,−1,−1,−1,−2,−2,−1,−3 ],
[ 2,−1,−2,−1,−2,−3,−1,−4 ],
[ 2,−1,−1,−1,−2,−3,−1,−4 ],
[ 2,−1,−1,−1,−1,−3,−1,−3 ],
[ −2, 0, 1, 1, 1, 2, 1, 2 ],
[ −2, 1, 1, 1, 1, 2, 0, 2 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 2 ],
[ −1, 0, 1, 0, 0, 1, 0, 0 ],
165
[ −2, 1, 1, 1, 1, 3, 1, 3 ],
[ −2, 1, 1, 1, 2, 3, 1, 4 ],
[ −2, 1, 2, 1, 2, 3, 1, 4 ],
[ −1, 1, 1, 1, 2, 2, 1, 3 ],
[ 1,−1,−1,−1,−2,−3,−1,−4 ],
[ 1,−1,−1,−1,−1,−2,−1,−3 ],
[ 2,−1,−1,−2,−2,−3,−1,−4 ],
[ 2,−1,−1,−1,−2,−3,−1,−3 ],
[ 2,−1,−1,−1,−1,−2,−1,−3 ],
[ −2, 1, 0, 1, 1, 2, 1, 2 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 2, 1, 2 ],
[ −1, 0, 1, 0, 0, 1, 0, 1 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, 1, 0, 0, 1, 1, 1 ],
−1, 0, 1, 0, 1, 1, 1, 2 ],
−1, 0, 1, 1, 1, 1, 0, 1 ],
−1, 0, 1, 1, 1, 2, 0, 2 ],
−1, 0, 1, 1, 2, 2, 1, 3 ],
−1, 1, 0, 0, 0, 1, 0, 1 ],
−1, 1, 0, 0, 1, 1, 1, 1 ],
−1, 1, 0, 1, 0, 1, 0, 1 ],
−1, 1, 0, 1, 1, 1, 1, 2 ],
−1, 1, 0, 1, 1, 2, 1, 3 ],
−1, 1, 1, 0, 1, 1, 0, 1 ],
−1, 1, 1, 0, 1, 2, 0, 2 ],
−1, 1, 1, 0, 2, 2, 1, 3 ],
−1, 1, 1, 1, 1, 2, 0, 3 ],
0, −1, 0, −1, −1, −1, 0, −2 ],
0, −1, 0, 0, −1, −1, 0, −1 ],
0, −1, 0, 0, 0, 0, 0, −1 ],
0, −1, 0, 1, 0, 0, 0, 0 ],
0, 0, −1, 0, −1, −1, −1, −2 ],
0, 0, −1, 0, −1, 0, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, 0, −1, −1, −1, −1, −2 ],
0, 0, 0, −1, −1, 0, 0, −1 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, 0, −1, −1, −1, −1 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 0, 1, 1, 1, 1 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 0, 1, 1, 0, 0, 1 ],
0, 0, 0, 1, 1, 1, 1, 2 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 0, 1, 0, 1, 1, 1, 2 ],
0, 1, 0, −1, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 1, 1, 0, 1 ],
0, 1, 0, 1, 1, 1, 0, 2 ],
1, −1, −1, −1, −1, −2, 0, −3 ],
1, −1, −1, 0, −2, −2, −1, −3 ],
1, −1, −1, 0, −1, −2, 0, −2 ],
1, −1, −1, 0, −1, −1, 0, −1 ],
1, −1, 0, −1, −1, −2, −1, −3 ],
1, −1, 0, −1, −1, −1, −1, −2 ],
1, −1, 0, −1, 0, −1, 0, −1 ],
1, −1, 0, 0, −1, −1, −1, −1 ],
1, −1, 0, 0, 0, −1, 0, −1 ],
1, 0, −1, −1, −2, −2, −1, −3 ],
1, 0, −1, −1, −1, −2, 0, −2 ],
1, 0, −1, −1, −1, −1, 0, −1 ],
1, 0, −1, 0, −1, −1, −1, −2 ],
1, 0, −1, 0, 0, −1, −1, −1 ],
1, 0, −1, 0, 0, 0, 0, 0 ],
1, 0, 0, −1, −1, −1, −1, −1 ],
1, 0, 0, −1, 0, −1, 0, −1 ],
1, 0, 0, 0, −1, −1, −1, −1 ],
1, 0, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
2, −1, −1, 0, −1, −2, −1, −2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, 1, 0, 1, 1, 0, 1 ],
−1, 0, 1, 0, 1, 2, 1, 2 ],
−1, 0, 1, 1, 1, 1, 0, 2 ],
−1, 0, 1, 1, 1, 2, 1, 2 ],
−1, 1, 0, 0, 0, 0, 0, 0 ],
−1, 1, 0, 0, 0, 1, 1, 1 ],
−1, 1, 0, 0, 1, 1, 1, 2 ],
−1, 1, 0, 1, 1, 1, 0, 1 ],
−1, 1, 0, 1, 1, 2, 0, 2 ],
−1, 1, 0, 1, 2, 2, 1, 3 ],
−1, 1, 1, 0, 1, 1, 0, 2 ],
−1, 1, 1, 0, 1, 2, 1, 2 ],
−1, 1, 1, 1, 1, 1, 0, 2 ],
−1, 1, 1, 1, 2, 2, 0, 3 ],
0, −1, 0, 0, −1, −1, −1, −2 ],
0, −1, 0, 0, −1, 0, 0, −1 ],
0, −1, 0, 0, 0, 0, 0, 0 ],
0, −1, 1, 0, 0, 0, 0, 0 ],
0, 0, −1, 0, −1, −1, 0, −2 ],
0, 0, −1, 0, 0, −1, 0, −1 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, 0, −1, −1, −1, 0, −2 ],
0, 0, 0, −1, 0, −1, 0, −1 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, −1, 0, −1 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 1, 1 ],
0, 0, 0, 0, 1, 0, 1, 1 ],
0, 0, 0, 0, 1, 1, 1, 2 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 1, 1, 0, 1 ],
0, 0, 1, −1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 1, 1, 0, 1 ],
0, 0, 1, 1, 1, 1, 0, 2 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 0, 0, 0, 1, 0, 1 ],
0, 1, 0, 0, 1, 1, 0, 2 ],
0, 1, 1, 0, 1, 1, 0, 2 ],
1, −1, −1, −1, −1, −2, 0, −2 ],
1, −1, −1, 0, −1, −2, −1, −3 ],
1, −1, −1, 0, −1, −1, −1, −2 ],
1, −1, −1, 0, 0, −1, 0, −1 ],
1, −1, 0, −1, −1, −2, −1, −2 ],
1, −1, 0, −1, −1, −1, 0, −2 ],
1, −1, 0, 0, −1, −2, −1, −2 ],
1, −1, 0, 0, −1, −1, 0, −1 ],
1, −1, 0, 0, 0, −1, 0, 0 ],
1, 0, −1, −1, −1, −2, −1, −3 ],
1, 0, −1, −1, −1, −1, −1, −2 ],
1, 0, −1, −1, 0, −1, 0, −1 ],
1, 0, −1, 0, −1, −1, −1, −1 ],
1, 0, −1, 0, 0, −1, 0, −1 ],
1, 0, 0, −1, −1, −2, −1, −2 ],
1, 0, 0, −1, −1, −1, 0, −1 ],
1, 0, 0, −1, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, −1, −1, −1 ],
1, 0, 0, 0, 0, 0, −1, 0 ],
1, 0, 0, 0, 1, 0, 0, 1 ],
2, −1, 0, −1, −1, −2, −1, −2 ],
166
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, 1, 0, 1, 1, 1, 1 ],
−1, 0, 1, 1, 0, 1, 0, 1 ],
−1, 0, 1, 1, 1, 1, 1, 2 ],
−1, 0, 1, 1, 1, 2, 1, 3 ],
−1, 1, 0, 0, 0, 1, 0, 0 ],
−1, 1, 0, 0, 1, 1, 0, 1 ],
−1, 1, 0, 0, 1, 2, 1, 2 ],
−1, 1, 0, 1, 1, 1, 0, 2 ],
−1, 1, 0, 1, 1, 2, 1, 2 ],
−1, 1, 1, 0, 0, 1, 0, 1 ],
−1, 1, 1, 0, 1, 1, 1, 2 ],
−1, 1, 1, 0, 1, 2, 1, 3 ],
−1, 1, 1, 1, 1, 2, 0, 2 ],
0, −1, −1, 0, −1, −1, 0, −2 ],
0, −1, 0, 0, −1, −1, 0, −2 ],
0, −1, 0, 0, 0, −1, 0, −1 ],
0, −1, 0, 0, 0, 0, 1, 0 ],
0, 0, −1, −1, −1, −1, 0, −2 ],
0, 0, −1, 0, −1, −1, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, −1, 1, 0, 0, 0, 0 ],
0, 0, 0, −1, −1, −1, 0, −1 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, 0, −1, −1, −1, −2 ],
0, 0, 0, 0, −1, 0, −1, −1 ],
0, 0, 0, 0, 0, −1, −1, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 0, 1, 1, 0, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 0, 1, 0, 1, 0, 1 ],
0, 0, 0, 1, 1, 1, 0, 2 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 0, 1, 0, 0, 1, 0, 1 ],
0, 0, 1, 0, 1, 1, 0, 2 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
0, 1, 0, 0, 1, 1, 1, 2 ],
1, −1, −1, −1, −2, −2, 0, −3 ],
1, −1, −1, −1, −1, −1, 0, −2 ],
1, −1, −1, 0, −1, −2, −1, −2 ],
1, −1, −1, 0, −1, −1, 0, −2 ],
1, −1, 0, −1, −2, −2, −1, −3 ],
1, −1, 0, −1, −1, −2, 0, −2 ],
1, −1, 0, −1, −1, −1, 0, −1 ],
1, −1, 0, 0, −1, −1, −1, −2 ],
1, −1, 0, 0, 0, −1, −1, −1 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, −1, −1, −1, −2, −1, −2 ],
1, 0, −1, −1, −1, −1, 0, −2 ],
1, 0, −1, 0, −1, −2, −1, −2 ],
1, 0, −1, 0, −1, −1, 0, −1 ],
1, 0, −1, 0, 0, −1, 0, 0 ],
1, 0, 0, −1, −1, −1, −1, −2 ],
1, 0, 0, −1, 0, −1, −1, −1 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, −1, −1, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
2, −1, −1, −1, −1, −2, 0, −2 ],
2, 0, −1, −1, −1, −2, −1, −2 ]
∗
7
6
• I ≡ P87 :
3
5
4
2
1





CI =








b I =
Cox




0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
−1
0
−1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
















BI =



1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
−1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
2
1
1
0
−1
0
−1
0
0
0
0
1
1
1
0
0
1
0
0
0
−1
−1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
−1
0
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
0
0
0
1
0
0











0
−1
0
−1
0
0
0
0
1
1
0
1
1
0
0
−1
Number of sincere Tits roots of poset I sI = 22.
Table of roots of qbI
[ −2,−1, 3, 2, 2,−1,−1, 1 ],
[ −1,−1, 2, 2, 1,−1,−1, 1 ],
[ −1,−1, 3, 2, 1,−1,−1, 1 ],
[ −1,−1, 3, 2, 2,−1,−1, 1 ],
[ 1, 1,−3,−2,−2, 1, 1,−1 ],
[ 1, 1,−3,−2,−1, 1, 1,−1 ],
[ 1, 1,−2,−2,−1, 1, 1,−1 ],
[ 2, 1,−3,−2,−2, 1, 1,−1 ],
[ −1, −1, 1, 1, 1, −1, 0, 0 ],
[ −1, −1, 1, 1, 1, 0, 0, 1 ],
[ −1, −1, 2, 1, 1, −1, 0, 1 ],
[ −1, −1, 2, 1, 1, 0, 0, 1 ],
[ −1, −1, 2, 1, 2, 0, −1, 1 ],
[ −1, −1, 2, 2, 1, 0, −1, 1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, −1, 0 ],
[ −1, 0, 1, 1, 0, −1, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, −1, 0, 1 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ −1, 0, 2, 1, 1, −1, 0, 1 ],
[ −1, 0, 2, 2, 1, −1, −1, 1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ −1,−2, 3, 2, 2,−1,−1, 1 ],
[ −1,−1, 2, 2, 2,−1,−1, 1 ],
[ −1,−1, 3, 2, 2,−2,−1, 1 ],
[ −1,−1, 3, 2, 2,−1,−1, 2 ],
[ 1, 1,−3,−2,−2, 1, 2,−1 ],
[ 1, 1,−3,−1,−2, 1, 1,−1 ],
[ 1, 1,−2,−1,−2, 1, 1,−1 ],
[ −1, −1, 1, 0, 1, 0, 0, 0 ],
[ −1, −1, 1, 1, 1, 0, −1, 0 ],
[ −1, −1, 2, 1, 1, −1, −1, 0 ],
[ −1, −1, 2, 1, 1, 0, −1, 0 ],
[ −1, −1, 2, 1, 2, −1, −1, 0 ],
[ −1, −1, 2, 2, 1, −1, −1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, −1, 0 ],
[ −1, 0, 1, 1, 1, −1, −1, 0 ],
[ −1, 0, 1, 1, 1, 0, −1, 0 ],
[ −1, 0, 2, 1, 1, −1, −1, 0 ],
[ −1, 0, 2, 1, 1, 0, −1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 1, 0, 0, 0, 0 ],
167
[ −1,−1, 2, 1, 2,−1,−1, 1 ],
[ −1,−1, 3, 1, 2,−1,−1, 1 ],
[ −1,−1, 3, 2, 2,−1,−2, 1 ],
[ 1, 1,−3,−2,−2, 1, 1,−2 ],
[ 1, 1,−3,−2,−2, 2, 1,−1 ],
[ 1, 1,−2,−2,−2, 1, 1,−1 ],
[ 1, 2,−3,−2,−2, 1, 1,−1 ],
[ −1, −1, 1, 1, 0, 0, 0, 0 ],
[ −1, −1, 1, 1, 1, 0, 0, 0 ],
[ −1, −1, 2, 1, 1, −1, 0, 0 ],
[ −1, −1, 2, 1, 1, 0, −1, 1 ],
[ −1, −1, 2, 1, 2, −1, 0, 1 ],
[ −1, −1, 2, 2, 1, −1, 0, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, −1, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, −1, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, −1, 1 ],
[ −1, 0, 2, 1, 1, −1, −1, 1 ],
[ −1, 0, 2, 1, 2, −1, −1, 1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 1, 0, 1, −1, 0, 0 ],
0, −1, 1, 0, 1, 0, 0, 1 ],
0, −1, 1, 1, 0, 0, 0, 0 ],
0, −1, 1, 1, 1, −1, 0, 0 ],
0, −1, 1, 1, 1, 0, −1, 1 ],
0, −1, 2, 1, 1, −1, −1, 1 ],
0, −1, 2, 1, 2, −1, −1, 1 ],
0, 0, −1, −1, −1, 0, 1, −1 ],
0, 0, −1, −1, −1, 1, 1, 0 ],
0, 0, −1, −1, 0, 0, 1, 0 ],
0, 0, −1, −1, 0, 1, 1, 0 ],
0, 0, −1, 0, −1, 0, 1, 0 ],
0, 0, −1, 0, −1, 1, 1, 0 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, −1, 1, 0, 0, 0 ],
0, 0, 0, 0, −1, 0, 1, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 1, −1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 0, 1, 0, 1, −1, −1, 0 ],
0, 0, 1, 0, 1, 0, −1, 0 ],
0, 0, 1, 1, 0, −1, −1, 0 ],
0, 0, 1, 1, 0, 0, −1, 0 ],
0, 0, 1, 1, 1, −1, −1, 0 ],
0, 0, 1, 1, 1, 0, −1, 1 ],
0, 1, −2, −1, −2, 1, 1, −1 ],
0, 1, −2, −1, −1, 1, 1, −1 ],
0, 1, −1, −1, −1, 0, 1, −1 ],
0, 1, −1, −1, −1, 1, 0, 0 ],
0, 1, −1, −1, 0, 0, 0, 0 ],
0, 1, −1, 0, −1, 0, 0, −1 ],
0, 1, −1, 0, −1, 1, 0, 0 ],
0, 1, 0, 0, −1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
1, 0, −2, −2, −1, 1, 1, −1 ],
1, 0, −2, −1, −1, 1, 0, −1 ],
1, 0, −1, −1, −1, 0, 0, −1 ],
1, 0, −1, −1, −1, 1, 0, −1 ],
1, 0, −1, −1, 0, 0, 0, −1 ],
1, 0, −1, −1, 0, 1, 0, 0 ],
1, 0, −1, 0, −1, 0, 1, 0 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, −1, 0 ],
1, 1, −2, −2, −1, 0, 1, −1 ],
1, 1, −2, −1, −2, 0, 1, −1 ],
1, 1, −2, −1, −1, 0, 0, −1 ],
1, 1, −2, −1, −1, 1, 0, −1 ],
1, 1, −1, −1, −1, 0, 0, −1 ],
1, 1, −1, −1, −1, 1, 0, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 1, 0, 1, 0, −1, 0 ],
0, −1, 1, 1, 0, −1, 0, 0 ],
0, −1, 1, 1, 0, 0, 0, 1 ],
0, −1, 1, 1, 1, −1, 0, 1 ],
0, −1, 1, 1, 1, 0, 0, 1 ],
0, −1, 2, 1, 1, −1, 0, 1 ],
0, −1, 2, 2, 1, −1, −1, 1 ],
0, 0, −1, −1, −1, 1, 0, −1 ],
0, 0, −1, −1, 0, 0, 0, −1 ],
0, 0, −1, −1, 0, 1, 0, −1 ],
0, 0, −1, 0, −1, 0, 0, −1 ],
0, 0, −1, 0, −1, 1, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 1, 0, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, −1, 1, 0, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 1, −1, 0, 0 ],
0, 0, 1, 0, 1, 0, −1, 1 ],
0, 0, 1, 1, 0, −1, 0, 0 ],
0, 0, 1, 1, 0, 0, −1, 1 ],
0, 0, 1, 1, 1, −1, −1, 1 ],
0, 0, 2, 1, 1, −1, −1, 1 ],
0, 1, −2, −1, −1, 0, 1, −1 ],
0, 1, −2, −1, −1, 1, 1, 0 ],
0, 1, −1, −1, −1, 0, 1, 0 ],
0, 1, −1, −1, −1, 1, 1, 0 ],
0, 1, −1, −1, 0, 0, 1, 0 ],
0, 1, −1, 0, −1, 0, 0, 0 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
1, 0, −2, −1, −2, 1, 1, −1 ],
1, 0, −2, −1, −1, 1, 1, −1 ],
1, 0, −1, −1, −1, 0, 1, −1 ],
1, 0, −1, −1, −1, 1, 0, 0 ],
1, 0, −1, −1, 0, 0, 0, 0 ],
1, 0, −1, 0, −1, 0, 0, −1 ],
1, 0, −1, 0, −1, 1, 0, 0 ],
1, 0, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 1, −2, −2, −1, 1, 0, −1 ],
1, 1, −2, −1, −2, 1, 0, −1 ],
1, 1, −2, −1, −1, 0, 1, −1 ],
1, 1, −2, −1, −1, 1, 0, 0 ],
1, 1, −1, −1, −1, 0, 0, 0 ],
1, 1, −1, −1, 0, 0, 0, 0 ],
∗
7
4
• I ≡ P88 :
6
5
3
2
1
168
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 1, 0, 1, 0, 0, 0 ],
0, −1, 1, 1, 0, 0, −1, 0 ],
0, −1, 1, 1, 1, −1, −1, 0 ],
0, −1, 1, 1, 1, 0, −1, 0 ],
0, −1, 2, 1, 1, −1, −1, 0 ],
0, −1, 2, 1, 1, 0, −1, 1 ],
0, 0, −2, −1, −1, 1, 1, −1 ],
0, 0, −1, −1, −1, 1, 1, −1 ],
0, 0, −1, −1, 0, 0, 1, −1 ],
0, 0, −1, −1, 0, 1, 0, 0 ],
0, 0, −1, 0, −1, 0, 1, −1 ],
0, 0, −1, 0, −1, 1, 0, 0 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 1, 0, 0 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1, −1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 1, 0, 0, −1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 1, −1, 0, 1 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 0, 1, 1, 0, −1, 0, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 0, 1, 1, 1, −1, 0, 1 ],
0, 1, −2, −2, −1, 1, 1, −1 ],
0, 1, −2, −1, −1, 1, 0, −1 ],
0, 1, −1, −1, −1, 0, 0, −1 ],
0, 1, −1, −1, −1, 1, 0, −1 ],
0, 1, −1, −1, 0, 0, 0, −1 ],
0, 1, −1, −1, 0, 1, 0, 0 ],
0, 1, −1, 0, −1, 0, 1, 0 ],
0, 1, 0, −1, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, −2, −1, −1, 0, 1, −1 ],
1, 0, −2, −1, −1, 1, 1, 0 ],
1, 0, −1, −1, −1, 0, 1, 0 ],
1, 0, −1, −1, −1, 1, 1, 0 ],
1, 0, −1, −1, 0, 0, 1, 0 ],
1, 0, −1, 0, −1, 0, 0, 0 ],
1, 0, −1, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 1, −2, −2, −1, 1, 1, 0 ],
1, 1, −2, −1, −2, 1, 1, 0 ],
1, 1, −2, −1, −1, 0, 1, 0 ],
1, 1, −2, −1, −1, 1, 1, 0 ],
1, 1, −1, −1, −1, 0, 1, 0 ],
1, 1, −1, 0, −1, 0, 0, 0 ]





CI =








b I =
Cox




0
0
0
0
0
1
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
−1
0
0
0
0
0
1
0
0
0
−1
−1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
−1
1
1
1
1
1
1
1
1
















bI =
C




















BI =



1
1
1
1
1
0
1
0
−1
−1
−1
0
0
0
0
0
0
1
1
1
1
0
1
0
−1
−1
0
−1
0
−1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
2
1
1
0
1
0
−1
0
0
0
0
1
0
1
0
2
2
1
1
0
1
−1
−1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
2
2
1
1
1
0
0
−1
1
1
1
1
0
0
0
−1











−1
−1
0
−1
0
0
0
0
1
2
1
1
0
0
−1
−1
Number of sincere Tits roots of poset I sI = 28.
Table of roots of qbI
[ −2,−1, 2, 3, 2, 1,−1, 2 ],
[ −1,−1, 1, 2, 2, 1,−1, 1 ],
[ −1,−1, 2, 2, 1, 1,−1, 1 ],
[ −1,−1, 2, 3, 1, 1,−1, 2 ],
[ −1,−1, 2, 3, 2, 1,−1, 3 ],
[ 1, 1,−2,−3,−2,−1, 1,−3 ],
[ 1, 1,−2,−3,−1,−1, 1,−2 ],
[ 1, 1,−2,−2,−1,−1, 1,−1 ],
[ 1, 1,−1,−2,−2,−1, 1,−1 ],
[ 2, 1,−2,−3,−2,−1, 1,−2 ],
[ −1, −1, 1, 1, 1, 0, −1, 0 ],
[ −1, −1, 1, 1, 1, 1, 0, 1 ],
[ −1, −1, 1, 2, 1, 0, 0, 1 ],
[ −1, −1, 1, 2, 2, 0, −1, 1 ],
[ −1, −1, 2, 2, 1, 1, 0, 2 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 0, 0, −1, 0 ],
[ −1, 0, 1, 1, 0, 1, 0, 1 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 0, 2 ],
[ −1, 0, 1, 2, 1, 1, −1, 2 ],
[ −1, 0, 2, 2, 1, 1, −1, 2 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ 0, −1, 0, 1, 1, 0, 0, 0 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, 1, 0, 0, 0, 1 ],
[ 0, −1, 1, 1, 1, 0, −1, 1 ],
[ 0, −1, 1, 1, 1, 1, 0, 1 ],
[ 0, −1, 1, 2, 1, 1, −1, 1 ],
[ 0, −1, 1, 2, 2, 1, −1, 2 ],
[ 0, 0, −1, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, −1, 0, −1, 1, −1 ],
[ 0, 0, −1, −1, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, −1, 0, −2 ],
[ 0, 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ −1,−2, 2, 3, 2, 1,−1, 2 ],
[ −1,−1, 1, 2, 2, 1,−1, 2 ],
[ −1,−1, 2, 2, 1, 1,−1, 2 ],
[ −1,−1, 2, 3, 2, 1,−2, 2 ],
[ −1,−1, 2, 3, 2, 2,−1, 3 ],
[ 1, 1,−2,−3,−2,−1, 1,−2 ],
[ 1, 1,−2,−2,−2,−1, 1,−2 ],
[ 1, 1,−1,−3,−2,−1, 1,−2 ],
[ 1, 1,−1,−2,−1,−1, 1,−1 ],
[ −1, −1, 0, 1, 1, 0, 0, 0 ],
[ −1, −1, 1, 1, 1, 0, 0, 0 ],
[ −1, −1, 1, 2, 1, 0, −1, 0 ],
[ −1, −1, 1, 2, 1, 1, 0, 1 ],
[ −1, −1, 1, 2, 2, 1, 0, 2 ],
[ −1, 0, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 0, −1, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, −1, 0 ],
[ −1, 0, 1, 1, 1, 1, −1, 1 ],
[ −1, 0, 1, 2, 1, 0, −1, 1 ],
[ −1, 0, 1, 2, 1, 1, 0, 2 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 1, 0, 0, 0, 0 ],
[ 0, −1, 0, 1, 1, 0, 0, 1 ],
[ 0, −1, 1, 1, 0, 0, −1, 0 ],
[ 0, −1, 1, 1, 0, 1, 0, 1 ],
[ 0, −1, 1, 1, 1, 0, 0, 1 ],
[ 0, −1, 1, 1, 1, 1, 0, 2 ],
[ 0, −1, 1, 2, 1, 1, −1, 2 ],
[ 0, −1, 2, 2, 1, 1, −1, 2 ],
[ 0, 0, −1, −1, −1, −1, 1, −2 ],
[ 0, 0, −1, −1, 0, −1, 0, −2 ],
[ 0, 0, −1, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, −1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, −1, −1, 0, −1 ],
[ 0, 0, 0, −1, −1, 0, 1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
169
[ −1,−1, 1, 2, 1, 1,−1, 1 ],
[ −1,−1, 1, 3, 2, 1,−1, 2 ],
[ −1,−1, 2, 2, 2, 1,−1, 2 ],
[ −1,−1, 2, 3, 2, 1,−1, 2 ],
[ 1, 1,−2,−3,−2,−2, 1,−3 ],
[ 1, 1,−2,−3,−2,−1, 2,−2 ],
[ 1, 1,−2,−2,−1,−1, 1,−2 ],
[ 1, 1,−1,−2,−2,−1, 1,−2 ],
[ 1, 2,−2,−3,−2,−1, 1,−2 ],
[ −1, −1, 1, 1, 0, 0, 0, 0 ],
[ −1, −1, 1, 1, 1, 0, 0, 1 ],
[ −1, −1, 1, 2, 1, 0, −1, 1 ],
[ −1, −1, 1, 2, 1, 1, 0, 2 ],
[ −1, −1, 2, 2, 1, 0, −1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 0, −1, 1 ],
[ −1, 0, 1, 1, 1, 1, 0, 1 ],
[ −1, 0, 1, 2, 1, 1, −1, 1 ],
[ −1, 0, 1, 2, 2, 1, −1, 2 ],
[ 0, −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 1, 1, 0, −1, 0 ],
[ 0, −1, 0, 1, 1, 1, 0, 1 ],
[ 0, −1, 1, 1, 0, 0, 0, 0 ],
[ 0, −1, 1, 1, 1, 0, −1, 0 ],
[ 0, −1, 1, 1, 1, 1, −1, 1 ],
[ 0, −1, 1, 2, 1, 0, −1, 1 ],
[ 0, −1, 1, 2, 1, 1, 0, 2 ],
[ 0, 0, −1, −2, −1, −1, 1, −2 ],
[ 0, 0, −1, −1, −1, −1, 1, −1 ],
[ 0, 0, −1, −1, 0, −1, 0, −1 ],
[ 0, 0, −1, −1, 0, 0, 1, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, −1, 1, −1 ],
[ 0, 0, 0, −1, −1, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 1, 0, 0, 0 ],
0, 0, 1, 0, 0, −1, 0 ],
0, 0, 1, 0, 1, 0, 1 ],
0, 0, 1, 1, 0, 0, 1 ],
0, 0, 1, 1, 1, 0, 2 ],
0, 1, 0, 0, 0, 0, 0 ],
0, 1, 1, 0, 0, −1, 0 ],
0, 1, 1, 0, 1, −1, 1 ],
0, 1, 1, 1, 0, −1, 1 ],
0, 1, 1, 1, 1, 0, 2 ],
1, −1, −2, −2, −1, 1, −2 ],
1, −1, −2, −1, −1, 1, −1 ],
1, −1, −1, −1, −1, 0, −1 ],
1, −1, −1, −1, 0, 1, −1 ],
1, −1, −1, 0, 0, 0, −1 ],
1, −1, 0, 0, 0, 0, 0 ],
1, 0, −1, −1, 0, 0, 0 ],
1, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 1 ],
0, −2, −2, −1, −1, 1, −2 ],
0, −1, −2, −1, −1, 1, −2 ],
0, −1, −1, −1, −1, 0, −2 ],
0, −1, −1, −1, 0, 0, −1 ],
0, −1, −1, 0, −1, 0, −1 ],
0, −1, −1, 0, 0, 1, 0 ],
0, 0, −1, −1, 0, 0, −1 ],
0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, 0, 0, 0, 0 ],
1, −2, −2, −1, −1, 0, −2 ],
1, −1, −2, −2, 0, 1, −1 ],
1, −1, −2, −1, 0, 0, −1 ],
1, −1, −1, −1, −1, 0, −1 ],
1, −1, −1, −1, 0, 1, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 1, 1, 1 ],
0, 0, 0, 1, 0, 0, 1 ],
0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 1, 0, −1, 0 ],
0, 0, 1, 1, 1, −1, 1 ],
0, 1, 0, −1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 1 ],
0, 1, 1, 0, 0, −1, 1 ],
0, 1, 1, 0, 1, 0, 1 ],
0, 1, 1, 1, 1, −1, 1 ],
0, 1, 2, 1, 1, −1, 2 ],
1, −1, −2, −1, −1, 0, −2 ],
1, −1, −2, −1, 0, 1, −1 ],
1, −1, −1, −1, −1, 1, −1 ],
1, −1, −1, −1, 0, 1, 0 ],
1, −1, −1, 0, 0, 0, 0 ],
1, 0, −1, −1, −1, 0, −1 ],
1, 0, −1, −1, 0, 1, 0 ],
1, 0, 0, 0, 0, −1, 0 ],
1, 0, 0, 0, 1, 0, 1 ],
0, −1, −2, −2, −1, 1, −2 ],
0, −1, −2, −1, −1, 1, −1 ],
0, −1, −1, −1, −1, 0, −1 ],
0, −1, −1, −1, 0, 1, −1 ],
0, −1, −1, 0, 0, 0, −1 ],
0, −1, 0, 0, 0, 0, 0 ],
0, 0, −1, −1, 0, 0, 0 ],
0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, 0, 1 ],
1, −2, −2, −1, 0, 1, −1 ],
1, −1, −2, −1, −1, 0, −2 ],
1, −1, −2, −1, 0, 1, −1 ],
1, −1, −1, −1, 0, 0, −1 ],
1, −1, −1, 0, 0, 0, 0 ],
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 0, 1, 1, 0, 1 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 1, 0, −1, 1 ],
0, 0, 0, 1, 1, 1, 0, 1 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 0, 1, 0, 0, 1, 0, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 0, 1, 1, 0, 1, 0, 2 ],
0, 0, 1, 1, 1, 1, −1, 2 ],
0, 1, −2, −2, −1, −1, 1, −2 ],
0, 1, −1, −2, −1, −1, 1, −2 ],
0, 1, −1, −1, −1, −1, 0, −2 ],
0, 1, −1, −1, −1, 0, 0, −1 ],
0, 1, −1, −1, 0, −1, 0, −1 ],
0, 1, −1, −1, 0, 0, 1, 0 ],
0, 1, 0, −1, −1, 0, 0, −1 ],
0, 1, 0, −1, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, −1, −2, −1, −1, 0, −2 ],
1, 0, −1, −2, −1, 0, 1, −1 ],
1, 0, −1, −1, −1, −1, 1, −1 ],
1, 0, −1, −1, −1, 0, 1, 0 ],
1, 0, −1, −1, 0, 0, 0, 0 ],
1, 0, 0, −1, −1, −1, 0, −1 ],
1, 0, 0, −1, −1, 0, 1, 0 ],
1, 0, 0, 0, 0, 0, −1, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
1, 1, −1, −2, −2, −1, 0, −2 ],
1, 1, −1, −2, −1, −1, 0, −1 ],
1, 1, −1, −2, −1, 0, 1, 0 ],
1, 1, −1, −1, −1, 0, 0, 0 ],
1, 1, 0, −1, −1, 0, 0, 0 ]
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
−1
∗
5
• I ≡ P89 :
7
6
4
3
2
1





CI =








b I =
Cox




0
0
1
0
0
1
0
−1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
−1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
















b
CI =



1
1
1
1
1
1
1
−1
















BI =



170
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
0
1
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
1
0
0
1
0
−1











0
0
0
−1
0
0
0
0
1
0
1
0
0
0
0
−1











Number of sincere Tits roots of poset I sI = 28.
Table of roots of qbI
[ −2,−1, 1, 2, 3, 1, 2, 3 ],
[ −1,−1, 1, 1, 2, 1, 2, 2 ],
[ −1,−1, 1, 2, 2, 1, 1, 2 ],
[ −1,−1, 1, 2, 3, 1, 1, 3 ],
[ −1,−1, 1, 2, 3, 2, 2, 4 ],
[ 1, 1,−1,−2,−3,−2,−2,−4 ],
[ 1, 1,−1,−2,−3,−1,−1,−3 ],
[ 1, 1,−1,−2,−2,−1,−1,−2 ],
[ 1, 1,−1,−1,−2,−1,−2,−2 ],
[ 2, 1,−1,−2,−3,−1,−2,−3 ],
[ −1, −1, 0, 1, 1, 0, 1, 0 ],
[ −1, −1, 0, 1, 2, 0, 1, 1 ],
[ −1, −1, 0, 1, 2, 1, 2, 2 ],
[ −1, −1, 1, 1, 2, 0, 1, 1 ],
[ −1, −1, 1, 2, 2, 0, 1, 2 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 0, 1, 1 ],
[ −1, 0, 1, 1, 1, 0, 1, 2 ],
[ −1, 0, 1, 1, 2, 1, 1, 2 ],
[ −1, 0, 1, 2, 2, 1, 1, 3 ],
[ 0, −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, 1, 0, 1, 1 ],
[ 0, −1, 0, 1, 1, 0, 0, 0 ],
[ 0, −1, 0, 1, 1, 1, 0, 1 ],
[ 0, −1, 0, 1, 2, 1, 1, 2 ],
[ 0, −1, 1, 1, 1, 0, 1, 1 ],
[ 0, −1, 1, 1, 2, 0, 1, 2 ],
[ 0, −1, 1, 1, 2, 1, 2, 3 ],
[ 0, 0, −1, −1, −1, −1, −1, −3 ],
[ 0, 0, −1, −1, −1, 0, −1, −2 ],
[ 0, 0, −1, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 0, −1, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, −1, −1, −1, −2 ],
[ 0, 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, −1, −1, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 1, 2 ],
[ 0, 0, 1, 1, 1, 1, 1, 3 ],
[ 0, 1, −1, −1, −2, −1, −2, −3 ],
[ 0, 1, −1, −1, −2, 0, −1, −2 ],
[ 0, 1, −1, −1, −1, 0, −1, −1 ],
[ 0, 1, 0, −1, −2, −1, −1, −2 ],
[ 0, 1, 0, −1, −1, −1, 0, −1 ],
[ 0, 1, 0, −1, −1, 0, 0, 0 ],
[ 0, 1, 0, 0, −1, 0, −1, −1 ],
[ −1,−2, 1, 2, 3, 1, 2, 3 ],
[ −1,−1, 1, 1, 2, 1, 2, 3 ],
[ −1,−1, 1, 2, 2, 1, 1, 3 ],
[ −1,−1, 1, 2, 3, 1, 2, 3 ],
[ −1,−1, 2, 2, 3, 1, 2, 4 ],
[ 1, 1,−1,−2,−3,−1,−2,−4 ],
[ 1, 1,−1,−2,−2,−1,−2,−3 ],
[ 1, 1,−1,−1,−3,−1,−2,−3 ],
[ 1, 1,−1,−1,−2,−1,−1,−2 ],
[ −1, −1, 0, 0, 1, 0, 1, 0 ],
[ −1, −1, 0, 1, 1, 0, 1, 1 ],
[ −1, −1, 0, 1, 2, 1, 1, 1 ],
[ −1, −1, 0, 2, 2, 1, 1, 2 ],
[ −1, −1, 1, 1, 2, 0, 1, 2 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 2 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 1, 2 ],
[ −1, 0, 1, 1, 2, 1, 1, 3 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 1, 1 ],
[ 0, −1, 0, 1, 1, 0, 0, 1 ],
[ 0, −1, 0, 1, 1, 1, 1, 1 ],
[ 0, −1, 1, 0, 1, 0, 1, 1 ],
[ 0, −1, 1, 1, 1, 0, 1, 2 ],
[ 0, −1, 1, 1, 2, 1, 1, 2 ],
[ 0, −1, 1, 2, 2, 1, 1, 3 ],
[ 0, 0, −1, −1, −1, −1, −1, −2 ],
[ 0, 0, −1, −1, −1, 0, 0, −2 ],
[ 0, 0, −1, 0, −1, −1, −1, −2 ],
[ 0, 0, −1, 0, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, −1, 0, −2 ],
[ 0, 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 0, 0, 1, 1, 1, 2 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 1, 0, 1, 2 ],
[ 0, 0, 1, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 1, 0, 2 ],
[ 0, 0, 1, 1, 2, 1, 1, 3 ],
[ 0, 1, −1, −1, −2, −1, −1, −3 ],
[ 0, 1, −1, −1, −1, −1, −1, −2 ],
[ 0, 1, −1, −1, −1, 0, 0, −1 ],
[ 0, 1, 0, −1, −1, −1, −1, −2 ],
[ 0, 1, 0, −1, −1, 0, −1, −1 ],
[ 0, 1, 0, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, −1, 0, −1, 0 ],
171
[ −1,−1, 1, 1, 2, 1, 1, 2 ],
[ −1,−1, 1, 1, 3, 1, 2, 3 ],
[ −1,−1, 1, 2, 2, 1, 2, 3 ],
[ −1,−1, 1, 2, 3, 1, 2, 4 ],
[ 1, 1,−2,−2,−3,−1,−2,−4 ],
[ 1, 1,−1,−2,−3,−1,−2,−3 ],
[ 1, 1,−1,−2,−2,−1,−1,−3 ],
[ 1, 1,−1,−1,−2,−1,−2,−3 ],
[ 1, 2,−1,−2,−3,−1,−2,−3 ],
[ −1, −1, 0, 1, 1, 0, 0, 0 ],
[ −1, −1, 0, 1, 1, 1, 1, 1 ],
[ −1, −1, 0, 1, 2, 1, 1, 2 ],
[ −1, −1, 1, 1, 1, 0, 1, 1 ],
[ −1, −1, 1, 1, 2, 0, 2, 2 ],
[ −1, 0, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 1, 1 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 2, 1, 1, 2 ],
[ −1, 0, 1, 1, 1, 0, 1, 1 ],
[ −1, 0, 1, 1, 2, 0, 1, 2 ],
[ −1, 0, 1, 1, 2, 1, 2, 3 ],
[ 0, −1, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 1, 0 ],
[ 0, −1, 0, 1, 0, 0, 0, 0 ],
[ 0, −1, 0, 1, 1, 0, 1, 1 ],
[ 0, −1, 0, 1, 1, 1, 1, 2 ],
[ 0, −1, 1, 1, 1, 0, 0, 1 ],
[ 0, −1, 1, 1, 1, 1, 1, 2 ],
[ 0, −1, 1, 1, 2, 1, 1, 3 ],
[ 0, 0, −1, −1, −2, −1, −1, −3 ],
[ 0, 0, −1, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 0, −1, −2 ],
[ 0, 0, −1, 0, 0, 0, −1, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, −1, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1, −2 ],
[ 0, 0, 0, 0, −1, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 1, 1, 2 ],
[ 0, 0, 1, 1, 1, 0, 0, 2 ],
[ 0, 0, 1, 1, 1, 1, 1, 2 ],
[ 0, 1, −1, −2, −2, −1, −1, −3 ],
[ 0, 1, −1, −1, −2, −1, −1, −2 ],
[ 0, 1, −1, −1, −1, 0, −1, −2 ],
[ 0, 1, −1, 0, −1, 0, −1, −1 ],
[ 0, 1, 0, −1, −1, −1, −1, −1 ],
[ 0, 1, 0, −1, −1, 0, 0, −1 ],
[ 0, 1, 0, 0, −1, −1, −1, −1 ],
[ 0, 1, 0, 0, −1, 0, 0, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1, 0, 0, 0, 0, −1, 0 ],
1, 0, 0, 0, 1, 0, 1 ],
0, −1, −2, −2, −1, −1, −3 ],
0, −1, −1, −2, −1, −1, −2 ],
0, −1, −1, −1, 0, −1, −2 ],
0, −1, 0, −1, 0, −1, −1 ],
0, 0, −1, −1, −1, −1, −1 ],
0, 0, −1, −1, 0, 0, −1 ],
0, 0, 0, −1, −1, −1, −1 ],
0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, 0, 1 ],
1, −1, −2, −2, 0, −1, −2 ],
1, −1, −1, −2, 0, −1, −1 ],
1, 0, −1, −2, −1, −2, −2 ],
1, 0, −1, −2, 0, −1, −1 ],
1, 0, −1, −1, 0, −1, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1, 0, 0, 0, 0, 0, 0 ],
1, 1, 0, 0, 0, 0, 1 ],
0, −1, −1, −2, −1, −2, −3 ],
0, −1, −1, −2, 0, −1, −2 ],
0, −1, −1, −1, 0, −1, −1 ],
0, 0, −1, −2, −1, −1, −2 ],
0, 0, −1, −1, −1, 0, −1 ],
0, 0, −1, −1, 0, 0, 0 ],
0, 0, 0, −1, 0, −1, −1 ],
0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 1, 0, 1 ],
1, −1, −1, −2, 0, −2, −2 ],
1, −1, −1, −1, 0, −1, −1 ],
1, 0, −1, −2, −1, −1, −2 ],
1, 0, −1, −1, −1, −1, −1 ],
1, 0, −1, −1, 0, 0, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 1, 0, 0, 0, 0, 0, 1 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, −1, −1, −2, −1, −1, −3 ],
1, 0, −1, −1, −1, −1, −1, −2 ],
1, 0, −1, −1, −1, 0, 0, −1 ],
1, 0, 0, −1, −1, −1, −1, −2 ],
1, 0, 0, −1, −1, 0, −1, −1 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, −1, 0, −1, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 1, −1, −1, −2, 0, −1, −2 ],
1, 1, 0, −2, −2, −1, −1, −2 ],
1, 1, 0, −1, −2, −1, −1, −1 ],
1, 1, 0, −1, −1, 0, −1, −1 ],
1, 1, 0, 0, −1, 0, −1, 0 ]
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
∗
7
5
6
• I ≡ P90 :
4
3
2
1





CI =








b I =
Cox




0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
−1
−1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
−1
1
1
1
1
1
1
1
1
















b
CI =














1
1
1
1
1
1
1
0
0
 0

 −1

BI = 00

 0
 1
0

0
−1
−1
−1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
−1
−1
−1
0
−1
0
0
0
1
1
2
1
1
0
0
0
1
2
2
1
1
0
−1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
1
2
2
1
1
1
0
−1











0
−1
−1
0
−1
0
0
0
1
1
1
1
1
0
0
−1
Number of sincere Tits roots of poset I sI = 22.
Table of roots of qbI
[ −2,−1,−1, 2, 3, 2,−1, 1 ],
[ −1,−1,−1, 1, 2, 2,−1, 1 ],
[ −1,−1,−1, 2, 2, 2,−1, 1 ],
[ −1,−1,−1, 2, 3, 2,−1, 1 ],
[ 1, 1, 1,−2,−3,−2, 1,−1 ],
[ 1, 1, 1,−2,−2,−2, 1,−1 ],
[ −1,−2,−1, 2, 3, 2,−1, 1 ],
[ −1,−1,−1, 1, 3, 2,−1, 1 ],
[ −1,−1,−1, 2, 3, 1,−1, 1 ],
[ −1,−1,−1, 2, 3, 2,−1, 2 ],
[ 1, 1, 1,−2,−3,−2, 2,−1 ],
[ 1, 1, 1,−2,−2,−1, 1,−1 ],
172
[ −1,−1,−2, 2, 3, 2,−1, 1 ],
[ −1,−1,−1, 2, 2, 1,−1, 1 ],
[ −1,−1,−1, 2, 3, 2,−2, 1 ],
[ 1, 1, 1,−2,−3,−2, 1,−2 ],
[ 1, 1, 1,−2,−3,−1, 1,−1 ],
[ 1, 1, 1,−1,−3,−2, 1,−1 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
1, 1, 1,−1,−2,−2, 1,−1 ],
2, 1, 1,−2,−3,−2, 1,−1 ],
−1, −1, −1, 1, 2, 1, 0, 0 ],
−1, −1, −1, 1, 2, 2, 0, 1 ],
−1, −1, 0, 0, 1, 1, 0, 0 ],
−1, −1, 0, 1, 1, 1, 0, 0 ],
−1, −1, 0, 1, 2, 1, −1, 1 ],
−1, −1, 0, 2, 2, 1, −1, 1 ],
−1, 0, −1, 1, 1, 1, −1, 0 ],
−1, 0, −1, 1, 2, 1, −1, 0 ],
−1, 0, −1, 1, 2, 2, −1, 1 ],
−1, 0, 0, 0, 0, 0, 0, 0 ],
−1, 0, 0, 0, 1, 0, 0, 0 ],
−1, 0, 0, 0, 1, 1, 0, 1 ],
−1, 0, 0, 1, 1, 0, 0, 0 ],
−1, 0, 0, 1, 1, 1, −1, 1 ],
−1, 0, 1, 0, 0, 0, 0, 0 ],
0, −1, −1, 1, 1, 0, 0, 0 ],
0, −1, −1, 1, 1, 1, 0, 1 ],
0, −1, −1, 1, 2, 1, 0, 1 ],
0, −1, 0, 0, 0, 0, 0, −1 ],
0, −1, 0, 0, 0, 1, 0, 0 ],
0, −1, 0, 0, 1, 1, 0, 0 ],
0, −1, 0, 1, 1, 0, −1, 0 ],
0, −1, 0, 1, 1, 1, −1, 0 ],
0, −1, 0, 1, 2, 1, −1, 1 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, −1, 0, 1, 0, 0, 0 ],
0, 0, −1, 0, 1, 1, 0, 1 ],
0, 0, −1, 1, 1, 0, 0, 0 ],
0, 0, −1, 1, 1, 1, −1, 1 ],
0, 0, 0, −1, −1, −1, 1, −1 ],
0, 0, 0, −1, −1, 0, 1, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, −1, 1, −1 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 0, 1, 1, −1, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 0, 1, 1, 0, −1, 0 ],
0, 0, 0, 1, 1, 1, −1, 1 ],
0, 0, 1, −1, −1, −1, 1, −1 ],
0, 0, 1, −1, −1, 0, 0, 0 ],
0, 0, 1, 0, −1, −1, 0, −1 ],
0, 0, 1, 0, −1, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 1, 0, −1, −2, −1, 1, −1 ],
0, 1, 0, −1, −1, −1, 1, 0 ],
0, 1, 0, −1, −1, 0, 1, 0 ],
0, 1, 0, 0, −1, −1, 0, 0 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 1, −1, −2, −1, 0, −1 ],
0, 1, 1, −1, −1, −1, 0, −1 ],
0, 1, 1, −1, −1, 0, 0, 0 ],
1, 0, −1, 0, 0, 0, 0, 0 ],
1, 0, 0, −1, −1, −1, 1, −1 ],
1, 0, 0, −1, −1, 0, 0, 0 ],
1, 0, 0, 0, −1, −1, 0, −1 ],
1, 0, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 1, −1, −2, −2, 1, −1 ],
1, 0, 1, −1, −2, −1, 1, 0 ],
1, 0, 1, −1, −1, −1, 1, 0 ],
1, 1, 0, −2, −2, −1, 1, −1 ],
1, 1, 0, −1, −2, −1, 1, −1 ],
1, 1, 0, −1, −1, −1, 0, 0 ],
1, 1, 0, 0, −1, −1, 0, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
1, 1, 2,−2,−3,−2, 1,−1 ],
−1, −1, −1, 1, 1, 1, 0, 0 ],
−1, −1, −1, 1, 2, 1, 0, 1 ],
−1, −1, −1, 2, 2, 1, −1, 0 ],
−1, −1, 0, 1, 1, 0, 0, 0 ],
−1, −1, 0, 1, 1, 1, 0, 1 ],
−1, −1, 0, 1, 2, 1, 0, 1 ],
−1, 0, −1, 0, 1, 1, 0, 0 ],
−1, 0, −1, 1, 1, 1, 0, 0 ],
−1, 0, −1, 1, 2, 1, −1, 1 ],
−1, 0, −1, 2, 2, 1, −1, 1 ],
−1, 0, 0, 0, 0, 0, 1, 0 ],
−1, 0, 0, 0, 1, 1, −1, 0 ],
−1, 0, 0, 1, 0, 0, 0, 0 ],
−1, 0, 0, 1, 1, 0, 0, 1 ],
−1, 0, 0, 1, 1, 1, 0, 1 ],
−1, 1, 0, 0, 0, 0, 0, 0 ],
0, −1, −1, 1, 1, 1, −1, 0 ],
0, −1, −1, 1, 2, 1, −1, 0 ],
0, −1, −1, 1, 2, 2, −1, 1 ],
0, −1, 0, 0, 0, 0, 0, 0 ],
0, −1, 0, 0, 1, 0, 0, 0 ],
0, −1, 0, 0, 1, 1, 0, 1 ],
0, −1, 0, 1, 1, 0, 0, 0 ],
0, −1, 0, 1, 1, 1, −1, 1 ],
0, −1, 1, 0, 0, 0, 0, 0 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, −1, 0, 1, 1, −1, 0 ],
0, 0, −1, 1, 0, 0, 0, 0 ],
0, 0, −1, 1, 1, 0, 0, 1 ],
0, 0, −1, 1, 1, 1, 0, 1 ],
0, 0, 0, −1, −1, 0, 0, −1 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 1, 0, 0 ],
0, 0, 0, 0, −1, −1, 1, 0 ],
0, 0, 0, 0, −1, 0, 1, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 0, 1, 1, 0, 1 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 0, 1, 1, 0, −1, 1 ],
0, 0, 1, −1, −2, −1, 1, −1 ],
0, 0, 1, −1, −1, −1, 1, 0 ],
0, 0, 1, −1, −1, 0, 1, 0 ],
0, 0, 1, 0, −1, −1, 0, 0 ],
0, 0, 1, 0, 0, −1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 1, 0, −1, −1, −1, 0, −1 ],
0, 1, 0, −1, −1, 0, 0, −1 ],
0, 1, 0, −1, 0, 0, 0, 0 ],
0, 1, 0, 0, −1, −1, 1, 0 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 1, −2, −2, −1, 1, −1 ],
0, 1, 1, −1, −2, −1, 1, −1 ],
0, 1, 1, −1, −1, −1, 0, 0 ],
0, 1, 1, 0, −1, −1, 0, 0 ],
1, 0, 0, −1, −2, −1, 1, −1 ],
1, 0, 0, −1, −1, −1, 1, 0 ],
1, 0, 0, −1, −1, 0, 1, 0 ],
1, 0, 0, 0, −1, −1, 0, 0 ],
1, 0, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 1, −1, −2, −1, 0, −1 ],
1, 0, 1, −1, −1, −1, 0, −1 ],
1, 0, 1, −1, −1, 0, 0, 0 ],
1, 1, 0, −1, −2, −2, 1, −1 ],
1, 1, 0, −1, −2, −1, 1, 0 ],
1, 1, 0, −1, −1, −1, 1, 0 ],
1, 1, 1, −2, −2, −1, 0, −1 ],
173
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
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[
[
[
[
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[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
1, 2, 1,−2,−3,−2, 1,−1 ],
−1, −1, −1, 1, 2, 1, −1, 0 ],
−1, −1, −1, 1, 2, 2, −1, 0 ],
−1, −1, −1, 2, 2, 1, 0, 1 ],
−1, −1, 0, 1, 1, 1, −1, 0 ],
−1, −1, 0, 1, 2, 1, −1, 0 ],
−1, −1, 0, 1, 2, 2, −1, 1 ],
−1, 0, −1, 1, 1, 0, 0, 0 ],
−1, 0, −1, 1, 1, 1, 0, 1 ],
−1, 0, −1, 1, 2, 1, 0, 1 ],
−1, 0, 0, 0, 0, 0, 0, −1 ],
−1, 0, 0, 0, 0, 1, 0, 0 ],
−1, 0, 0, 0, 1, 1, 0, 0 ],
−1, 0, 0, 1, 1, 0, −1, 0 ],
−1, 0, 0, 1, 1, 1, −1, 0 ],
−1, 0, 0, 1, 2, 1, −1, 1 ],
0, −1, −1, 0, 1, 1, 0, 0 ],
0, −1, −1, 1, 1, 1, 0, 0 ],
0, −1, −1, 1, 2, 1, −1, 1 ],
0, −1, −1, 2, 2, 1, −1, 1 ],
0, −1, 0, 0, 0, 0, 1, 0 ],
0, −1, 0, 0, 1, 1, −1, 0 ],
0, −1, 0, 1, 0, 0, 0, 0 ],
0, −1, 0, 1, 1, 0, 0, 1 ],
0, −1, 0, 1, 1, 1, 0, 1 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 1, 0, 0 ],
0, 0, −1, 0, 1, 1, 0, 0 ],
0, 0, −1, 1, 1, 0, −1, 0 ],
0, 0, −1, 1, 1, 1, −1, 0 ],
0, 0, −1, 1, 2, 1, −1, 1 ],
0, 0, 0, −1, −1, 0, 1, −1 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, 0, −1, −1, 0, −1 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 0, 1, 1, −1, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 1, 0, 0, 1 ],
0, 0, 1, −1, −1, −1, 0, −1 ],
0, 0, 1, −1, −1, 0, 0, −1 ],
0, 0, 1, −1, 0, 0, 0, 0 ],
0, 0, 1, 0, −1, −1, 1, 0 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, 0, −1, −1, −1, 1, −1 ],
0, 1, 0, −1, −1, 0, 0, 0 ],
0, 1, 0, 0, −1, −1, 0, −1 ],
0, 1, 0, 0, −1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 1, −1, −2, −2, 1, −1 ],
0, 1, 1, −1, −2, −1, 1, 0 ],
0, 1, 1, −1, −1, −1, 1, 0 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, −1, −1, −1, 0, −1 ],
1, 0, 0, −1, −1, 0, 0, −1 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, −1, −1, 1, 0 ],
1, 0, 0, 0, 0, 0, −1, 0 ],
1, 0, 1, −2, −2, −1, 1, −1 ],
1, 0, 1, −1, −2, −1, 1, −1 ],
1, 0, 1, −1, −1, −1, 0, 0 ],
1, 0, 1, 0, −1, −1, 0, 0 ],
1, 1, 0, −1, −2, −1, 0, −1 ],
1, 1, 0, −1, −1, −1, 0, −1 ],
1, 1, 0, −1, −1, 0, 0, 0 ],
1, 1, 1, −2, −2, −1, 1, 0 ],
[
[
1,
1,
1,
1,
1, −1, −2, −2,
1, −1, −2, −1,
0, −1 ],
0, 0 ],
[
[
1,
1,
1, −1, −2, −2,
1, −1, −2, −1,
1,
1,
1,
1,
0 ],
0 ],
[
[
1,
1,
1,
1,
1, −1, −2, −1,
1, −1, −1, −1,
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0, −1 ],
0, 0 ]
∗
6
7
5
4
• I ≡ P91 :
3
2
1





CI =








b
CoxI =



0
0
0
0
1
0
0
−1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
−1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
















BI =



1
1
1
1
0
1
1
−1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
−1
0
0
−1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
−1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
−1
−1
−1
0
−1
0
0











0
−1
−1
−1
0
0
−1
0
0
0
0
0
0
0
0
−1
Number of sincere Tits roots of poset I sI = 28.
Table of roots of qbI
[ −2,−1,−1, 2, 1, 3, 2, 2 ],
[ −1,−1,−1, 1, 1, 2, 1, 1 ],
[ −1,−1,−1, 1, 1, 3, 2, 2 ],
[ −1,−1,−1, 2, 1, 2, 2, 2 ],
[ −1,−1,−1, 2, 1, 3, 2, 3 ],
[ 1, 1, 1,−2,−1,−3,−2,−3 ],
[ 1, 1, 1,−2,−1,−2,−2,−2 ],
[ 1, 1, 1,−1,−1,−3,−2,−2 ],
[ 1, 1, 1,−1,−1,−2,−1,−1 ],
[ 2, 1, 1,−2,−1,−3,−2,−2 ],
[ −1, −1, −1, 1, 0, 2, 1, 1 ],
[ −1, −1, 0, 0, 0, 1, 1, 0 ],
[ −1, −1, 0, 1, 0, 1, 1, 1 ],
[ −1, −1, 0, 1, 1, 2, 1, 1 ],
[ −1, −1, 0, 2, 1, 2, 1, 2 ],
[ −1, 0, −1, 1, 0, 1, 1, 0 ],
[ −1, 0, −1, 1, 1, 1, 1, 1 ],
[ −1, 0, −1, 1, 1, 2, 2, 2 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 1, 0, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 1 ],
[ −1,−2,−1, 2, 1, 3, 2, 2 ],
[ −1,−1,−1, 1, 1, 2, 2, 1 ],
[ −1,−1,−1, 2, 1, 2, 1, 1 ],
[ −1,−1,−1, 2, 1, 3, 1, 2 ],
[ −1,−1,−1, 2, 2, 3, 2, 3 ],
[ 1, 1, 1,−2,−1,−3,−2,−2 ],
[ 1, 1, 1,−2,−1,−2,−1,−2 ],
[ 1, 1, 1,−1,−1,−2,−2,−2 ],
[ 1, 1, 2,−2,−1,−3,−2,−2 ],
[ −1, −1, −1, 1, 0, 1, 1, 0 ],
[ −1, −1, −1, 1, 0, 2, 2, 1 ],
[ −1, −1, 0, 1, 0, 1, 0, 0 ],
[ −1, −1, 0, 1, 0, 2, 1, 1 ],
[ −1, −1, 0, 1, 1, 2, 1, 2 ],
[ −1, 0, −1, 0, 0, 1, 1, 0 ],
[ −1, 0, −1, 1, 0, 1, 1, 1 ],
[ −1, 0, −1, 1, 1, 2, 1, 1 ],
[ −1, 0, −1, 2, 1, 2, 1, 2 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 2 ],
174
[ −1,−1,−2, 2, 1, 3, 2, 2 ],
[ −1,−1,−1, 1, 1, 2, 2, 2 ],
[ −1,−1,−1, 2, 1, 2, 1, 2 ],
[ −1,−1,−1, 2, 1, 3, 2, 2 ],
[ 1, 1, 1,−2,−2,−3,−2,−3 ],
[ 1, 1, 1,−2,−1,−3,−1,−2 ],
[ 1, 1, 1,−2,−1,−2,−1,−1 ],
[ 1, 1, 1,−1,−1,−2,−2,−1 ],
[ 1, 2, 1,−2,−1,−3,−2,−2 ],
[ −1, −1, −1, 1, 0, 2, 1, 0 ],
[ −1, −1, −1, 2, 0, 2, 1, 1 ],
[ −1, −1, 0, 1, 0, 1, 1, 0 ],
[ −1, −1, 0, 1, 1, 1, 1, 1 ],
[ −1, −1, 0, 1, 1, 2, 2, 2 ],
[ −1, 0, −1, 1, 0, 1, 0, 0 ],
[ −1, 0, −1, 1, 0, 2, 1, 1 ],
[ −1, 0, −1, 1, 1, 2, 1, 2 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 2, 1, 2 ],











[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, 1, 0, 1, 0, 0 ],
[ 0, −1, −1, 1, 0, 2, 1, 1 ],
[ 0, −1, −1, 1, 1, 2, 1, 2 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 1, 1, 1 ],
[ 0, −1, 0, 1, 0, 1, 0, 0 ],
[ 0, −1, 0, 1, 1, 1, 0, 1 ],
[ 0, −1, 0, 1, 1, 2, 1, 2 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, 1, 1, 1, 1 ],
[ 0, 0, −1, 1, 0, 1, 0, 1 ],
[ 0, 0, −1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, −1, −1, −1, −1, −2 ],
[ 0, 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, −1, −1, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 0, 1, −1, −1, −1, −1, −1 ],
[ 0, 0, 1, −1, 0, −1, 0, −1 ],
[ 0, 0, 1, 0, −1, −1, −1, −1 ],
[ 0, 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, −1, −1, −2, −1, −2 ],
[ 0, 1, 0, −1, −1, −1, 0, −1 ],
[ 0, 1, 0, −1, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, 0, −1, −1, −1 ],
[ 0, 1, 0, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, −1, −1, −2, −1, −2 ],
[ 0, 1, 1, −1, 0, −2, −1, −1 ],
[ 0, 1, 1, −1, 0, −1, 0, 0 ],
[ 1, 0, −1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, −1, −1, −1, −1, −1 ],
[ 1, 0, 0, −1, 0, −1, 0, −1 ],
[ 1, 0, 0, 0, −1, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, −1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, −1, −1, −2, −2, −2 ],
[ 1, 0, 1, −1, −1, −1, −1, −1 ],
[ 1, 0, 1, −1, 0, −1, −1, 0 ],
[ 1, 1, 0, −2, −1, −2, −1, −2 ],
[ 1, 1, 0, −1, −1, −2, −1, −1 ],
[ 1, 1, 0, −1, 0, −1, −1, −1 ],
[ 1, 1, 0, 0, 0, −1, −1, 0 ],
[ 1, 1, 1, −1, 0, −2, −1, −1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, 1, 0, 1, 1, 0 ],
[ 0, −1, −1, 1, 1, 1, 1, 1 ],
[ 0, −1, −1, 1, 1, 2, 2, 2 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 1, 1 ],
[ 0, −1, 0, 1, 0, 1, 0, 1 ],
[ 0, −1, 0, 1, 1, 1, 1, 1 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 1, 1, 0 ],
[ 0, 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, 1, 0, 1, 1, 1 ],
[ 0, 0, −1, 1, 1, 1, 1, 2 ],
[ 0, 0, 0, −1, −1, −1, 0, −2 ],
[ 0, 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 0, 0, 1, 1, 1, 2 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 0, 1, −1, −1, −2, −1, −2 ],
[ 0, 0, 1, −1, −1, −1, 0, −1 ],
[ 0, 0, 1, −1, 0, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, −1, −1, −1 ],
[ 0, 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, −1, −1, −1, −1, −2 ],
[ 0, 1, 0, −1, 0, −1, −1, −1 ],
[ 0, 1, 0, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, −1, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, −2, −1, −2, −1, −2 ],
[ 0, 1, 1, −1, −1, −2, −1, −1 ],
[ 0, 1, 1, −1, 0, −1, −1, −1 ],
[ 0, 1, 1, 0, 0, −1, −1, 0 ],
[ 1, 0, 0, −1, −1, −2, −1, −2 ],
[ 1, 0, 0, −1, −1, −1, 0, −1 ],
[ 1, 0, 0, −1, 0, −1, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, 0, −1, 0 ],
[ 1, 0, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, −1, −1, −2, −1, −2 ],
[ 1, 0, 1, −1, 0, −2, −1, −1 ],
[ 1, 0, 1, −1, 0, −1, 0, 0 ],
[ 1, 1, 0, −1, −1, −2, −2, −2 ],
[ 1, 1, 0, −1, −1, −1, −1, −1 ],
[ 1, 1, 0, −1, 0, −1, −1, 0 ],
[ 1, 1, 1, −2, 0, −2, −1, −1 ],
[ 1, 1, 1, −1, 0, −2, −1, 0 ],
175
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, −1, 0, 0, 1, 1, 0 ],
0, −1, −1, 1, 0, 1, 1, 1 ],
0, −1, −1, 1, 1, 2, 1, 1 ],
0, −1, −1, 2, 1, 2, 1, 2 ],
0, −1, 0, 0, 0, 0, 0, 0 ],
0, −1, 0, 0, 0, 1, 1, 0 ],
0, −1, 0, 1, 0, 0, 0, 0 ],
0, −1, 0, 1, 0, 1, 1, 1 ],
0, −1, 0, 1, 1, 1, 1, 2 ],
0, 0, −1, 0, −1, 0, 0, −1 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, −1, 0, 0, 1, 1, 1 ],
0, 0, −1, 1, 0, 1, 0, 0 ],
0, 0, −1, 1, 1, 1, 0, 1 ],
0, 0, −1, 1, 1, 2, 1, 2 ],
0, 0, 0, −1, −1, −1, 0, −1 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, 0, −1, −1, −1, −2 ],
0, 0, 0, 0, −1, 0, −1, −1 ],
0, 0, 0, 0, 0, −1, −1, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 0, 1, 1, 0, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 0, 1, 0, 1, 0, 1 ],
0, 0, 0, 1, 1, 1, 0, 2 ],
0, 0, 1, −1, −1, −1, −1, −2 ],
0, 0, 1, −1, 0, −1, −1, −1 ],
0, 0, 1, −1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, −1, −1, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, 0, −1, −1, −1, −1, −1 ],
0, 1, 0, −1, 0, −1, 0, −1 ],
0, 1, 0, 0, −1, −1, −1, −1 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 1, −1, −1, −2, −2, −2 ],
0, 1, 1, −1, −1, −1, −1, −1 ],
0, 1, 1, −1, 0, −1, −1, 0 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, −1, −1, −1, −1, −2 ],
1, 0, 0, −1, 0, −1, −1, −1 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, −1, −1, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 1, −2, −1, −2, −1, −2 ],
1, 0, 1, −1, −1, −2, −1, −1 ],
1, 0, 1, −1, 0, −1, −1, −1 ],
1, 0, 1, 0, 0, −1, −1, 0 ],
1, 1, 0, −1, −1, −2, −1, −2 ],
1, 1, 0, −1, 0, −2, −1, −1 ],
1, 1, 0, −1, 0, −1, 0, 0 ],
1, 1, 1, −1, 0, −2, −2, −1 ],
1, 1, 1, −1, 0, −1, −1, 0 ]
∗
6
7
5
• I ≡ P92 :
4
3
2
1





CI =








b I =
Cox




0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
















BI =



1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
−1
−1
−1
−1
−1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
−1
−1
−2
−2
−2
−1
−1
0
−1
−1
−1
−2
−1
−1
−1
0











−1
−1
−1
−1
−1
−1
−1
1











Number of sincere Tits roots of poset I sI = 22.
Table of roots of qbI
[ −2,−1,−1,−1, 2, 3, 2, 1 ],
[ −1,−1,−1,−2, 2, 3, 2, 1 ],
[ −1,−1,−1,−1, 2, 2, 1, 1 ],
[ −1,−1,−1,−1, 2, 3, 2, 1 ],
[ 1, 1, 1, 1,−2,−3,−2,−1 ],
[ 1, 1, 1, 1,−2,−2,−1,−1 ],
[ 1, 1, 1, 2,−2,−3,−2,−1 ],
[ 2, 1, 1, 1,−2,−3,−2,−1 ],
[ −1, −1, −1, −1, 2, 2, 1, 0 ],
[ −1, −1, −1, 0, 1, 2, 1, 1 ],
[ −1, −1, 0, −1, 1, 1, 1, 0 ],
[ −1, −1, 0, −1, 1, 2, 2, 1 ],
[ −1, −1, 0, 0, 1, 1, 0, 0 ],
[ −1, −1, 0, 0, 1, 2, 1, 1 ],
[ −1, 0, −1, −1, 1, 2, 1, 1 ],
[ −1, 0, −1, 0, 0, 1, 1, 0 ],
[ −1, 0, −1, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, −1, 1, 1, 0, 0 ],
[ −1, 0, 0, −1, 1, 2, 1, 1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, 1, 2, 1, 0 ],
[ 0, −1, −1, −1, 2, 2, 1, 1 ],
[ −1,−2,−1,−1, 2, 3, 2, 1 ],
[ −1,−1,−1,−1, 1, 2, 2, 1 ],
[ −1,−1,−1,−1, 2, 2, 2, 1 ],
[ −1,−1,−1,−1, 2, 3, 2, 2 ],
[ 1, 1, 1, 1,−2,−3,−1,−1 ],
[ 1, 1, 1, 1,−1,−3,−2,−1 ],
[ 1, 1, 2, 1,−2,−3,−2,−1 ],
[ −1, −1, −1, −1, 1, 2, 1, 0 ],
[ −1, −1, −1, 0, 1, 1, 1, 0 ],
[ −1, −1, −1, 0, 1, 2, 2, 1 ],
[ −1, −1, 0, −1, 1, 2, 1, 0 ],
[ −1, −1, 0, −1, 2, 2, 1, 1 ],
[ −1, −1, 0, 0, 1, 1, 1, 0 ],
[ −1, 0, −1, −1, 1, 1, 1, 0 ],
[ −1, 0, −1, −1, 1, 2, 2, 1 ],
[ −1, 0, −1, 0, 1, 1, 0, 0 ],
[ −1, 0, −1, 0, 1, 2, 1, 1 ],
[ −1, 0, 0, −1, 1, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, 1, 2, 1, 1 ],
[ 0, −1, −1, 0, 0, 1, 1, 0 ],
176
[ −1,−1,−2,−1, 2, 3, 2, 1 ],
[ −1,−1,−1,−1, 1, 3, 2, 1 ],
[ −1,−1,−1,−1, 2, 3, 1, 1 ],
[ 1, 1, 1, 1,−2,−3,−2,−2 ],
[ 1, 1, 1, 1,−2,−2,−2,−1 ],
[ 1, 1, 1, 1,−1,−2,−2,−1 ],
[ 1, 2, 1, 1,−2,−3,−2,−1 ],
[ −1, −1, −1, −1, 1, 2, 2, 0 ],
[ −1, −1, −1, 0, 1, 2, 1, 0 ],
[ −1, −1, −1, 0, 2, 2, 1, 1 ],
[ −1, −1, 0, −1, 1, 2, 1, 1 ],
[ −1, −1, 0, 0, 0, 1, 1, 0 ],
[ −1, −1, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, −1, −1, 1, 2, 1, 0 ],
[ −1, 0, −1, −1, 2, 2, 1, 1 ],
[ −1, 0, −1, 0, 1, 1, 1, 0 ],
[ −1, 0, 0, −1, 0, 1, 1, 0 ],
[ −1, 0, 0, −1, 1, 1, 1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, 1, 1, 1, 0 ],
[ 0, −1, −1, −1, 1, 2, 2, 1 ],
[ 0, −1, −1, 0, 1, 1, 0, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, −1, 0, 1, 1, 1, 0 ],
0, −1, 0, −1, 0, 1, 1, 0 ],
0, −1, 0, −1, 1, 1, 1, 1 ],
0, −1, 0, 0, 0, 0, 0, 0 ],
0, −1, 0, 0, 0, 1, 1, 0 ],
0, −1, 0, 0, 1, 1, 0, 0 ],
0, −1, 0, 1, 0, 0, 0, 0 ],
0, 0, −1, −1, 1, 1, 0, 0 ],
0, 0, −1, −1, 1, 2, 1, 1 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, −1, 0, 0, 1, 1, 1 ],
0, 0, −1, 0, 1, 1, 0, 1 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 1, 0, 0 ],
0, 0, 0, −1, 1, 0, 0, 0 ],
0, 0, 0, −1, 1, 1, 1, 1 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, −1, −1, −1, −1 ],
0, 0, 0, 1, −1, 0, 0, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, −1, −1, 0, −1 ],
0, 0, 1, 0, 0, −1, −1, −1 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 0, 1, 1, −1, −2, −1, −1 ],
0, 0, 1, 1, −1, −1, 0, 0 ],
0, 1, 0, −1, 0, 0, 0, 0 ],
0, 1, 0, 0, −1, −1, 0, 0 ],
0, 1, 0, 0, 0, −1, −1, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 1, −1, −1, −1, −1 ],
0, 1, 0, 1, 0, −1, −1, 0 ],
0, 1, 1, 0, −1, −1, −1, 0 ],
0, 1, 1, 1, −2, −2, −1, −1 ],
0, 1, 1, 1, −1, −2, −1, 0 ],
1, 0, −1, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, −1, −1, 0, −1 ],
1, 0, 0, 0, 0, −1, −1, −1 ],
1, 0, 0, 0, 0, 0, −1, 0 ],
1, 0, 0, 1, −1, −2, −1, −1 ],
1, 0, 0, 1, −1, −1, 0, 0 ],
1, 0, 1, 0, −1, −1, −1, −1 ],
1, 0, 1, 0, 0, −1, −1, 0 ],
1, 0, 1, 1, −1, −2, −1, −1 ],
1, 1, 0, 0, −1, −2, −1, −1 ],
1, 1, 0, 0, −1, −1, 0, 0 ],
1, 1, 0, 1, −1, −2, −2, −1 ],
1, 1, 0, 1, −1, −1, −1, 0 ],
1, 1, 1, 0, −1, −2, −1, −1 ],
1, 1, 1, 1, −2, −2, −1, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, −1, 0, 1, 1, 1, 1 ],
0, −1, 0, −1, 1, 1, 0, 0 ],
0, −1, 0, −1, 1, 2, 1, 1 ],
0, −1, 0, 0, 0, 0, 1, 0 ],
0, −1, 0, 0, 0, 1, 1, 1 ],
0, −1, 0, 0, 1, 1, 0, 1 ],
0, −1, 1, 0, 0, 0, 0, 0 ],
0, 0, −1, −1, 1, 1, 1, 0 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 1, 0, 0 ],
0, 0, −1, 0, 1, 0, 0, 0 ],
0, 0, −1, 0, 1, 1, 1, 1 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, −1, 0, 1, 1, 0 ],
0, 0, 0, −1, 1, 1, 0, 0 ],
0, 0, 0, 0, −1, −1, 0, −1 ],
0, 0, 0, 0, −1, 0, 1, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 1, 1 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, −1, −1, 0, −1 ],
0, 0, 0, 1, 0, −1, −1, −1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 1, −1, 0, 0, 0, 0 ],
0, 0, 1, 0, −1, −1, 0, 0 ],
0, 0, 1, 0, 0, −1, −1, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 1, −1, −1, −1, −1 ],
0, 0, 1, 1, 0, −1, −1, 0 ],
0, 1, 0, 0, −1, −1, −1, −1 ],
0, 1, 0, 0, −1, 0, 0, 0 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 1, −1, −1, −1, 0 ],
0, 1, 1, 0, −1, −2, −1, −1 ],
0, 1, 1, 0, −1, −1, 0, 0 ],
0, 1, 1, 1, −1, −2, −2, −1 ],
0, 1, 1, 1, −1, −1, −1, 0 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, −1, −1, 0, 0 ],
1, 0, 0, 0, 0, −1, −1, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 1, −1, −1, −1, −1 ],
1, 0, 0, 1, 0, −1, −1, 0 ],
1, 0, 1, 0, −1, −1, −1, 0 ],
1, 0, 1, 1, −2, −2, −1, −1 ],
1, 0, 1, 1, −1, −2, −1, 0 ],
1, 1, 0, 0, −1, −1, −1, −1 ],
1, 1, 0, 0, 0, −1, −1, 0 ],
1, 1, 0, 1, −1, −2, −1, −1 ],
1, 1, 1, 0, −2, −2, −1, −1 ],
1, 1, 1, 0, −1, −2, −1, 0 ],
1, 1, 1, 1, −1, −2, −2, 0 ],
∗
• I ≡ P93 :
6
7
4
5
3
2
1
177
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, −1, 0, 1, 2, 1, 1 ],
0, −1, 0, −1, 1, 1, 1, 0 ],
0, −1, 0, 0, 0, 0, 0, −1 ],
0, −1, 0, 0, 0, 1, 0, 0 ],
0, −1, 0, 0, 1, 0, 0, 0 ],
0, −1, 0, 0, 1, 1, 1, 1 ],
0, 0, −1, −1, 0, 1, 1, 0 ],
0, 0, −1, −1, 1, 1, 1, 1 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, −1, 0, 0, 1, 1, 0 ],
0, 0, −1, 0, 1, 1, 0, 0 ],
0, 0, −1, 1, 0, 0, 0, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, −1, 0, 1, 1, 1 ],
0, 0, 0, −1, 1, 1, 0, 1 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, 0, −1, −1, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 0, 1, 1, 0, 1 ],
0, 0, 0, 1, −1, −1, 0, 0 ],
0, 0, 0, 1, 0, −1, −1, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 0, −1, −1, −1, −1 ],
0, 0, 1, 0, −1, 0, 0, 0 ],
0, 0, 1, 0, 0, −1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 1, −1, −1, −1, 0 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, −1, −1, 0, −1 ],
0, 1, 0, 0, 0, −1, −1, −1 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 0, 1, −1, −2, −1, −1 ],
0, 1, 0, 1, −1, −1, 0, 0 ],
0, 1, 1, 0, −1, −1, −1, −1 ],
0, 1, 1, 0, 0, −1, −1, 0 ],
0, 1, 1, 1, −1, −2, −1, −1 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, −1, −1, −1, −1 ],
1, 0, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 1, −1, −1, −1, 0 ],
1, 0, 1, 0, −1, −2, −1, −1 ],
1, 0, 1, 0, −1, −1, 0, 0 ],
1, 0, 1, 1, −1, −2, −2, −1 ],
1, 0, 1, 1, −1, −1, −1, 0 ],
1, 1, 0, 0, −1, −1, −1, 0 ],
1, 1, 0, 1, −2, −2, −1, −1 ],
1, 1, 0, 1, −1, −2, −1, 0 ],
1, 1, 1, 0, −1, −2, −2, −1 ],
1, 1, 1, 0, −1, −1, −1, 0 ],
1, 1, 1, 1, −1, −2, −1, 0 ]





CI =








b I =
Cox




0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
−1
1
1
1
1
1
1
1
1
















bI =
C




















BI =



1
1
1
1
1
1
1
0
−2
−1
−1
−1
0
−1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
−1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
1
1
1
0
−1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
−1
−1
−1
−1
−1
−1
−1
−1
1











1
1
1
0
1
0
1
−1
2
2
1
1
1
0
0
−1
Number of sincere Tits roots of poset I sI = 28.
Table of roots of qbI
[ −3, 1, 1, 1, 1, 2, 1, 2 ],
[ −3, 1, 1, 2, 1, 2, 1, 3 ],
[ −3, 1, 2, 2, 1, 2, 1, 3 ],
[ −2, 1, 1, 1, 1, 2, 1, 2 ],
[ −2, 1, 1, 2, 1, 1, 1, 3 ],
[ 2,−1,−1,−2,−1,−1,−1,−3 ],
[ 2,−1,−1,−1,−1,−2,−1,−2 ],
[ 3,−1,−2,−2,−1,−2,−1,−3 ],
[ 3,−1,−1,−2,−1,−2,−1,−3 ],
[ 3,−1,−1,−1,−1,−2,−1,−2 ],
[ −2, 0, 1, 1, 1, 1, 0, 1 ],
[ −2, 0, 1, 1, 1, 2, 1, 2 ],
[ −2, 1, 0, 1, 1, 1, 0, 1 ],
[ −2, 1, 0, 1, 1, 2, 1, 2 ],
[ −2, 1, 1, 1, 0, 1, 1, 1 ],
[ −2, 1, 1, 1, 1, 1, 0, 1 ],
[ −2, 1, 1, 2, 0, 1, 1, 2 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 0, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 2 ],
[ −1, 0, 1, 0, 0, 1, 0, 1 ],
[ −1, 0, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 1, 0, 1 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 1, 2 ],
[ −1, 1, 0, 0, 0, 1, 0, 1 ],
[ −1, 1, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 1, 0, 1 ],
[ −1, 1, 0, 1, 1, 0, 0, 1 ],
[ −1, 1, 0, 1, 1, 1, 1, 2 ],
[ −1, 1, 1, 1, 0, 1, 0, 1 ],
[ −1, 1, 1, 1, 1, 1, 0, 2 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, −1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, −1, −1 ],
[ 0, 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ −3, 1, 1, 2, 1, 1, 1, 2 ],
[ −3, 1, 1, 2, 1, 2, 2, 3 ],
[ −3, 2, 1, 2, 1, 2, 1, 3 ],
[ −2, 1, 1, 1, 1, 2, 1, 3 ],
[ −2, 1, 1, 2, 1, 2, 1, 3 ],
[ 2,−1,−1,−2,−1,−1,−1,−2 ],
[ 2,−1,−1,−1,−1,−1,−1,−2 ],
[ 3,−1,−1,−2,−2,−2,−1,−3 ],
[ 3,−1,−1,−2,−1,−2,−1,−2 ],
[ −2, 0, 0, 1, 1, 1, 1, 1 ],
[ −2, 0, 1, 1, 1, 1, 1, 1 ],
[ −2, 0, 1, 2, 1, 1, 1, 2 ],
[ −2, 1, 0, 1, 1, 1, 1, 1 ],
[ −2, 1, 0, 2, 1, 1, 1, 2 ],
[ −2, 1, 1, 1, 0, 1, 1, 2 ],
[ −2, 1, 1, 1, 1, 1, 0, 2 ],
[ −2, 1, 1, 2, 1, 1, 0, 2 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 1, 1, 1 ],
[ −1, 0, 1, 1, 0, 0, 0, 1 ],
[ −1, 0, 1, 1, 0, 1, 1, 1 ],
[ −1, 0, 1, 1, 1, 1, 0, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 1, 1, 1 ],
[ −1, 1, 0, 1, 0, 0, 0, 1 ],
[ −1, 1, 0, 1, 0, 1, 1, 1 ],
[ −1, 1, 0, 1, 1, 1, 0, 1 ],
[ −1, 1, 1, 0, 0, 1, 0, 1 ],
[ −1, 1, 1, 1, 0, 1, 0, 2 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
178
[ −3, 1, 1, 2, 1, 2, 1, 2 ],
[ −3, 1, 1, 2, 2, 2, 1, 3 ],
[ −2, 1, 1, 1, 1, 1, 1, 2 ],
[ −2, 1, 1, 2, 1, 1, 1, 2 ],
[ 2,−1,−1,−2,−1,−2,−1,−3 ],
[ 2,−1,−1,−1,−1,−2,−1,−3 ],
[ 3,−2,−1,−2,−1,−2,−1,−3 ],
[ 3,−1,−1,−2,−1,−2,−2,−3 ],
[ 3,−1,−1,−2,−1,−1,−1,−2 ],
[ −2, 0, 1, 1, 0, 1, 1, 1 ],
[ −2, 0, 1, 1, 1, 1, 1, 2 ],
[ −2, 1, 0, 1, 0, 1, 1, 1 ],
[ −2, 1, 0, 1, 1, 1, 1, 2 ],
[ −2, 1, 1, 1, 0, 1, 0, 1 ],
[ −2, 1, 1, 1, 0, 2, 1, 2 ],
[ −2, 1, 1, 1, 1, 2, 0, 2 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 1, 0, 0, 1, 1 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 1, 0, 0, 1, 1 ],
[ −1, 0, 1, 1, 0, 1, 1, 2 ],
[ −1, 0, 1, 1, 1, 1, 0, 2 ],
[ −1, 1, 0, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 0, 1, 1, 0, 1 ],
[ −1, 1, 0, 1, 0, 0, 1, 1 ],
[ −1, 1, 0, 1, 0, 1, 1, 2 ],
[ −1, 1, 0, 1, 1, 1, 0, 2 ],
[ −1, 1, 1, 1, 0, 0, 0, 1 ],
[ −1, 1, 1, 1, 0, 1, 1, 2 ],
[ 0, −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 1, 1 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 0, 1, 0, 0, 1, 0, 1 ],
0, 1, 0, 0, −1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
1, −1, −1, −1, −1, −1, 0, −2 ],
1, −1, −1, −1, 0, −1, 0, −1 ],
1, −1, 0, −1, −1, −1, −1, −2 ],
1, −1, 0, −1, −1, 0, 0, −1 ],
1, −1, 0, −1, 0, −1, 0, −1 ],
1, −1, 0, −1, 0, 0, 0, 0 ],
1, −1, 0, 0, 0, −1, 0, −1 ],
1, 0, −1, −1, −1, −1, −1, −2 ],
1, 0, −1, −1, −1, 0, 0, −1 ],
1, 0, −1, −1, 0, −1, 0, −1 ],
1, 0, −1, −1, 0, 0, 0, 0 ],
1, 0, −1, 0, 0, −1, 0, −1 ],
1, 0, 0, −1, −1, −1, −1, −2 ],
1, 0, 0, −1, −1, 0, −1, −1 ],
1, 0, 0, −1, 0, −1, −1, −1 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, −1, −1, 0, 0 ],
1, 0, 0, 0, 0, −1, −1, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
2, −1, −1, −2, 0, −1, −1, −2 ],
2, −1, −1, −1, −1, −1, 0, −1 ],
2, −1, −1, −1, 0, −1, −1, −1 ],
2, −1, 0, −1, −1, −2, −1, −2 ],
2, −1, 0, −1, −1, −1, 0, −1 ],
2, 0, −1, −1, −1, −2, −1, −2 ],
2, 0, −1, −1, −1, −1, 0, −1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 1, 1 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 0, 1, 1, 0, 0, 1 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 0, 0, 0, 1, 0, 1 ],
1, −1, −1, −1, 0, −1, −1, −2 ],
1, −1, −1, −1, 0, 0, 0, −1 ],
1, −1, 0, −1, −1, −1, 0, −2 ],
1, −1, 0, −1, 0, −1, −1, −2 ],
1, −1, 0, −1, 0, 0, −1, −1 ],
1, −1, 0, 0, −1, −1, 0, −1 ],
1, −1, 0, 0, 0, −1, 0, 0 ],
1, 0, −1, −1, −1, −1, 0, −2 ],
1, 0, −1, −1, 0, −1, −1, −2 ],
1, 0, −1, −1, 0, 0, −1, −1 ],
1, 0, −1, 0, −1, −1, 0, −1 ],
1, 0, −1, 0, 0, −1, 0, 0 ],
1, 0, 0, −1, −1, −1, −1, −1 ],
1, 0, 0, −1, −1, 0, 0, −1 ],
1, 0, 0, −1, 0, 0, −1, −1 ],
1, 0, 0, 0, −1, −1, −1, −1 ],
1, 0, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
2, −1, −1, −1, −1, −2, 0, −2 ],
2, −1, −1, −1, 0, −2, −1, −2 ],
2, −1, −1, −1, 0, −1, 0, −1 ],
2, −1, 0, −1, −1, −1, −1, −2 ],
2, −1, 0, −1, 0, −1, −1, −1 ],
2, 0, −1, −1, −1, −1, −1, −2 ],
2, 0, −1, −1, 0, −1, −1, −1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 0, 1, 1, 0, 1 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, −1, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
1, −1, −1, −1, 0, −1, 0, −2 ],
1, −1, −1, 0, 0, −1, 0, −1 ],
1, −1, 0, −1, −1, −1, 0, −1 ],
1, −1, 0, −1, 0, −1, −1, −1 ],
1, −1, 0, −1, 0, 0, 0, −1 ],
1, −1, 0, 0, 0, −1, −1, −1 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, −1, −1, −1, −1, 0, −1 ],
1, 0, −1, −1, 0, −1, −1, −1 ],
1, 0, −1, −1, 0, 0, 0, −1 ],
1, 0, −1, 0, 0, −1, −1, −1 ],
1, 0, −1, 0, 0, 0, 0, 0 ],
1, 0, 0, −1, −1, −1, 0, −1 ],
1, 0, 0, −1, −1, 0, 0, 0 ],
1, 0, 0, −1, 0, 0, −1, 0 ],
1, 0, 0, 0, −1, −1, 0, −1 ],
1, 0, 0, 0, 0, −1, −1, −1 ],
1, 0, 0, 0, 0, 0, −1, 0 ],
2, −1, −1, −2, −1, −1, 0, −2 ],
2, −1, −1, −1, −1, −1, 0, −2 ],
2, −1, −1, −1, 0, −1, −1, −2 ],
2, −1, 0, −2, −1, −1, −1, −2 ],
2, −1, 0, −1, −1, −1, −1, −1 ],
2, 0, −1, −2, −1, −1, −1, −2 ],
2, 0, −1, −1, −1, −1, −1, −1 ],
2, 0, 0, −1, −1, −1, −1, −1 ]
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
∗
6
7
5
• I ≡ P94 :
4
3
2
1





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
















bI =
C




179
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
−1











−1
 −1

 −1

BI = −10

 0
 0
0

−1
−1
−1
0
0
−1
0
1
1
1
1
1
0
1
0
−1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
2
1
1
1
0
−1
1
1
1
1
1
0
1
−1
1
2
1
1
1
1
0
−1
Number of sincere Tits roots of poset I sI = 28.
Table of roots of qbI
[ −2,−2, 1, 1, 1, 2, 1, 1 ],
[ −2,−2, 1, 1, 1, 3, 2, 2 ],
[ −2,−2, 2, 1, 1, 3, 1, 2 ],
[ −2,−1, 1, 1, 1, 3, 1, 2 ],
[ −1,−2, 1, 1, 1, 3, 1, 2 ],
[ 1, 2,−1,−1,−1,−3,−1,−2 ],
[ 2, 1,−1,−1,−1,−3,−1,−2 ],
[ 2, 2,−2,−1,−1,−3,−1,−2 ],
[ 2, 2,−1,−1,−1,−3,−2,−2 ],
[ 2, 2,−1,−1,−1,−2,−1,−1 ],
[ −2, −1, 1, 1, 0, 2, 1, 1 ],
[ −1, −2, 1, 0, 1, 2, 1, 1 ],
[ −1, −1, 0, 0, 0, 1, 1, 0 ],
[ −1, −1, 0, 0, 1, 1, 1, 1 ],
[ −1, −1, 0, 1, 0, 1, 1, 0 ],
[ −1, −1, 0, 1, 1, 1, 0, 0 ],
[ −1, −1, 0, 1, 1, 2, 0, 1 ],
[ −1, −1, 1, 0, 0, 1, 0, 0 ],
[ −1, −1, 1, 0, 0, 2, 1, 1 ],
[ −1, −1, 1, 0, 1, 1, 1, 1 ],
[ −1, −1, 1, 0, 1, 2, 1, 2 ],
[ −1, −1, 1, 1, 0, 1, 1, 1 ],
[ −1, −1, 1, 1, 0, 2, 1, 2 ],
[ −1, −1, 1, 1, 1, 2, 0, 2 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 1, 0, 0, 1, 0, 1 ],
[ −1, 0, 1, 1, 0, 1, 0, 1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 1, 1, 0 ],
[ 0, −1, 0, 0, 1, 1, 0, 0 ],
[ 0, −1, 0, 1, 0, 0, 0, 0 ],
[ 0, −1, 0, 1, 0, 1, 1, 1 ],
[ 0, −1, 1, 0, 0, 1, 0, 0 ],
[ 0, −1, 1, 0, 1, 1, 0, 1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, −1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, −1, 0, −1, −1, 0, −1 ],
[ 0, 1, −1, 0, 0, −1, 0, 0 ],
[ 0, 1, 0, −1, 0, −1, −1, −1 ],
[ −2,−2, 1, 1, 1, 3, 1, 1 ],
[ −2,−2, 1, 1, 2, 3, 1, 2 ],
[ −2,−1, 1, 1, 1, 2, 1, 1 ],
[ −1,−2, 1, 1, 1, 2, 1, 1 ],
[ −1,−1, 1, 1, 1, 2, 1, 2 ],
[ 1, 2,−1,−1,−1,−2,−1,−2 ],
[ 2, 1,−1,−1,−1,−2,−1,−2 ],
[ 2, 2,−1,−2,−1,−3,−1,−2 ],
[ 2, 2,−1,−1,−1,−3,−1,−2 ],
[ −2, −1, 0, 1, 1, 2, 1, 1 ],
[ −2, −1, 1, 1, 1, 2, 0, 1 ],
[ −1, −2, 1, 1, 0, 2, 1, 1 ],
[ −1, −1, 0, 0, 1, 1, 0, 0 ],
[ −1, −1, 0, 0, 1, 2, 1, 1 ],
[ −1, −1, 0, 1, 0, 1, 1, 1 ],
[ −1, −1, 0, 1, 1, 1, 0, 1 ],
[ −1, −1, 0, 1, 1, 2, 1, 1 ],
[ −1, −1, 1, 0, 0, 1, 1, 0 ],
[ −1, −1, 1, 0, 1, 1, 0, 0 ],
[ −1, −1, 1, 0, 1, 2, 0, 1 ],
[ −1, −1, 1, 1, 0, 1, 0, 0 ],
[ −1, −1, 1, 1, 0, 2, 0, 1 ],
[ −1, −1, 1, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 1, 0, 1, 0, 1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 1, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 1, 1, 1 ],
[ 0, −1, 0, 0, 1, 1, 0, 1 ],
[ 0, −1, 0, 1, 0, 1, 0, 0 ],
[ 0, −1, 0, 1, 1, 1, 0, 1 ],
[ 0, −1, 1, 0, 0, 1, 0, 1 ],
[ 0, −1, 1, 1, 0, 1, 0, 1 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, −1, 0, 0, −1, −1, −1 ],
[ 0, 1, −1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, −1, 0, −1, 0, −1 ],
180
[ −2,−2, 1, 1, 1, 3, 1, 2 ],
[ −2,−2, 1, 2, 1, 3, 1, 2 ],
[ −2,−1, 1, 1, 1, 2, 1, 2 ],
[ −1,−2, 1, 1, 1, 2, 1, 2 ],
[ 1, 1,−1,−1,−1,−2,−1,−2 ],
[ 1, 2,−1,−1,−1,−2,−1,−1 ],
[ 2, 1,−1,−1,−1,−2,−1,−1 ],
[ 2, 2,−1,−1,−2,−3,−1,−2 ],
[ 2, 2,−1,−1,−1,−3,−1,−1 ],
[ −2, −1, 1, 0, 1, 2, 1, 1 ],
[ −1, −2, 0, 1, 1, 2, 1, 1 ],
[ −1, −2, 1, 1, 1, 2, 0, 1 ],
[ −1, −1, 0, 0, 1, 1, 1, 0 ],
[ −1, −1, 0, 1, 0, 1, 0, 0 ],
[ −1, −1, 0, 1, 0, 2, 1, 1 ],
[ −1, −1, 0, 1, 1, 1, 1, 1 ],
[ −1, −1, 0, 1, 1, 2, 1, 2 ],
[ −1, −1, 1, 0, 0, 1, 1, 1 ],
[ −1, −1, 1, 0, 1, 1, 0, 1 ],
[ −1, −1, 1, 0, 1, 2, 1, 1 ],
[ −1, −1, 1, 1, 0, 1, 0, 1 ],
[ −1, −1, 1, 1, 0, 2, 1, 1 ],
[ −1, −1, 1, 1, 1, 2, 0, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 1, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 1, 1, 0, 1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 1, 1 ],
[ 0, −1, 0, 1, 0, 1, 0, 1 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, 0, 0, 1, 1, 1 ],
[ 0, 0, −1, 0, 0, −1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, −1, −1, 0, −1, 0, −1 ],
[ 0, 1, −1, 0, 0, −1, 0, −1 ],
[ 0, 1, 0, −1, −1, −1, 0, −1 ],
[ 0, 1, 0, −1, 0, −1, 0, 0 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
1, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, −1, −1, 0, 0 ],
1, 0, 0, 0, −1, −1, 0 ],
1, 0, 0, 0, 0, 0, 0 ],
0, −1, −1, 0, −1, 0, −1 ],
0, −1, 0, 0, −1, 0, −1 ],
0, 0, −1, −1, −1, 0, −1 ],
0, 0, −1, 0, −1, 0, 0 ],
0, 0, 0, −1, −1, 0, −1 ],
0, 0, 0, 0, −1, −1, −1 ],
0, 0, 0, 0, 0, −1, 0 ],
1, −1, −1, −1, −2, 0, −2 ],
1, −1, −1, 0, −2, −1, −2 ],
1, −1, −1, 0, −1, −1, −1 ],
1, −1, 0, −1, −2, −1, −2 ],
1, −1, 0, −1, −1, −1, −1 ],
1, −1, 0, 0, −2, −1, −1 ],
1, −1, 0, 0, −1, 0, 0 ],
1, 0, −1, −1, −2, 0, −1 ],
1, 0, −1, −1, −1, 0, 0 ],
1, 0, −1, 0, −1, −1, 0 ],
1, 0, 0, −1, −1, −1, −1 ],
1, 0, 0, 0, −1, −1, 0 ],
2, −1, 0, −1, −2, −1, −1 ],
1, −1, −1, 0, −2, −1, −1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
1, 0, 0, −1, −1, −1, −1 ],
1, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 1 ],
0, −1, 0, −1, −1, 0, −1 ],
0, −1, 0, 0, −1, 0, 0 ],
0, 0, −1, 0, −1, −1, −1 ],
0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, −1, −1, 0, 0 ],
0, 0, 0, 0, −1, −1, 0 ],
0, 0, 0, 0, 0, 0, 0 ],
1, −1, −1, −1, −2, 0, −1 ],
1, −1, −1, 0, −2, −1, −1 ],
1, −1, −1, 0, −1, 0, −1 ],
1, −1, 0, −1, −2, −1, −1 ],
1, −1, 0, −1, −1, 0, −1 ],
1, −1, 0, 0, −1, −1, −1 ],
1, 0, −1, −1, −2, −1, −2 ],
1, 0, −1, −1, −1, −1, −1 ],
1, 0, −1, 0, −2, −1, −1 ],
1, 0, −1, 0, −1, 0, 0 ],
1, 0, 0, −1, −1, −1, 0 ],
2, −1, −1, −1, −2, 0, −1 ],
2, 0, −1, −1, −2, −1, −1 ],
1, −1, 0, −1, −2, −1, −1 ],
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 1, 0, 0, −1, −1, 0, −1 ],
0, 1, 0, 0, 0, −1, −1, −1 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, −1, 0, 0, −1, −1, −1 ],
1, 0, −1, 0, 0, 0, 0, 0 ],
1, 0, 0, −1, 0, −1, 0, −1 ],
1, 0, 0, 0, −1, −1, −1, −1 ],
1, 0, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 1, −1, −1, −1, −1, 0, −1 ],
1, 1, −1, −1, 0, −2, 0, −1 ],
1, 1, −1, −1, 0, −1, 0, 0 ],
1, 1, −1, 0, −1, −2, 0, −1 ],
1, 1, −1, 0, −1, −1, 0, 0 ],
1, 1, −1, 0, 0, −1, −1, 0 ],
1, 1, 0, −1, −1, −2, −1, −1 ],
1, 1, 0, −1, −1, −1, 0, −1 ],
1, 1, 0, −1, 0, −1, −1, −1 ],
1, 1, 0, 0, −1, −2, −1, −1 ],
1, 1, 0, 0, −1, −1, 0, 0 ],
1, 2, −1, −1, 0, −2, −1, −1 ],
2, 1, −1, −1, −1, −2, 0, −1 ],
2, 1, 0, −1, −1, −2, −1, −1 ]
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
∗
• I ≡ P95 :
6
5
7
3
2
4
1





CI =








b I =
Cox




0
1
0
1
0
0
1
−1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
−1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
−1
1
1
0
0
1
0
0
0
0
0
0
−1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
−1
0
−1
0
0
−1
0
1
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
1
0
1
0
1
1
0
0
















BI =



0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
−1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
−1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
0
1
0
0
0
−1
1
0
1
0
0
1
0
−1











0
0
−1
0
0
0
0
0
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,
[ −1, −2,
[ −1, −1,
[ −1, −1,
[ −1, −1,
1, 1,
0,−1,
0,−1,
0,−1,
0,−1,
2,
1,
0,
1,
1,
1,
0,
0,
0,
1,
1, 2 ],
1,−1 ],
0,−2 ],
0,−1 ],
1, 0 ],
[ 1, 1,−1,−1,−2,−1,−1,−2 ],
[ −1,−1, −1, −1, 0, 0, 0, −2 ],
[ −1,−1, 0, −1, 0, 0, 0, −1 ],
[ −1,−1, 0, −1, 1, 0, 1, −1 ],
[ −1,−1, 0, 0, 0, 0, 0, −1 ],
181
[ −2,−1,
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1,−1,
1, 0,
0,−1,
0,−1,
0,−1,
0, 0,
2, 1,
0,−1,
0, 0,
1, 0,
1, 0,
1, 1 ],
0,−2 ],
1,−1 ],
1, 0 ],
0,−1 ],
1
1
1
0
0
0
0
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, −1, 0, 0, 1, 0, 0, 0 ],
−1, −1, 0, 0, 1, 1, 1, 0 ],
−1, −1, 1,−1, 1, 0, 1, 0 ],
−1, −1, 1, 0, 1, 0, 1, 1 ],
−1, −1, 1, 0, 2, 1, 1, 1 ],
−1, 0, 0,−1, 0, 0, 0,−1 ],
−1, 0, 0, 0, 0, 0, 0, 0 ],
−1, 0, 0, 0, 1, 1, 0, 0 ],
−1, 0, 0, 1, 1, 1, 0, 1 ],
−1, 0, 1, 0, 1, 0, 0, 1 ],
−1, 0, 1, 0, 1, 1, 1, 1 ],
−1, 0, 1, 1, 1, 0, 0, 1 ],
−1, 0, 1, 1, 1, 1, 1, 2 ],
−1, 0, 1, 1, 2, 1, 1, 3 ],
−1, 1, 1, 1, 1, 1, 0, 2 ],
0, −1,−1,−1,−1,−1, 0,−3 ],
0, −1,−1,−1, 0,−1, 0,−2 ],
0, −1,−1,−1, 0, 0, 1,−1 ],
0, −1, 0,−1, 0,−1, 0,−2 ],
0, −1, 0,−1, 0, 0, 0,−1 ],
0, −1, 0,−1, 1, 0, 1, 0 ],
0, −1, 0, 0, 0, 0, 0, 0 ],
0, −1, 0, 0, 1, 0, 1, 0 ],
0, −1, 1, 0, 1, 0, 1, 1 ],
0, 0,−1,−1,−1,−1,−1,−2 ],
0, 0,−1,−1,−1, 0, 0,−2 ],
0, 0,−1, 0,−1,−1,−1,−2 ],
0, 0,−1, 0,−1, 0, 0,−1 ],
0, 0,−1, 0, 0, 0, 0, 0 ],
0, 0, 0,−1,−1,−1, 0,−2 ],
0, 0, 0,−1, 0,−1, 0,−1 ],
0, 0, 0,−1, 0, 0, 1, 0 ],
0, 0, 0, 0,−1,−1, 0,−1 ],
0, 0, 0, 0,−1, 0, 0, 0 ],
0, 0, 0, 0, 0,−1, 0, 0 ],
0, 0, 0, 0, 0, 0, 0,−1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 1, 1 ],
0, 0, 0, 0, 1, 0, 1, 1 ],
0, 0, 0, 0, 1, 1, 1, 2 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 1, 1, 0, 1 ],
0, 0, 1, 0, 0,−1, 0, 0 ],
0, 0, 1, 0, 0, 0, 1, 1 ],
0, 0, 1, 0, 1, 0, 1, 2 ],
0, 0, 1, 1, 1, 0, 0, 1 ],
0, 0, 1, 1, 1, 1, 0, 2 ],
0, 0, 1, 1, 2, 1, 1, 3 ],
0, 1, 0, 0,−1, 0,−1,−1 ],
0, 1, 0, 0, 0, 0,−1, 0 ],
0, 1, 0, 0, 0, 1, 0, 1 ],
0, 1, 0, 1, 0, 0,−1, 1 ],
0, 1, 0, 1, 0, 1, 0, 1 ],
0, 1, 1, 0, 0, 0, 0, 1 ],
0, 1, 1, 1, 0, 0, 0, 2 ],
0, 1, 1, 1, 1, 1, 0, 2 ],
0, 1, 1, 2, 1, 1, 0, 3 ],
1, 0,−1,−1,−2,−2,−1,−3 ],
1, 0,−1,−1,−2,−1, 0,−2 ],
1, 0,−1,−1,−1,−1, 0,−1 ],
1, 0,−1, 0,−1,−1,−1,−2 ],
1, 0,−1, 0,−1, 0,−1,−1 ],
1, 0,−1, 0, 0, 0, 0, 0 ],
1, 0, 0, 0,−1,−1, 0,−1 ],
1, 0, 0, 0, 0,−1, 0, 0 ],
1, 0, 0, 0, 0, 0, 1, 1 ],
1, 1,−1, 0,−2,−1,−1,−2 ],
1, 1,−1, 0,−1,−1,−1,−1 ],
1, 1,−1, 0,−1, 0, 0, 0 ],
1, 1, 0, 0,−1,−1,−1,−1 ],
1, 1, 0, 0,−1, 0,−1, 0 ],
1, 1, 0, 0, 0, 0, 0, 1 ],
[ −1,−1, 0, 0, 1, 0, 1, 0 ],
[ −1,−1, 0, 0, 1, 1, 1, 1 ],
[ −1,−1, 1, 0, 1, 0, 0, 0 ],
[ −1,−1, 1, 0, 1, 1, 1, 1 ],
[ −1,−1, 1, 0, 2, 1, 1, 2 ],
[ −1, 0, 0, 0, 0, 0, −1, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 1, 1 ],
[ −1, 0, 1, 0, 1, 1, 1, 2 ],
[ −1, 0, 1, 1, 1, 1, 0, 1 ],
[ −1, 0, 1, 1, 2, 1, 0, 2 ],
[ −1, 0, 1, 1, 2, 2, 1, 3 ],
[ 0,−1, −1, −2, −1, −1, 0, −3 ],
[ 0,−1, −1, −1, −1, −1, 0, −2 ],
[ 0,−1, −1, −1, 0, 0, 0, −2 ],
[ 0,−1, −1, 0, 0, 0, 0, −1 ],
[ 0,−1, 0, −1, 0, −1, 0, −1 ],
[ 0,−1, 0, −1, 0, 0, 1, −1 ],
[ 0,−1, 0, 0, 0, −1, 0, −1 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, −1, −1, −2, −1, −1, −3 ],
[ 0, 0, −1, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 0, −1, −2 ],
[ 0, 0, −1, 0, 0, 0, −1, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, −1, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1, −2 ],
[ 0, 0, 0, 0, −1, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 1, 1, 2 ],
[ 0, 0, 1, 1, 1, 0, 0, 2 ],
[ 0, 0, 1, 1, 1, 1, 1, 2 ],
[ 0, 1, −1, 0, −1, 0, −1, −1 ],
[ 0, 1, 0, 0, −1, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, −1, 0, −1, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 1, 0, 2 ],
[ 0, 1, 1, 1, 0, 0, −1, 1 ],
[ 0, 1, 1, 1, 0, 1, 0, 2 ],
[ 0, 1, 1, 1, 1, 1, 0, 3 ],
[ 1,−1, −1, −1, −1, −1, 0, −2 ],
[ 1, 0, −1, −1, −2, −1, −1, −3 ],
[ 1, 0, −1, −1, −1, −1, −1, −2 ],
[ 1, 0, −1, −1, −1, 0, 0, −1 ],
[ 1, 0, −1, 0, −1, −1, −1, −1 ],
[ 1, 0, −1, 0, −1, 0, 0, −1 ],
[ 1, 0, 0, −1, −1, −1, 0, −1 ],
[ 1, 0, 0, 0, −1, −1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, 0, 1 ],
[ 1, 1, −1, 0, −2, −1, −1, −1 ],
[ 1, 1, −1, 0, −1, 0, −1, −1 ],
[ 1, 1, −1, 1, −1, 0, −1, 0 ],
[ 1, 1, 0, 0, −1, −1, −1, 0 ],
[ 1, 1, 0, 0, −1, 0, 0, 0 ],
[ 1, 1, 0, 1, −1, −1, −1, 0 ],
182
[ −1,−1, 0, 0, 1, 1, 0, 0 ],
[ −1,−1, 0, 0, 2, 1, 1, 1 ],
[ −1,−1, 1, 0, 1, 0, 1, 0 ],
[ −1,−1, 1, 0, 2, 0, 1, 1 ],
[ −1,−1, 1, 0, 2, 1, 2, 2 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 0, 2, 1, 1, 2 ],
[ −1, 0, 1, 1, 1, 1, 0, 2 ],
[ −1, 0, 1, 1, 2, 1, 1, 2 ],
[ −1, 0, 2, 1, 2, 1, 1, 3 ],
[ 0,−1,−1,−1,−1,−1,−1,−3 ],
[ 0,−1,−1,−1,−1, 0, 0,−2 ],
[ 0,−1,−1,−1, 0, 0, 0,−1 ],
[ 0,−1, 0,−1,−1,−1, 0,−2 ],
[ 0,−1, 0,−1, 0,−1, 1,−1 ],
[ 0,−1, 0,−1, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 1, 1 ],
[ 0, 0,−1,−1,−1,−1,−1,−3 ],
[ 0, 0,−1,−1,−1, 0,−1,−2 ],
[ 0, 0,−1,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0, 0,−1,−1,−1,−1,−2 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1,−1,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 1, 2 ],
[ 0, 0, 1, 1, 1, 1, 1, 3 ],
[ 0, 1, 0, 0,−1,−1,−1,−1 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0, 1, 0, 1,−1, 1 ],
[ 0, 1, 0, 1, 1, 1, 0, 2 ],
[ 0, 1, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 1, 0, 0, 2 ],
[ 0, 1, 1, 1, 1, 1, 1, 3 ],
[ 1, 0,−2,−1,−2,−1,−1,−3 ],
[ 1, 0,−1,−1,−2,−1,−1,−2 ],
[ 1, 0,−1,−1,−1,−1, 0,−2 ],
[ 1, 0,−1, 0,−2,−1,−1,−2 ],
[ 1, 0,−1, 0,−1,−1, 0,−1 ],
[ 1, 0,−1, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0,−1,−1,−1,−1 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 1,−1, 0,−2,−1,−2,−2 ],
[ 1, 1,−1, 0,−2, 0,−1,−1 ],
[ 1, 1,−1, 0,−1, 0,−1, 0 ],
[ 1, 1, 0, 0,−2,−1,−1,−1 ],
[ 1, 1, 0, 0,−1,−1, 0, 0 ],
[ 1, 1, 0, 0,−1, 0, 0, 1 ],
[ 1, 1, 0, 1,−1, 0,−1, 0 ],
[
[
[
1,
1,
1,
1, 0, 1,−1, 0,−1, 1 ],
1, 0, 1, 0, 0, 0, 1 ],
1, 1, 1, 0, 0, 0, 2 ],
[
[
[
1, 1,
1, 1,
1, 2,
1, −1,
1, 0,
1, −1,
0,
0,
0,
0, 0,
0, 0,
0, −1,
1 ],
2 ],
1 ],
[
[
[
1, 1, 0, 1, 0, 0,−1, 1 ],
1, 1, 0, 1, 0, 1, 0, 2 ],
2, 1,−1, 0,−2,−1,−1,−1 ]
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
∗
• I ≡ P96 :
2
4
7
1
3
6
5




CI =



1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
−1
1
1
0
0
1
1
0
−1






b I =
Cox




1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
−1
−1
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
−1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
−1
−1
0
0
−1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1

0
 0

 0

BI = 00

 0
 −1
0










1
1
0
0
0
0
0
−1

0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
−1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
−1
−1
−1
−1
−1
−1
−1
−1
1











0
0
0
−1
0
0
0
0
−1
0
0
0
0
0
0
0
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−2, 1,−1,−1, 1,−2 ],
[ −1, −1, −2, 0, −2, −1, 1, −3 ],
[ −1, −1, −2, 0, −1, −1, 1, −3 ],
[ −1, −1, −1, 0, −1, −1, 0, −3 ],
[ −1, −1, −1, 0, −1, 0, 0, −2 ],
[ −1, 0, −2, 1, −1, −1, 1, −2 ],
[ −1, 0, −2, 1, −1, 0, 1, −1 ],
[ −1, 0, −1, 0, −1, −1, 1, −2 ],
[ −1, 0, −1, 0, −1, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, −1, 0, −1 ],
[ −1, 0, −1, 1, −1, −1, 1, −1 ],
[ −1, 0, −1, 1, −1, 0, 1, 0 ],
[ −1, 0, −1, 1, 0, −1, 1, 0 ],
[ −1, 0, −1, 1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0,−1, −1 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, −1, 1, 0, 0, 0, 0 ],
[ −1, 1, −1, 2, 0, 0, 1, 1 ],
[ −1, 1, 0, 1, 0, 0, 0, 1 ],
[ −1, 1, 0, 1, 1, 0, 0, 1 ],
[ 0, −1, −1,−1, −1, −1, 0, −3 ],
[ 0, −1, −1,−1, −1, 0, 0, −2 ],
[ 0, −1, −1, 0, −1, −1, 1, −2 ],
[ 0, −1, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, −1, 0, 0, −1, 0, −1 ],
[ 0, −1, 0,−1, −1, −1, 0, −2 ],
[ 0, −1, 0,−1, −1, 0, 0, −1 ],
[ 1, 1, 2,−1, 1, 1,−1, 2 ],
[ −1,−1,−2, 0,−1,−2, 1,−3 ],
[ −1,−1,−2, 0,−1,−1, 1,−2 ],
[ −1,−1,−1, 0,−1,−1, 0,−2 ],
[ −1,−1,−1, 0, 0,−1, 0,−2 ],
[ −1, 0,−2, 1,−1,−1, 1,−1 ],
[ −1, 0,−2, 1, 0,−1, 1,−1 ],
[ −1, 0,−1, 0,−1,−1, 1,−1 ],
[ −1, 0,−1, 0,−1, 0, 1,−1 ],
[ −1, 0,−1, 0, 0,−1, 1,−1 ],
[ −1, 0,−1, 1,−1, 0, 0,−1 ],
[ −1, 0,−1, 1, 0,−1, 0,−1 ],
[ −1, 0,−1, 1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 1,−1, 1,−1, 0, 1, 0 ],
[ −1, 1,−1, 1, 0, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 1, 1 ],
[ 0,−2,−1, −1,−1,−1, 0,−3 ],
[ 0,−1,−1, −1,−1,−1, 0,−2 ],
[ 0,−1,−1, −1, 0,−1, 0,−2 ],
[ 0,−1,−1, 0,−1,−1, 1,−1 ],
[ 0,−1,−1, 0,−1, 0, 1,−1 ],
[ 0,−1,−1, 0, 0,−1, 1,−1 ],
[ 0,−1, 0, −1,−1, 0, −1,−2 ],
[ 0,−1, 0, −1, 0,−1, −1,−2 ],
183
[ −2, 0,−2, 1,−1,−1,
[ −1,−1,−2, 0,−1,−1,
[ −1,−1,−1,−1,−1,−1,
[ −1,−1,−1, 0,−1,−1,
[ −1, 0,−2, 0,−1,−1,
[ −1, 0,−2, 1,−1,−1,
[ −1, 0,−1, 0,−1,−1,
[ −1, 0,−1, 0,−1, 0,
[ −1, 0,−1, 0, 0,−1,
[ −1, 0,−1, 0, 0, 0,
[ −1, 0,−1, 1,−1, 0,
[ −1, 0,−1, 1, 0,−1,
[ −1, 0,−1, 1, 0, 0,
[ −1, 0, 0, 0, 0,−1,
[ −1, 0, 0, 0, 0, 0,
[ −1, 1,−1, 1, 0,−1,
[ −1, 1,−1, 1, 0, 0,
[ −1, 1, 0, 1, 0, 0,
[ −1, 1, 0, 1, 0, 1,
[ 0,−1,−2, 0,−1,−1,
[ 0,−1,−1,−1,−1,−1,
[ 0,−1,−1, 0,−1,−1,
[ 0,−1,−1, 0,−1, 0,
[ 0,−1,−1, 0, 0,−1,
[ 0,−1,−1, 0, 0, 0,
[ 0,−1, 0,−1,−1, 0,
[ 0,−1, 0,−1, 0,−1,
1,−2 ],
0,−3 ],
0,−3 ],
1,−2 ],
1,−2 ],
2,−1 ],
0,−2 ],
0,−2 ],
0,−2 ],
0,−1 ],
1,−1 ],
1,−1 ],
0, 0 ],
0,−1 ],
0, 0 ],
1, 0 ],
1, 1 ],
0, 0 ],
0, 1 ],
1,−2 ],
1,−2 ],
0,−2 ],
0,−2 ],
0,−2 ],
0,−1 ],
0,−2 ],
0,−2 ],
1
0
0
0
0
0
−1
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 0,−1, 0, −1, 0, −1 ],
0, −1, 0,−1, 0, 0, 0, −1 ],
0, −1, 0, 0, 0, 0,−1, −1 ],
0, −1, 1,−1, 0, 0,−1, −1 ],
0, 0, −1, 0, −1, 0, 1, −1 ],
0, 0, −1, 0, 0, −1, 1, −1 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, −1, 1, 0, −1, 1, 0 ],
0, 0, −1, 1, 0, 0, 1, 1 ],
0, 0, 0,−1, 0, 0,−1, −1 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, −1, 1, 0, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 1, 0, 0, 1 ],
0, 0, 1,−1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0,−1, 0 ],
0, 0, 1, 0, 0, 1,−1, 0 ],
0, 0, 1, 0, 1, 0,−1, 0 ],
0, 0, 1, 0, 1, 1,−1, 1 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
0, 1, 0, 1, 0, 0, 1, 2 ],
0, 1, 0, 1, 0, 1, 1, 2 ],
0, 1, 0, 1, 1, 0, 1, 2 ],
0, 1, 1, 0, 0, 1,−1, 1 ],
0, 1, 1, 0, 1, 0,−1, 1 ],
0, 1, 1, 0, 1, 1,−1, 1 ],
0, 1, 1, 1, 0, 1, 0, 2 ],
0, 1, 1, 1, 1, 1, 0, 2 ],
0, 2, 1, 1, 1, 1, 0, 3 ],
1, −1, 0,−1, 0, 0,−1, −1 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, −1, 1,−1, 0, 0,−1, 0 ],
1, −1, 1,−1, 1, 0,−1, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 0, 1, 0, 0, 1 ],
1, 0, 1,−1, 0, 0, 0, 1 ],
1, 0, 1,−1, 0, 1, 0, 1 ],
1, 0, 1,−1, 1, 0, 0, 1 ],
1, 0, 1, 0, 0, 1,−1, 1 ],
1, 0, 1, 0, 1, 0,−1, 1 ],
1, 0, 1, 0, 1, 1,−1, 1 ],
1, 0, 2,−1, 0, 1,−1, 1 ],
1, 0, 2,−1, 1, 1,−1, 1 ],
1, 1, 1, 0, 0, 1, 0, 2 ],
1, 1, 1, 0, 1, 1, 0, 2 ],
1, 1, 2, 0, 1, 1,−1, 2 ],
1, 1, 2, 0, 1, 2,−1, 3 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,−1, 0, −1, 0, 0, −1,−2 ],
0,−1, 0, 0,−1, 0, 0,−1 ],
0,−1, 0, 0, 0, 0, 0,−1 ],
0, 0,−1, 0,−1,−1, 1,−1 ],
0, 0,−1, 0,−1, 0, 1, 0 ],
0, 0,−1, 0, 0,−1, 1, 0 ],
0, 0,−1, 0, 0, 0, 1, 0 ],
0, 0,−1, 1, 0, 0, 0, 0 ],
0, 0, 0, −1,−1, 0, 0,−1 ],
0, 0, 0, −1, 0, 0, 0,−1 ],
0, 0, 0, 0,−1, 0, 0, 0 ],
0, 0, 0, 0, 0,−1, 0,−1 ],
0, 0, 0, 0, 0, 0, −1,−1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1,−1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, 1, 1 ],
0, 0, 1, −1, 0, 0, −1,−1 ],
0, 0, 1, −1, 0, 1, −1, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 1, −1, 1 ],
0, 0, 1, 0, 1, 0, −1, 1 ],
0, 1,−1, 1, 0, 0, 1, 1 ],
0, 1, 0, 0, 0, 0, 1, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
0, 1, 0, 1, 0, 1, 0, 1 ],
0, 1, 0, 1, 1, 0, 0, 1 ],
0, 1, 0, 1, 1, 1, 0, 2 ],
0, 1, 1, 0, 0, 1, 0, 1 ],
0, 1, 1, 0, 1, 0, 0, 1 ],
0, 1, 1, 0, 1, 1, −1, 2 ],
0, 1, 1, 1, 1, 0, 0, 2 ],
0, 1, 1, 1, 1, 1, 0, 3 ],
1,−1, 0, −1,−1, 0, 0,−1 ],
1,−1, 0, −1, 0, 0, 0,−1 ],
1,−1, 1, −2, 0, 0, −1,−1 ],
1,−1, 1, −1, 0, 0, 0, 0 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 1, 1 ],
1, 0, 1, −1, 0, 0, −1, 0 ],
1, 0, 1, −1, 0, 1, −1, 0 ],
1, 0, 1, −1, 1, 0, −1, 0 ],
1, 0, 1, −1, 1, 1, −1, 1 ],
1, 0, 1, 0, 0, 1, 0, 1 ],
1, 0, 1, 0, 1, 0, 0, 1 ],
1, 0, 1, 0, 1, 1, −1, 2 ],
1, 0, 2, −1, 1, 0, −1, 1 ],
1, 0, 2, −1, 1, 1, −1, 2 ],
1, 1, 1, 0, 1, 0, 0, 2 ],
1, 1, 1, 0, 1, 1, 0, 3 ],
1, 1, 2, 0, 1, 1, −1, 3 ],
1, 1, 2, 0, 2, 1, −1, 3 ],
∗
7
6
• I ≡ P97 :
5
2
4
1
3
184
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,−1, 0,−1, 0, 0,−1,−1 ],
0,−1, 0, 0, 0,−1, 0,−1 ],
0,−1, 0, 0, 0, 0, 0, 0 ],
0, 0,−1, 0,−1, 0, 0,−1 ],
0, 0,−1, 0, 0,−1, 0,−1 ],
0, 0,−1, 0, 0, 0, 0,−1 ],
0, 0,−1, 1,−1, 0, 1, 0 ],
0, 0,−1, 1, 0, 0, 1, 0 ],
0, 0, 0,−1, 0,−1, 0,−1 ],
0, 0, 0,−1, 0, 0, 0, 0 ],
0, 0, 0, 0,−1, 0, 1, 0 ],
0, 0, 0, 0, 0,−1, 0, 0 ],
0, 0, 0, 0, 0, 0,−1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0,−1, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 0, 1, 0, 1, 0, 1 ],
0, 0, 1,−1, 0, 0,−1, 0 ],
0, 0, 1,−1, 1, 0,−1, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, 1, 0, 1 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 1, 0, 1 ],
0, 1, 0, 1, 0, 0, 1, 1 ],
0, 1, 0, 1, 0, 1, 0, 2 ],
0, 1, 0, 1, 1, 0, 0, 2 ],
0, 1, 1, 0, 0, 0, 0, 1 ],
0, 1, 1, 0, 0, 1, 0, 2 ],
0, 1, 1, 0, 1, 0, 0, 2 ],
0, 1, 1, 0, 1, 1, 0, 2 ],
0, 1, 1, 1, 1, 1,−1, 2 ],
0, 1, 2, 0, 1, 1,−1, 2 ],
1,−1, 0,−1, 0,−1, 0,−1 ],
1,−1, 0,−1, 0, 0, 0, 0 ],
1,−1, 1,−1, 0, 0,−1,−1 ],
1,−1, 1,−1, 0, 1,−1, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
1, 0, 1,−1, 0, 0, 0, 0 ],
1, 0, 1,−1, 0, 1,−1, 1 ],
1, 0, 1,−1, 1, 0,−1, 1 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 0, 1, 0, 0, 1, 0, 2 ],
1, 0, 1, 0, 1, 0, 0, 2 ],
1, 0, 1, 0, 1, 1, 0, 2 ],
1, 0, 2,−1, 1, 1,−2, 1 ],
1, 0, 2, 0, 1, 1,−1, 2 ],
1, 1, 1, 0, 1, 1,−1, 2 ],
1, 1, 1, 1, 1, 1, 0, 3 ],
1, 1, 2, 0, 1, 1, 0, 3 ],
2, 0, 2,−1, 1, 1,−1, 2 ]





CI =








b I =
Cox




0
0
1
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
−1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
−1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
















BI =



1
1
1
1
1
1
1
−1
















bI =
C




0
0
1
1
1
1
1
0
0
−1
0
0
−1
−1
−1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1

0
0
−1
−1
−1
−1
−1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0










0
0
1
0
0
0
0
−1
Number of sincere Tits roots of poset I sI = 16.
Table of roots of qbI
[ −1,−2,−2,−1, 1, 1, 1,−2 ],
[ −1,−2,−2,−1, 1, 2, 1,−1 ],
[ −1,−1,−2,−1, 1, 1, 1,−1 ],
[ 1, 1, 2, 1,−1,−1,−1, 1 ],
[ 1, 2, 2, 1,−1,−2,−1, 1 ],
[ 1, 2, 2, 1,−1,−1,−1, 2 ],
[ −1, −1, −2, 0, 0, 1, 1, −1 ],
[ −1, −1, −2, 0, 1, 1, 1, −1 ],
[ −1, −1, −1, −1, 1, 0, 1, −1 ],
[ −1, −1, −1, 0, 0, 0, 1, −1 ],
[ −1, −1, −1, 0, 0, 1, 1, 0 ],
[ −1, −1, −1, 0, 1, 0, 1, 0 ],
[ −1, −1, −1, 0, 1, 1, 1, 0 ],
[ −1, 0, −1, 0, 0, 0, 1, 0 ],
[ −1, 0, −1, 0, 0, 1, 1, 0 ],
[ −1, 0, −1, 0, 1, 0, 1, 0 ],
[ −1, 0, −1, 1, 0, 0, 0, 0 ],
[ −1, 0, −1, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, −1, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 0, 0 ],
[ 0, −2, −1, −2, 1, 1, 1, −1 ],
[ 0, −2, −1, −1, 1, 1, 0, −1 ],
[ 0, −1, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 1, 0 ],
[ 0, −1, −1, −1, 1, 0, 1, 0 ],
[ 0, −1, −1, −1, 1, 1, 1, 0 ],
[ 0, −1, −1, 0, 0, 0, 1, 0 ],
[ 0, −1, −1, 0, 0, 1, 1, 0 ],
[ 0, −1, −1, 0, 1, 0, 1, 0 ],
[ 0, −1, 0, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 1, 0, 0 ],
[ 0, −1, 0, −1, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ −1,−2,−2,−1, 1, 1, 1,−1 ],
[ −1,−2,−2,−1, 2, 1, 1,−1 ],
[ −1,−1,−1,−1, 1, 1, 1,−1 ],
[ 1, 2, 1, 1,−1,−1,−1, 1 ],
[ 1, 2, 2, 1,−1,−1,−2, 1 ],
[ −2, −1, −2, 0, 1, 1, 1, −1 ],
[ −1, −1, −2, 0, 1, 0, 1, −1 ],
[ −1, −1, −2, 0, 1, 1, 1, 0 ],
[ −1, −1, −1, −1, 1, 1, 0, −1 ],
[ −1, −1, −1, 0, 0, 1, 0, −1 ],
[ −1, −1, −1, 0, 1, 0, 0, −1 ],
[ −1, −1, −1, 0, 1, 1, 0, −1 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, 1, 0, −1 ],
[ −1, 0, −1, 0, 1, 0, 0, −1 ],
[ −1, 0, −1, 0, 1, 1, 0, 0 ],
[ −1, 0, −1, 1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 1, −1, 1, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, −1, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 0, 1 ],
[ 0, −2, −1, −1, 0, 1, 1, −1 ],
[ 0, −2, −1, −1, 1, 1, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 0, −1 ],
[ 0, −1, −1, −1, 1, 0, 0, −1 ],
[ 0, −1, −1, −1, 1, 1, 0, −1 ],
[ 0, −1, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, −1, 0, 0, 1, 0, −1 ],
[ 0, −1, −1, 0, 1, 0, 0, −1 ],
[ 0, −1, −1, 0, 1, 1, 0, 0 ],
[ 0, −1, 0, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, −1, 1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
185
[ −1,−2,−2,−1, 1, 1, 2,−1 ],
[ −1,−2,−1,−1, 1, 1, 1,−1 ],
[ 1, 1, 1, 1,−1,−1,−1, 1 ],
[ 1, 2, 2, 1,−2,−1,−1, 1 ],
[ 1, 2, 2, 1,−1,−1,−1, 1 ],
[ −1, −2, −2, 0, 1, 1, 1, −1 ],
[ −1, −1, −2, 0, 1, 1, 0, −1 ],
[ −1, −1, −1, −1, 0, 1, 1, −1 ],
[ −1, −1, −1, −1, 1, 1, 1, 0 ],
[ −1, −1, −1, 0, 0, 1, 1, −1 ],
[ −1, −1, −1, 0, 1, 0, 1, −1 ],
[ −1, −1, −1, 0, 1, 1, 0, 0 ],
[ −1, 0, −1, 0, 0, 0, 1, −1 ],
[ −1, 0, −1, 0, 0, 1, 0, 0 ],
[ −1, 0, −1, 0, 1, 0, 0, 0 ],
[ −1, 0, −1, 1, 0, 0, 0, −1 ],
[ −1, 0, −1, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, −1, 0 ],
[ 0, −2, −2, −1, 1, 1, 1, −1 ],
[ 0, −2, −1, −1, 1, 0, 1, −1 ],
[ 0, −2, −1, −1, 1, 1, 1, 0 ],
[ 0, −1, −1, −1, 0, 1, 1, −1 ],
[ 0, −1, −1, −1, 1, 0, 1, −1 ],
[ 0, −1, −1, −1, 1, 1, 0, 0 ],
[ 0, −1, −1, 0, 0, 0, 1, −1 ],
[ 0, −1, −1, 0, 0, 1, 0, 0 ],
[ 0, −1, −1, 0, 1, 0, 0, 0 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 1, 0, −1 ],
[ 0, −1, 0, −1, 1, 0, 0, −1 ],
[ 0, −1, 0, −1, 1, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, −1, 0 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 2,
0, 2,
1, −1,
1, −1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
0, 0, 0, 1, 0,
0, 0, 1, 0, −1,
0, 1, −1, 0, 0,
0, 1, 0, 0, 0,
1, 0, −1, 0, 0,
1, 0, 0, 0, 0,
0, 0, 0, −1, 0,
0, 0, 0, 0, 0,
0, 1, −1, 0, 0,
0, 1, 0, −1, 0,
0, 1, 0, 0, −1,
1, 0, −1, 0, −1,
1, 0, 0, −1, −1,
1, 0, 0, 0, −1,
1, 1, −1, −1, −1,
1, 1, −1, 0, −1,
1, 1, 0, −1, −1,
1, 1, 0, 0, −1,
1, 1, −1, −1, 0,
1, 2, −1, −1, −1,
0, −1, 0, 0, 0,
0, −1, 1, 0, 0,
0, −1, 0, 0, 0,
0, 0, 0, 0, −1,
1, −1, −1, 0, 0,
1, −1, 0, 0, 0,
1, 0, −1, 0, −1,
1, 0, 0, −1, −1,
1, 0, 0, 0, −1,
1, 0, −1, −1, −1,
1, 0, −1, 0, −1,
1, 0, 0, −1, −1,
1, 0, 0, 0, −1,
1, 1, −1, 0, −1,
2, 0, −1, −1, −1,
2, 0, 0, −1, −1,
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
1 ],
0 ],
0 ],
1 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
1 ],
1 ],
1 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
1 ],
1 ],
1 ],
1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 2,
0, 2,
0, 2,
1, −1,
1, −1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
1, 2,
1 ],
0 ],
0 ],
1 ],
0 ],
1 ],
0 ],
0 ],
1 ],
1 ],
1 ],
0 ],
0 ],
1 ],
0 ],
1 ],
1 ],
0 ],
1 ],
1 ],
0 ],
0 ],
0 ],
0 ],
0 ],
1 ],
0 ],
0 ],
1 ],
0 ],
1 ],
1 ],
0 ],
1 ],
1 ],
1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 2,
0, 2,
1, −1,
1, −1,
1, −1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
2, 1,
0, 0, 1, −1, 0, 0 ],
0, 0, 1, 0, 0, 1 ],
0, 1, 0, 0, −1, 0 ],
1, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, −1, 0 ],
0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, 0 ],
0, 1, −1, 0, −1, 0 ],
0, 1, 0, −1, −1, 0 ],
0, 1, 0, 0, −1, 0 ],
1, 0, −1, −1, 0, 0 ],
1, 0, −1, 0, 0, 1 ],
1, 0, 0, −1, 0, 1 ],
1, 0, 0, 0, 0, 1 ],
1, 1, −1, −1, 0, 1 ],
1, 1, −1, 0, 0, 1 ],
1, 1, 0, −1, 0, 1 ],
1, 1, −1, −1, −1, 1 ],
1, 1, 0, −1, −1, 1 ],
0, −1, 0, 0, 0, −1 ],
0, −1, 0, 1, 0, 0 ],
1, −1, 0, 0, 0, 0 ],
0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 1 ],
1, −1, 0, 0, −1, 0 ],
1, 0, −1, −1, 0, 0 ],
1, 0, −1, 0, 0, 1 ],
1, 0, 0, −1, 0, 1 ],
1, 0, 0, 0, 0, 1 ],
1, 0, −1, −1, 0, 1 ],
1, 0, −1, 0, 0, 1 ],
1, 0, 0, −1, 0, 1 ],
1, 1, −1, −1, 0, 1 ],
2, 0, −1, −1, −1, 0 ],
2, 0, −1, 0, −1, 1 ],
2, 0, −1, −1, −1, 1 ]
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
















BI =



1
0
0
0
0
0
0
−1
0, 0, 0, 1, 0,
0, 0, 1, 0, 0,
0, 1, 0, −1, 0,
0, 1, 0, 0, 0,
1, 0, 0, −1, 0,
1, 0, 0, 0, 0,
0, 0, 0, 0, −1,
0, 1, −1, −1, 0,
0, 1, −1, 0, 0,
0, 1, 0, −1, 0,
0, 1, 0, 0, 0,
1, 0, −1, 0, 0,
1, 0, 0, −1, 0,
1, 0, 0, 0, −1,
1, 1, −1, −1, 0,
1, 1, −1, 0, −1,
1, 1, 0, −1, −1,
1, 1, −1, −1, −1,
1, 1, −1, 0, −1,
2, 1, −1, −1, −1,
0, −1, 0, 0, 1,
0, 0, 0, 0, 0,
0, 0, −1, 0, 0,
0, 0, 0, 0, 0,
1, −1, 0, −1, 0,
1, −1, 0, 0, 0,
1, 0, −1, 0, 0,
1, 0, 0, −1, 0,
1, 0, 0, 0, −1,
1, 0, −1, −1, 0,
1, 0, −1, 0, −1,
1, 0, 0, −1, −1,
1, 1, −1, −1, −1,
1, 1, 0, −1, −1,
2, 0, −1, −1, 0,
2, 0, −1, −1, −1,
∗
7
• I ≡ P98 :
1
6
3
5
2
4





CI =








b I =
Cox




0
1
1
1
1
1
1
−1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
−1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
−1
0
0
0
1
0
0
0
0
−1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
−1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1
















b
CI =



186
0
0
0
1
0
0
0
−1
0
0
0
1
1
1
1
0
0
0
0
−1
−1
−1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
−1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
−1
−1
−1
−1
−1
−1
1











0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
−1











Number of sincere Tits roots of poset I sI = 18.
Table of roots of qbI
[ −2,−1,−2,−2,−1, 1, 1,−3 ],
[ −1,−1,−2,−2,−1, 1, 2,−2 ],
[ −1,−1,−1,−2,−1, 1, 1,−2 ],
[ 1, 1, 1, 1, 1,−1,−1, 1 ],
[ 1, 1, 2, 1, 1,−1,−1, 2 ],
[ 1, 1, 2, 2, 1,−1,−1, 2 ],
[ −1, −2, −1, −2, 0, 1, 1, −2 ],
[ −1, −1, −1, −2, 0, 1, 0, −2 ],
[ −1, −1, −1, −1, −1, 0, 1, −2 ],
[ −1, −1, −1, −1, 0, 0, 1, −2 ],
[ −1, −1, −1, −1, 0, 1, 0, −1 ],
[ −1, −1, 0, −1, 0, 0, 0, −1 ],
[ −1, −1, 0, −1, 1, 0, 0, −1 ],
[ −1, 0, −2, −1, −2, 1, 1, −2 ],
[ −1, 0, −2, −1, −1, 1, 1, −2 ],
[ −1, 0, −1, −1, −1, 0, 1, −2 ],
[ −1, 0, −1, −1, −1, 1, 0, −1 ],
[ −1, 0, −1, −1, 0, 0, 0, −1 ],
[ −1, 0, −1, 0, −1, 0, 0, −2 ],
[ −1, 0, −1, 0, −1, 1, 0, −1 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, −1, −2, 0, 1, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 0, −1 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 1, 0, −1 ],
[ 0, −1, 0, −1, 1, 0, 0, −1 ],
[ 0, −1, 0, −1, 1, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 1, −1, 1, 0, 0, 0 ],
[ 0, −1, 1, 0, 1, 0, −1, 0 ],
[ 0, 0, −2, −1, −1, 1, 1, −1 ],
[ 0, 0, −1, −1, −1, 1, 1, −1 ],
[ 0, 0, −1, −1, 0, 0, 1, −1 ],
[ 0, 0, −1, −1, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, −1, 0, 1, −1 ],
[ 0, 0, −1, 0, −1, 1, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, −1, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, −1, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, −1, 0, 1 ],
[ 0, 1, −1, 0, −1, 0, 0, −1 ],
[ 0, 1, −1, 0, −1, 1, 0, 0 ],
[ 0, 1, 0, 0, −1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, −1, 0, −1, 0 ],
[ 0, 1, 0, 1, 0, −1, −1, 0 ],
[ 0, 1, 0, 1, 0, 0, −1, 0 ],
[ 0, 1, 1, 1, 0, −1, −1, 0 ],
[ 0, 1, 1, 1, 0, 0, −1, 1 ],
[ −1,−1,−2,−2,−1, 1, 1,−3 ],
[ −1,−1,−2,−2,−1, 2, 1,−2 ],
[ −1,−1,−1,−1,−1, 1, 1,−2 ],
[ 1, 1, 1, 1, 1,−1,−1, 2 ],
[ 1, 1, 2, 2, 1,−2,−1, 2 ],
[ 1, 1, 2, 2, 1,−1,−1, 3 ],
[ −1, −1, −2, −2, 0, 1, 1, −2 ],
[ −1, −1, −1, −2, 0, 1, 1, −2 ],
[ −1, −1, −1, −1, −1, 1, 0, −2 ],
[ −1, −1, −1, −1, 0, 0, 1, −1 ],
[ −1, −1, −1, −1, 0, 1, 1, −1 ],
[ −1, −1, 0, −1, 0, 0, 1, −1 ],
[ −1, −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, −2, −1, −1, 0, 1, −2 ],
[ −1, 0, −2, −1, −1, 1, 1, −1 ],
[ −1, 0, −1, −1, −1, 0, 1, −1 ],
[ −1, 0, −1, −1, −1, 1, 1, −1 ],
[ −1, 0, −1, −1, 0, 0, 1, −1 ],
[ −1, 0, −1, 0, −1, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, −1, 1, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 1, −1 ],
[ 0, −1, 0, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 1, 0, 0 ],
[ 0, −1, 0, −1, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, 0, 1, 0, 0, 0 ],
[ 0, 0, −1, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, −1, −1, 1, 1, 0 ],
[ 0, 0, −1, −1, 0, 0, 1, 0 ],
[ 0, 0, −1, −1, 0, 1, 1, 0 ],
[ 0, 0, −1, 0, −1, 0, 1, 0 ],
[ 0, 0, −1, 0, −1, 1, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 0, 1, −1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 0, 1, 0, 1, −1, −1, 0 ],
[ 0, 0, 1, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 1, 0, −1, −1, 0 ],
[ 0, 0, 1, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, 1, 1, −1, −1, 0 ],
[ 0, 0, 1, 1, 1, 0, −1, 1 ],
[ 0, 1, −1, 0, −1, 0, 0, 0 ],
[ 0, 1, −1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, −1, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, −1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, −1, 1 ],
[ 0, 1, 1, 1, 0, −1, −1, 1 ],
[ 0, 1, 1, 1, 1, −1, −1, 1 ],
187
[ −1,−1,−2,−2,−1, 1, 1,−2 ],
[ −1,−1,−2,−1,−1, 1, 1,−2 ],
[ −1,−1,−1,−1,−1, 1, 1,−1 ],
[ 1, 1, 1, 2, 1,−1,−1, 2 ],
[ 1, 1, 2, 2, 1,−1,−2, 2 ],
[ 2, 1, 2, 2, 1,−1,−1, 3 ],
[ −1, −1, −1, −2, 0, 0, 1, −2 ],
[ −1, −1, −1, −2, 0, 1, 1, −1 ],
[ −1, −1, −1, −1, 0, 0, 0, −2 ],
[ −1, −1, −1, −1, 0, 1, 0, −2 ],
[ −1, −1, 0, −1, 0, 0, 0, −2 ],
[ −1, −1, 0, −1, 0, 1, 0, −1 ],
[ −1, 0, −2, −2, −1, 1, 1, −2 ],
[ −1, 0, −2, −1, −1, 1, 0, −2 ],
[ −1, 0, −1, −1, −1, 0, 0, −2 ],
[ −1, 0, −1, −1, −1, 1, 0, −2 ],
[ −1, 0, −1, −1, 0, 0, 0, −2 ],
[ −1, 0, −1, −1, 0, 1, 0, −1 ],
[ −1, 0, −1, 0, −1, 0, 1, −1 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1, −1 ],
[ −1, 1, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, −1, 1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ 0, −1, 1, 0, 1, −1, 0, 0 ],
[ 0, −1, 1, 0, 1, 0, 0, 1 ],
[ 0, 0, −1, −1, −1, 1, 0, −1 ],
[ 0, 0, −1, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, −1, 0, 1, 0, −1 ],
[ 0, 0, −1, 0, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, −1, 1 ],
[ 0, 0, 1, 1, 0, −1, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, −1, 1 ],
[ 0, 0, 1, 1, 1, −1, −1, 1 ],
[ 0, 0, 2, 1, 1, −1, −1, 1 ],
[ 0, 1, −1, 0, −1, 0, 1, 0 ],
[ 0, 1, −1, 1, −1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 1, −1, −1, 0, 0 ],
[ 0, 1, 0, 1, −1, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, −1, 0, 1 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 0, −1, 0, 1 ],
[ 0, 1, 1, 2, 0, −1, −1, 1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
1, −1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
1,
0,
0,
1,
1,
1,
1,
1,
2,
2,
0,
0,
1,
1,
1,
1,
0,
0,
1,
0,
1,
1,
1,
1,
1,
2,
1,
1,
1,
1,
2,
2,
1, 0, 0,
0, 0, 1,
0, 0, 0,
1, 0, −1,
0, −1, 0,
0, 0, 0,
1, −1, 0,
1, 0, 0,
1, −1, 0,
1, −1, −1,
0, −1, 0,
0, 0, 0,
0, −1, 0,
0, 0, 0,
0, −1, −1,
0, 0, −1,
1 ],
1 ],
1 ],
1 ],
1 ],
2 ],
2 ],
2 ],
2 ],
2 ],
1 ],
2 ],
2 ],
2 ],
1 ],
2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
0,
0,
1,
1,
1,
1,
1,
2,
2,
0,
0,
1,
1,
1,
1,
2,
0,
0,
0,
0,
1,
1,
1,
1,
1,
0,
1,
1,
1,
1,
2,
2,
0, 0, 0,
0, 1, 0,
0, 0, 0,
1, 0, 0,
0, 0, −1,
1, −1, −1,
1, 0, −1,
1, −1, −1,
1, 0, −1,
0, 0, 0,
0, 0, −1,
0, −1, −1,
0, 0, −1,
1, −1, 0,
0, −1, −1,
0, −1, −1,
0 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
1 ],
2 ],
1 ],
1 ],
1 ],
1 ],
2 ],
2 ],
2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
2,
0,
0,
1,
1,
1,
1,
1,
2,
2,
0,
0,
1,
1,
1,
1,
1,
0, 0, 0, 0,
0, 1, 0, 0,
0, 1, −1, 0,
0, 1, 0, 0,
1, 0, 0, 0,
1, 1, −1, 0,
1, 1, 0, −1,
1, 1, −1, −1,
1, 2, −1, −1,
1, −1, 0, 0,
1, 0, 0, 0,
1, 0, −1, 0,
1, 0, 0, −1,
1, 1, 0, −1,
2, 0, −1, 0,
2, 0, −1, −1,
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1 ],
1 ],
1 ],
2 ],
1 ],
1 ],
2 ],
2 ],
2 ],
1 ],
1 ],
1 ],
2 ],
2 ],
2 ],
2]
∗
• I ≡ P99 :
7
2
4
6
1
3
5




CI =



1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
−1
1
1
0
0
1
0
0
−1






b I =
Cox




1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
−1
0
0
0
0
1
0
0
0
−1
−1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
−1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
















b
CI =



1
1
1
1
1
1
1
−1

0
 0

 0

BI = 00

 −1
 0
0










1
1
0
0
0
0
0
−1

1
0
0
0
1
0
0
−1
0
0
0
0
−1
−1
−1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
−1
−1
−1
−1
−1
−1
−1
−1
1











−1
0
0
0
0
0
0
0
0
0
−1
−1
0
0
0
1
Number of sincere Tits roots of poset I sI = 18.
Table of roots of qbI
[ −2,−1,−1,−2,−2,−1, 1,−4 ],
[ −1,−1,−1,−2,−2,−1, 1,−3 ],
[ −1,−1,−1,−1,−2,−1, 1,−3 ],
[ 1, 1, 1, 1, 1, 1,−1, 2 ],
[ 1, 1, 1, 2, 1, 1,−1, 3 ],
[ 1, 1, 1, 2, 2, 1,−1, 4 ],
[ −1, −1, −2, −1, −2, 0, 1, −3 ],
[ −1, −1, −1, −1, −2, 0, 1, −3 ],
[ −1, −1, −1, −1, −1, 0, 0, −3 ],
[ −1, −1, −1, 0, −1, 0, 0, −2 ],
[ −1, −1, 0, −2, −1, −1, 0, −3 ],
[ −1, −1, 0, −1, −1, −1, 0, −3 ],
[ −1, −1, 0, −1, −1, 0, 0, −2 ],
[ −1, 0, −1, −1, −1, −1, 1, −2 ],
[ −1,−2,−1,−2,−2,−1, 1,−4 ],
[ −1,−1,−1,−2,−2,−1, 2,−3 ],
[ −1,−1,−1,−1,−1,−1, 1,−3 ],
[ 1, 1, 1, 1, 1, 1,−1, 3 ],
[ 1, 1, 1, 2, 2, 1,−2, 3 ],
[ 1, 2, 1, 2, 2, 1,−1, 4 ],
[ −1, −1, −1, −2, −2, 0, 1, −3 ],
[ −1, −1, −1, −1, −2, 0, 1, −2 ],
[ −1, −1, −1, −1, −1, 0, 0, −2 ],
[ −1, −1, 0, −2, −2, −1, 1, −3 ],
[ −1, −1, 0, −2, −1, −1, 1, −3 ],
[ −1, −1, 0, −1, −1, −1, 0, −2 ],
[ −1, −1, 0, −1, 0, −1, 0, −2 ],
[ −1, 0, −1, −1, −1, 0, 0, −2 ],
188
[ −1,−1,−1,−2,−2,−1, 1,−4 ],
[ −1,−1,−1,−2,−1,−1, 1,−3 ],
[ −1,−1,−1,−1,−1,−1, 1,−2 ],
[ 1, 1, 1, 1, 2, 1,−1, 3 ],
[ 1, 1, 1, 2, 2, 1,−1, 3 ],
[ 2, 1, 1, 2, 2, 1,−1, 4 ],
[ −1, −1, −1, −1, −2, 0, 0, −3 ],
[ −1, −1, −1, −1, −1, −1, 0, −3 ],
[ −1, −1, −1, −1, −1, 0, 1, −2 ],
[ −1, −1, 0, −2, −1, −2, 1, −3 ],
[ −1, −1, 0, −2, −1, −1, 1, −2 ],
[ −1, −1, 0, −1, −1, −1, 1, −2 ],
[ −1, 0, −1, −1, −2, 0, 1, −2 ],
[ −1, 0, −1, −1, −1, 0, 1, −2 ],
1
0
0
0
0
−1
0
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, −1, −1, −1, 0, 1, −1 ],
−1, 0, −1, 0, −1, 0, 1, −1 ],
−1, 0, 0, −2, −1, −1, 1, −2 ],
−1, 0, 0, −1, −1, −1, 1, −1 ],
−1, 0, 0, −1, −1, 0, 1, −1 ],
−1, 0, 0, −1, 0, −1, 1, −1 ],
−1, 0, 0, 0, 0, −1, 0, −1 ],
−1, 0, 0, 0, 0, 0, 0, 0 ],
0, −1, −1, −1, −2, 0, 1, −2 ],
0, −1, −1, −1, −1, 0, 1, −2 ],
0, −1, −1, 0, −1, 0, 0, −1 ],
0, −1, −1, 0, 0, 0, 0, −1 ],
0, −1, 0, −1, −1, −1, 1, −2 ],
0, −1, 0, −1, −1, 0, 0, −1 ],
0, −1, 0, −1, 0, −1, 0, −1 ],
0, −1, 0, 0, −1, 0, 0, −1 ],
0, −1, 0, 0, 0, 0, 0, −1 ],
0, 0, −1, −1, −1, 0, 1, −1 ],
0, 0, −1, 0, −1, 0, 1, 0 ],
0, 0, −1, 0, −1, 1, 1, 0 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, −1, 1, 0, 0, 0, 0 ],
0, 0, −1, 1, 0, 1, 0, 1 ],
0, 0, 0, −1, −1, 0, 1, −1 ],
0, 0, 0, −1, 0, −1, 1, −1 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1, −1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 0, 1, 0, 1 ],
0, 0, 0, 1, 1, 0, 0, 1 ],
0, 0, 1, −1, 0, −1, 0, 0 ],
0, 0, 1, −1, 1, −1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 1, −1, 0, 0 ],
0, 0, 1, 0, 1, 0, −1, 1 ],
0, 1, −1, 1, 0, 1, 0, 1 ],
0, 1, 0, 0, 0, 0, 1, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
0, 1, 0, 1, 0, 1, 0, 2 ],
0, 1, 0, 1, 1, 0, 0, 2 ],
0, 1, 0, 1, 1, 1, 0, 2 ],
0, 1, 1, 0, 1, −1, 0, 1 ],
0, 1, 1, 0, 1, 0, 0, 2 ],
0, 1, 1, 1, 1, 0, 0, 2 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 0, 1, 0, 0, 1 ],
1, 0, 0, 1, 0, 1, 0, 1 ],
1, 0, 0, 1, 1, 0, 0, 1 ],
1, 0, 0, 1, 1, 1, −1, 2 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 0, 1, 0, 1, 0, 0, 1 ],
1, 0, 1, 1, 1, 0, −1, 2 ],
1, 0, 1, 1, 2, 0, −1, 2 ],
1, 1, 0, 1, 1, 1, −1, 2 ],
1, 1, 0, 2, 1, 1, −1, 2 ],
1, 1, 0, 2, 1, 2, −1, 3 ],
1, 1, 1, 1, 1, 0, −1, 2 ],
1, 1, 1, 1, 1, 1, 0, 3 ],
1, 1, 1, 1, 2, 0, 0, 3 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, −1, 0, −1, 0, 0, −2 ],
−1, 0, −1, 0, −1, 1, 0, −1 ],
−1, 0, 0, −1, −1, −1, 0, −2 ],
−1, 0, 0, −1, −1, 0, 0, −2 ],
−1, 0, 0, −1, 0, −1, 0, −2 ],
−1, 0, 0, −1, 0, 0, 0, −1 ],
−1, 0, 0, 0, 0, 0, −1, −1 ],
−1, 0, 1, −1, 0, −1, 0, −1 ],
0, −1, −1, −1, −1, −1, 1, −2 ],
0, −1, −1, −1, −1, 0, 1, −1 ],
0, −1, −1, 0, −1, 0, 1, −1 ],
0, −1, 0, −2, −1, −1, 1, −2 ],
0, −1, 0, −1, −1, −1, 1, −1 ],
0, −1, 0, −1, −1, 0, 1, −1 ],
0, −1, 0, −1, 0, −1, 1, −1 ],
0, −1, 0, 0, 0, −1, 0, −1 ],
0, −1, 0, 0, 0, 0, 0, 0 ],
0, 0, −1, 0, −1, 0, 0, −1 ],
0, 0, −1, 0, −1, 1, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 1, 0, 0 ],
0, 0, −1, 1, 0, 1, −1, 0 ],
0, 0, 0, −1, −1, −1, 1, −1 ],
0, 0, 0, −1, −1, 0, 1, 0 ],
0, 0, 0, −1, 0, −1, 1, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, 0, 1, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 0, 1, 0, 1, −1, 0 ],
0, 0, 0, 1, 1, 0, −1, 0 ],
0, 0, 0, 1, 1, 1, −1, 1 ],
0, 0, 1, −1, 0, −1, 1, 0 ],
0, 0, 1, 0, 0, −1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 1, −1, 0, 1 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 1, 0, 1 ],
0, 1, 0, 1, 0, 1, −1, 1 ],
0, 1, 0, 1, 1, 0, −1, 1 ],
0, 1, 0, 1, 1, 1, −1, 1 ],
0, 1, 0, 2, 1, 1, −1, 2 ],
0, 1, 1, 0, 1, 0, −1, 1 ],
0, 1, 1, 1, 1, 0, −1, 1 ],
0, 1, 1, 1, 1, 1, −1, 2 ],
1, 0, −1, 1, 0, 1, 0, 1 ],
1, 0, 0, 0, 0, 0, 1, 1 ],
1, 0, 0, 1, 0, 0, 0, 1 ],
1, 0, 0, 1, 0, 1, 0, 2 ],
1, 0, 0, 1, 1, 0, 0, 2 ],
1, 0, 0, 1, 1, 1, 0, 2 ],
1, 0, 1, 0, 1, −1, 0, 1 ],
1, 0, 1, 0, 1, 0, 0, 2 ],
1, 0, 1, 1, 1, 0, 0, 2 ],
1, 1, 0, 1, 0, 1, 0, 2 ],
1, 1, 0, 1, 1, 1, 0, 2 ],
1, 1, 0, 2, 1, 1, −1, 3 ],
1, 1, 0, 2, 2, 1, −1, 3 ],
1, 1, 1, 1, 1, 0, 0, 2 ],
1, 1, 1, 1, 2, 0, −1, 2 ],
1, 1, 1, 2, 2, 0, −1, 3 ],
189
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, −1, 0, −1, 0, 0, −1 ],
−1, 0, −1, 0, 0, 0, 0, −1 ],
−1, 0, 0, −1, −1, −1, 1, −2 ],
−1, 0, 0, −1, −1, 0, 0, −1 ],
−1, 0, 0, −1, 0, −1, 0, −1 ],
−1, 0, 0, 0, −1, 0, 0, −1 ],
−1, 0, 0, 0, 0, 0, 0, −1 ],
−1, 1, 0, 0, 0, 0, 0, 0 ],
0, −1, −1, −1, −1, 0, 0, −2 ],
0, −1, −1, 0, −1, 0, 0, −2 ],
0, −1, −1, 0, −1, 1, 0, −1 ],
0, −1, 0, −1, −1, −1, 0, −2 ],
0, −1, 0, −1, −1, 0, 0, −2 ],
0, −1, 0, −1, 0, −1, 0, −2 ],
0, −1, 0, −1, 0, 0, 0, −1 ],
0, −1, 0, 0, 0, 0, −1, −1 ],
0, −1, 1, −1, 0, −1, 0, −1 ],
0, 0, −1, 0, −1, 0, 1, −1 ],
0, 0, −1, 0, −1, 1, 0, 0 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, −1, 1, −1, 1, 0, 0 ],
0, 0, −1, 1, 0, 1, 0, 0 ],
0, 0, 0, −1, −1, 0, 0, −1 ],
0, 0, 0, −1, 0, −1, 0, −1 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, −1, 1, 0, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 0, 1, 0, 1, −1, 1 ],
0, 0, 0, 1, 1, 0, −1, 1 ],
0, 0, 1, −1, 0, −1, 0, −1 ],
0, 0, 1, −1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 0, 1, 0, 1, −1, −1, 0 ],
0, 0, 1, 0, 1, 0, −1, 0 ],
0, 0, 1, 1, 1, 0, −1, 1 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
0, 1, 0, 1, 0, 1, 0, 1 ],
0, 1, 0, 1, 1, 0, 0, 1 ],
0, 1, 0, 1, 1, 1, −1, 2 ],
0, 1, 1, 0, 0, 0, 0, 1 ],
0, 1, 1, 0, 1, 0, 0, 1 ],
0, 1, 1, 1, 1, 0, −1, 2 ],
0, 1, 1, 1, 2, 0, −1, 2 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
1, 0, 0, 1, 0, 1, −1, 1 ],
1, 0, 0, 1, 1, 0, −1, 1 ],
1, 0, 0, 1, 1, 1, −1, 1 ],
1, 0, 0, 2, 1, 1, −1, 2 ],
1, 0, 1, 0, 1, 0, −1, 1 ],
1, 0, 1, 1, 1, 0, −1, 1 ],
1, 0, 1, 1, 1, 1, −1, 2 ],
1, 1, 0, 1, 1, 0, 0, 2 ],
1, 1, 0, 1, 1, 1, 0, 3 ],
1, 1, 0, 2, 1, 1, 0, 3 ],
1, 1, 1, 0, 1, 0, 0, 2 ],
1, 1, 1, 1, 1, 0, 0, 3 ],
1, 1, 1, 1, 2, 0, −1, 3 ],
1, 1, 2, 1, 2, 0, −1, 3 ]
∗
• I ≡ P100 :
7
5
3
6
4
2
1




CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
−1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
−1






b I =
Cox




1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
−1
0
0
0
0
0
1
0
0
−1
−1
−1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
















BI =



1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
−1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
−1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
−1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
−1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
−1
−1
−1
−1
−1
−1
−1
−1
1
1
1
0
1
0
0
0
−1











0
−1
0
0
0
0
0
0
Number of sincere Tits roots of poset I sI = 18.
Table of roots of qbI
[ −2,−1,−1,−1,−2,−2,−1,−5 ],
[ −1,−1,−1,−1,−2,−2,−1,−5 ],
[ −1,−1,−1,−1,−1,−2,−1,−4 ],
[ 1, 1, 1, 1, 1, 1, 1, 3 ],
[ 1, 1, 1, 1, 2, 1, 1, 4 ],
[ 1, 1, 2, 1, 2, 2, 1, 5 ],
[ −1, −1, −1, −2, −1, −2, 0, −4 ],
[ −1, −1, −1, −1, −1, −2, 0, −3 ],
[ −1, −1, −1, 0, −2, −1, −2, −4 ],
[ −1, −1, −1, 0, −1, −1, −1, −3 ],
[ −1, −1, 0, −1, −1, −1, 0, −3 ],
[ −1, −1, 0, 0, −2, −1, −1, −3 ],
[ −1, −1, 0, 0, −1, −1, 0, −2 ],
[ −1, 0, −1, −1, −1, −1, −1, −3 ],
[ −1, 0, −1, −1, 0, −1, 0, −2 ],
[ −1, 0, −1, 0, −1, −1, −1, −2 ],
[ −1, 0, 0, −1, −1, −1, 0, −2 ],
[ −1, 0, 0, −1, 0, −1, 1, −1 ],
[ −1, 0, 0, 0, −1, −1, 0, −2 ],
[ −1, 0, 0, 0, −1, 0, −1, −1 ],
[ −1, 0, 0, 0, 0, 0, −1, −1 ],
[ −1, 0, 0, 1, −1, 0, −1, −1 ],
[ 0, −1, −1, −1, −1, −2, 0, −3 ],
[ 0, −1, −1, −1, −1, −1, 0, −2 ],
[ 0, −1, −1, 0, −1, −1, −1, −3 ],
[ 0, −1, −1, 0, −1, 0, −1, −2 ],
[ 0, −1, 0, −1, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, −1, −1, −1, −2 ],
[ 0, −1, 0, 0, −1, 0, −1, −2 ],
[ 0, −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, −1, −1, 0, −2 ],
[ −1,−2,−1,−1,−2,−2,−1,−5 ],
[ −1,−1,−1,−1,−2,−2,−1,−4 ],
[ −1,−1,−1,−1,−1,−1,−1,−4 ],
[ 1, 1, 1, 1, 1, 1, 1, 4 ],
[ 1, 1, 1, 1, 2, 2, 1, 4 ],
[ 1, 2, 1, 1, 2, 2, 1, 5 ],
[ −1, −1, −1, −1, −2, −2, 0, −4 ],
[ −1, −1, −1, −1, −1, −1, 0, −3 ],
[ −1, −1, −1, 0, −2, −1, −1, −4 ],
[ −1, −1, 0, −1, −1, −2, 0, −3 ],
[ −1, −1, 0, −1, −1, −1, 0, −2 ],
[ −1, −1, 0, 0, −1, −1, −1, −3 ],
[ −1, −1, 0, 0, −1, 0, −1, −2 ],
[ −1, 0, −1, −1, −1, −1, 0, −3 ],
[ −1, 0, −1, 0, −2, −1, −1, −3 ],
[ −1, 0, −1, 0, −1, −1, 0, −2 ],
[ −1, 0, 0, −1, 0, −1, 0, −2 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, −1, −1, 0, −1 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, −1, −1, −1, −3 ],
[ 0, −1, −1, −1, 0, −1, 0, −2 ],
[ 0, −1, −1, 0, −1, −1, −1, −2 ],
[ 0, −1, 0, −1, −1, −1, 0, −2 ],
[ 0, −1, 0, −1, 0, −1, 1, −1 ],
[ 0, −1, 0, 0, −1, −1, 0, −2 ],
[ 0, −1, 0, 0, −1, 0, −1, −1 ],
[ 0, −1, 0, 0, 0, 0, −1, −1 ],
[ 0, −1, 0, 1, −1, 0, −1, −1 ],
[ 0, 0, −1, −1, 0, −1, 0, −2 ],
190
[ −1,−1,−2,−1,−2,−2,−1,−5 ],
[ −1,−1,−1,−1,−2,−1,−1,−4 ],
[ −1,−1,−1,−1,−1,−1,−1,−3 ],
[ 1, 1, 1, 1, 1, 2, 1, 4 ],
[ 1, 1, 1, 1, 2, 2, 1, 5 ],
[ 2, 1, 1, 1, 2, 2, 1, 5 ],
[ −1, −1, −1, −1, −1, −2, 0, −4 ],
[ −1, −1, −1, 0, −2, −2, −1, −4 ],
[ −1, −1, −1, 0, −2, −1, −1, −3 ],
[ −1, −1, 0, −1, −1, −1, −1, −3 ],
[ −1, −1, 0, −1, 0, −1, 0, −2 ],
[ −1, −1, 0, 0, −1, −1, −1, −2 ],
[ −1, 0, −1, −1, −1, −2, 0, −3 ],
[ −1, 0, −1, −1, −1, −1, 0, −2 ],
[ −1, 0, −1, 0, −1, −1, −1, −3 ],
[ −1, 0, −1, 0, −1, 0, −1, −2 ],
[ −1, 0, 0, −1, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, −1, −1, −1, −2 ],
[ −1, 0, 0, 0, −1, 0, −1, −2 ],
[ −1, 0, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, −1, −1, 0, −3 ],
[ 0, −1, −1, 0, −2, −1, −1, −3 ],
[ 0, −1, −1, 0, −1, −1, 0, −2 ],
[ 0, −1, 0, −1, 0, −1, 0, −2 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, −1, −1, 0, −1 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, 0, −1, 0, −1 ],
1
1
0
1
0
1
0
−2











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, −1, −1, 0, −1, 1, −1 ],
0, 0, −1, 0, −1, −1, 0, −2 ],
0, 0, −1, 0, −1, 0, −1, −1 ],
0, 0, −1, 0, 0, 0, −1, −1 ],
0, 0, −1, 1, −1, 0, −1, −1 ],
0, 0, 0, −1, 0, −1, 1, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, −1, 1, 0, 1, 0 ],
0, 0, 0, 0, −1, 0, −1, −1 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 0, 1, 1, 0, 1 ],
0, 0, 0, 1, −1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 0, 1, 0, 1, −1, 1 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 1, 0, 1 ],
0, 0, 1, 0, 1, 0, 1, 2 ],
0, 0, 1, 0, 1, 1, 1, 2 ],
0, 0, 1, 1, 0, 1, 0, 1 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
0, 1, 0, 0, 1, 1, 0, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
0, 1, 0, 1, 0, 1, 0, 2 ],
0, 1, 1, 0, 1, 1, 0, 2 ],
0, 1, 1, 0, 2, 1, 1, 3 ],
0, 1, 1, 1, 1, 1, 0, 3 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
1, 0, 0, 0, 1, 0, 1, 2 ],
1, 0, 0, 0, 1, 1, 1, 2 ],
1, 0, 0, 1, 0, 1, 0, 1 ],
1, 0, 1, 0, 1, 0, 1, 2 ],
1, 0, 1, 0, 1, 1, 1, 3 ],
1, 0, 1, 1, 1, 1, 0, 2 ],
1, 0, 1, 1, 1, 2, 0, 3 ],
1, 1, 0, 0, 1, 1, 1, 2 ],
1, 1, 0, 1, 0, 1, 0, 2 ],
1, 1, 0, 1, 1, 1, 1, 3 ],
1, 1, 1, 0, 2, 1, 1, 3 ],
1, 1, 1, 0, 2, 2, 1, 4 ],
1, 1, 1, 1, 1, 2, 0, 4 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, −1, −1, 0, 0, 0, −1 ],
0, −1, 0, −1, −1, 0, −1 ],
0, −1, 0, −1, 0, 0, −1 ],
0, −1, 0, 0, 0, 0, −1 ],
0, 0, −1, 0, −1, 0, −1 ],
0, 0, −1, 0, 0, 0, −1 ],
0, 0, −1, 1, −1, 1, 0 ],
0, 0, −1, 1, 0, 1, 1 ],
0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 1, 0, 0, 1 ],
0, 0, 1, −1, 0, −1, −1 ],
0, 0, 1, −1, 1, −1, 0 ],
0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, 1, 0, 1 ],
0, 1, 0, 0, 0, 0, 1 ],
0, 1, 0, 1, 0, 0, 1 ],
0, 1, 0, 1, 1, 0, 1 ],
0, 1, 1, 0, 0, 0, 1 ],
0, 1, 1, 0, 1, 0, 2 ],
1, 0, −1, 1, 0, 1, 1 ],
1, 0, 0, 0, 0, 1, 1 ],
1, 0, 0, 1, 0, 1, 1 ],
1, 0, 0, 1, 1, 0, 2 ],
1, 0, 1, 0, 1, −1, 1 ],
1, 0, 1, 1, 1, 0, 2 ],
1, 1, 0, 1, 1, 1, 2 ],
1, 1, 1, 0, 1, 0, 2 ],
1, 1, 1, 1, 1, 1, 3 ],
0, −1, 0, 0, 0, 0, 0 ],
0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 1, 0, 1 ],
0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, 1, 0, 2 ],
0, 1, 0, 1, 1, 0, 2 ],
0, 1, 0, 2, 1, 1, 3 ],
0, 1, 1, 1, 1, 0, 3 ],
1, 0, 0, 1, 0, 1, 2 ],
1, 0, 0, 1, 1, 1, 3 ],
1, 0, 1, 1, 1, 0, 2 ],
1, 0, 1, 1, 2, 0, 3 ],
1, 1, 0, 2, 1, 1, 4 ],
1, 1, 1, 1, 1, 0, 3 ],
1, 1, 1, 2, 2, 0, 4 ],
∗
7
6
• I ≡ P101 :
3
5
2
4
1
191
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, −1, 0, −1, −1, −1, −2 ],
0, −1, 0, −1, 0, −1, −2 ],
0, −1, 0, 0, −1, 0, −1 ],
0, −1, 0, 0, 0, 0, 0 ],
0, 0, −1, 0, −1, 1, −1 ],
0, 0, −1, 0, 0, 0, 0 ],
0, 0, −1, 1, 0, 0, 0 ],
0, 0, 0, −1, −1, 0, −1 ],
0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 1, 0, 1, 1 ],
0, 0, 1, −1, 0, −1, 0 ],
0, 0, 1, 0, 0, −1, 0 ],
0, 0, 1, 0, 1, −1, 0 ],
0, 1, −1, 1, 0, 1, 1 ],
0, 1, 0, 0, 0, 1, 1 ],
0, 1, 0, 1, 0, 1, 1 ],
0, 1, 0, 1, 1, 0, 2 ],
0, 1, 1, 0, 1, −1, 1 ],
0, 1, 1, 1, 1, 0, 2 ],
1, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 1, 0, 1 ],
1, 0, 0, 1, 0, 1, 2 ],
1, 0, 0, 1, 1, 1, 2 ],
1, 0, 1, 0, 1, 0, 1 ],
1, 1, 0, 1, 0, 1, 2 ],
1, 1, 0, 1, 1, 1, 3 ],
1, 1, 1, 1, 1, 0, 2 ],
1, 1, 1, 1, 2, 0, 3 ],
0, 0, −1, 1, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 1, 0, 1, 1 ],
0, 0, 0, 1, 1, 0, 2 ],
0, 0, 1, 0, 1, −1, 1 ],
0, 0, 1, 1, 1, 0, 2 ],
0, 1, 0, 1, 1, 1, 2 ],
0, 1, 1, 0, 1, 0, 2 ],
0, 1, 1, 1, 1, 1, 3 ],
1, 0, 0, 1, 1, 0, 2 ],
1, 0, 0, 2, 1, 1, 3 ],
1, 0, 1, 1, 1, 0, 3 ],
1, 1, 0, 1, 1, 1, 3 ],
1, 1, 0, 2, 1, 2, 4 ],
1, 1, 1, 1, 2, 0, 3 ],
1, 1, 2, 1, 2, 0, 4 ]





CI =








b I =
Cox




0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
−1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
−1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1
















bI =
C




1
1
1
1
1
1
1
0
















BI =



0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
−1
−1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
−1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
−1
−1
−1
−1
−1
−1
−1
1
1
0
0
1
0
0
0
−1











0
0
0
−1
−1
−1
−1
0
0
0
0
0
1
0
0
0
Number of sincere Tits roots of poset I sI = 16.
Table of roots of qbI
[ −2, 1, 2, 2, 1,−1,−1, 1 ],
[ −1, 1, 2, 1, 1,−1,−1, 1 ],
[ −1, 1, 2, 2, 1,−1,−1, 1 ],
[ 1,−1,−2,−2,−1, 1, 1,−1 ],
[ 1,−1,−2,−1,−1, 1, 1,−1 ],
[ 2,−1,−2,−2,−1, 1, 1,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, −1, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, −1, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, −1, 1 ],
[ −1, 0, 2, 1, 1, −1, −1, 1 ],
[ −1, 0, 2, 1, 2, −1, −1, 1 ],
[ −1, 1, 0, 1, −1, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 1, 1, 0, −1, 0, 0 ],
[ −1, 1, 1, 1, 0, 0, −1, 1 ],
[ −1, 1, 1, 1, 1, −1, 0, 1 ],
[ −1, 1, 1, 2, 0, −1, −1, 1 ],
[ −1, 1, 2, 2, 0, −1, −1, 1 ],
[ 0, −1, −1, −1, −1, 1, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 1, −1 ],
[ 0, −1, 0, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 1, 0, 0 ],
[ 0, −1, 0, −1, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, 0, 1, 0, 0, 0 ],
[ 0, 0, −1, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, −1, −1, 1, 1, 0 ],
[ 0, 0, −1, −1, 0, 0, 1, 0 ],
[ 0, 0, −1, −1, 0, 1, 1, 0 ],
[ 0, 0, −1, 0, −1, 0, 1, 0 ],
[ 0, 0, −1, 0, −1, 1, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 1, 1, 1, 1,−1,−1, 1 ],
[ −1, 1, 2, 2, 1,−2,−1, 1 ],
[ −1, 1, 2, 2, 1,−1,−1, 2 ],
[ 1,−1,−2,−2,−1, 1, 2,−1 ],
[ 1,−1,−1,−2,−1, 1, 1,−1 ],
[ −1, −1, 1, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, −1, 0 ],
[ −1, 0, 1, 1, 0, −1, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, −1, 0, 1 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ −1, 0, 2, 1, 1, −1, 0, 1 ],
[ −1, 0, 2, 2, 1, −1, −1, 1 ],
[ −1, 1, 0, 1, 0, −1, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 0, 1 ],
[ −1, 1, 1, 1, 0, −1, 0, 1 ],
[ −1, 1, 1, 1, 0, 0, 0, 1 ],
[ −1, 1, 1, 1, 1, 0, −1, 1 ],
[ −1, 1, 1, 2, 0, −1, 0, 1 ],
[ −1, 2, 1, 2, 0, −1, −1, 1 ],
[ 0, −1, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, −1, 1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ 0, −1, 1, 0, 1, −1, 0, 0 ],
[ 0, −1, 1, 0, 1, 0, 0, 1 ],
[ 0, 0, −1, −1, −1, 1, 0, −1 ],
[ 0, 0, −1, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, −1, 0, 1, 0, −1 ],
[ 0, 0, −1, 0, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
192
[ −1, 1, 1, 2, 1,−1,−1, 1 ],
[ −1, 1, 2, 2, 1,−1,−2, 1 ],
[ 1,−1,−2,−2,−1, 1, 1,−2 ],
[ 1,−1,−2,−2,−1, 2, 1,−1 ],
[ 1,−1,−1,−1,−1, 1, 1,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, −1, 0 ],
[ −1, 0, 1, 1, 1, −1, −1, 0 ],
[ −1, 0, 1, 1, 1, 0, −1, 0 ],
[ −1, 0, 2, 1, 1, −1, −1, 0 ],
[ −1, 0, 2, 1, 1, 0, −1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, −1, 0 ],
[ −1, 1, 1, 1, 0, −1, −1, 0 ],
[ −1, 1, 1, 1, 0, 0, −1, 0 ],
[ −1, 1, 1, 1, 1, −1, −1, 0 ],
[ −1, 1, 1, 2, 0, −1, −1, 0 ],
[ −1, 1, 1, 2, 0, 0, −1, 1 ],
[ 0, −1, −1, −2, 0, 1, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 0, −1 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 1, 0, −1 ],
[ 0, −1, 0, −1, 1, 0, 0, −1 ],
[ 0, −1, 0, −1, 1, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 1, −1, 1, 0, 0, 0 ],
[ 0, −1, 1, 0, 1, 0, −1, 0 ],
[ 0, 0, −2, −1, −1, 1, 1, −1 ],
[ 0, 0, −1, −1, −1, 1, 1, −1 ],
[ 0, 0, −1, −1, 0, 0, 1, −1 ],
[ 0, 0, −1, −1, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, −1, 0, 1, −1 ],
[ 0, 0, −1, 0, −1, 1, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, −1, 0 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 1, −1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 0, 1, 0, 1, −1, −1, 0 ],
0, 0, 1, 0, 1, 0, −1, 0 ],
0, 0, 1, 1, 0, −1, −1, 0 ],
0, 0, 1, 1, 0, 0, −1, 0 ],
0, 0, 1, 1, 1, −1, −1, 0 ],
0, 0, 1, 1, 1, 0, −1, 1 ],
0, 1, −1, 0, −1, 0, 0, 0 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 1, −1, 0, 0, 0 ],
0, 1, 0, 1, 0, −1, 0, 0 ],
0, 1, 0, 1, 0, 0, −1, 1 ],
0, 1, 1, 1, 0, −1, −1, 1 ],
0, 1, 1, 1, 1, −1, −1, 1 ],
1, −1, −2, −2, 0, 1, 1, −1 ],
1, −1, −1, −2, 0, 1, 1, −1 ],
1, −1, −1, −1, −1, 1, 0, −1 ],
1, −1, −1, −1, 0, 0, 1, −1 ],
1, −1, −1, −1, 0, 1, 0, 0 ],
1, −1, 0, −1, 0, 0, 0, 0 ],
1, −1, 0, −1, 1, 0, 0, 0 ],
1, 0, −2, −1, −2, 1, 1, −1 ],
1, 0, −2, −1, −1, 1, 1, −1 ],
1, 0, −1, −1, −1, 0, 1, −1 ],
1, 0, −1, −1, −1, 1, 0, 0 ],
1, 0, −1, −1, 0, 0, 0, 0 ],
1, 0, −1, 0, −1, 0, 0, −1 ],
1, 0, −1, 0, −1, 1, 0, 0 ],
1, 0, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 1, −1, 0, 0 ],
0, 0, 1, 0, 1, 0, −1, 1 ],
0, 0, 1, 1, 0, −1, 0, 0 ],
0, 0, 1, 1, 0, 0, −1, 1 ],
0, 0, 1, 1, 1, −1, −1, 1 ],
0, 0, 2, 1, 1, −1, −1, 1 ],
0, 1, −1, 0, −1, 0, 1, 0 ],
0, 1, −1, 1, −1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 0, 1, −1, −1, 0, 0 ],
0, 1, 0, 1, −1, 0, 0, 1 ],
0, 1, 0, 1, 0, −1, 0, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
0, 1, 1, 1, 0, −1, 0, 1 ],
0, 1, 1, 2, 0, −1, −1, 1 ],
1, −1, −1, −2, 0, 0, 1, −1 ],
1, −1, −1, −2, 0, 1, 1, 0 ],
1, −1, −1, −1, −1, 1, 1, 0 ],
1, −1, −1, −1, 0, 0, 1, 0 ],
1, −1, −1, −1, 0, 1, 1, 0 ],
1, −1, 0, −1, 0, 0, 1, 0 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, −2, −1, −1, 0, 1, −1 ],
1, 0, −2, −1, −1, 1, 1, 0 ],
1, 0, −1, −1, −1, 0, 1, 0 ],
1, 0, −1, −1, −1, 1, 1, 0 ],
1, 0, −1, −1, 0, 0, 1, 0 ],
1, 0, −1, 0, −1, 0, 0, 0 ],
1, 0, −1, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 0, 0, 1, −1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 1, 0, 0, −1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 1, −1, 0, 1 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 0, 1, 1, 0, −1, 0, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 0, 1, 1, 1, −1, 0, 1 ],
0, 1, −1, 0, −1, 0, 0, −1 ],
0, 1, −1, 0, −1, 1, 0, 0 ],
0, 1, 0, 0, −1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 1, −1, 0, −1, 0 ],
0, 1, 0, 1, 0, −1, −1, 0 ],
0, 1, 0, 1, 0, 0, −1, 0 ],
0, 1, 1, 1, 0, −1, −1, 0 ],
0, 1, 1, 1, 0, 0, −1, 1 ],
1, −2, −1, −2, 0, 1, 1, −1 ],
1, −1, −1, −2, 0, 1, 0, −1 ],
1, −1, −1, −1, −1, 0, 1, −1 ],
1, −1, −1, −1, 0, 0, 0, −1 ],
1, −1, −1, −1, 0, 1, 0, −1 ],
1, −1, 0, −1, 0, 0, 0, −1 ],
1, −1, 0, −1, 0, 1, 0, 0 ],
1, 0, −2, −2, −1, 1, 1, −1 ],
1, 0, −2, −1, −1, 1, 0, −1 ],
1, 0, −1, −1, −1, 0, 0, −1 ],
1, 0, −1, −1, −1, 1, 0, −1 ],
1, 0, −1, −1, 0, 0, 0, −1 ],
1, 0, −1, −1, 0, 1, 0, 0 ],
1, 0, −1, 0, −1, 0, 1, 0 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, −1, 0 ],
1, 1, −1, 0, −1, 0, 0, 0 ]
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
∗
7
• I ≡ P102 :
6
4
5
3
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
−1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
−1
0
0
0
0
0
0





CI =








b I =
Cox




0
1
1
1
1
1
1
−1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
−1
0
0
0
0
0
1
1
1
1
1
1
1
1
















b
CI =



1
1
1
1
1
1
1
−1
1
0
0
0
0
0
0
0
















BI =



193
1
0
0
0
0
0
0
−1
0
1
1
1
1
1
1
−1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
−1
0
0
−1
0
0
0
0
0
0
1
1
0
0
0
−1
0
0
−1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
0
0
−1
−1
−1
0
0
0
0
0
0
0
1
0











0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
−1











Number of sincere Tits roots of poset I sI = 18.
Table of roots of qbI
[ −2, 1,−1,−2,−2,−1, 1,−3 ],
[ −1, 1,−1,−2,−2,−1, 2,−2 ],
[ −1, 1,−1,−1,−1,−1, 1,−2 ],
[ 1,−2, 1, 2, 2, 1,−1, 2 ],
[ 1,−1, 1, 1, 2, 1,−1, 2 ],
[ 1,−1, 1, 2, 2, 1,−1, 2 ],
[ −1, −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, −1, −1, −1, 0, 0, −2 ],
[ −1, 0, −1, 0, −1, 0, 0, −2 ],
[ −1, 0, −1, 0, −1, 1, 0, −1 ],
[ −1, 0, 0, −1, −1, −1, 0, −2 ],
[ −1, 0, 0, −1, −1, 0, 0, −2 ],
[ −1, 0, 0, −1, 0, −1, 0, −2 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1, −1 ],
[ −1, 0, 1, −1, 0, −1, 0, −1 ],
[ −1, 1, −1, −1, −2, 0, 0, −2 ],
[ −1, 1, −1, −1, −1, −1, 0, −2 ],
[ −1, 1, −1, −1, −1, 0, 1, −1 ],
[ −1, 1, 0, −2, −1, −2, 1, −2 ],
[ −1, 1, 0, −2, −1, −1, 1, −1 ],
[ −1, 1, 0, −1, −1, −1, 1, −1 ],
[ 0, −1, −1, 1, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 1, 0, 0, 0, 0 ],
[ 0, −1, 0, 1, 0, 1, 0, 1 ],
[ 0, −1, 0, 1, 1, 0, 0, 1 ],
[ 0, −1, 0, 1, 1, 1, 0, 1 ],
[ 0, −1, 1, 0, 1, −1, 0, 0 ],
[ 0, −1, 1, 0, 1, 0, 0, 1 ],
[ 0, −1, 1, 1, 1, 0, 0, 1 ],
[ 0, 0, −1, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, 0, −1, 0, 1, 0 ],
[ 0, 0, −1, 0, −1, 1, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, 1, 0, 1, 0, 1 ],
[ 0, 0, 0, −1, −1, 0, 1, −1 ],
[ 0, 0, 0, −1, 0, −1, 1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, −1, 0, −1, 0, 0 ],
[ 0, 0, 1, −1, 1, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, −1, 1 ],
[ 0, 1, −1, −1, −2, 0, 1, −1 ],
[ 0, 1, −1, −1, −1, 0, 1, −1 ],
[ 0, 1, −1, 0, −1, 0, 0, 0 ],
[ 0, 1, −1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, −1, −1, −1, 1, −1 ],
[ 0, 1, 0, −1, −1, 0, 0, 0 ],
[ 0, 1, 0, −1, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, −1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1,−1,−2,−2,−1, 1,−3 ],
[ −1, 1,−1,−2,−1,−1, 1,−2 ],
[ −1, 1,−1,−1,−1,−1, 1,−1 ],
[ 1,−1, 1, 1, 1, 1,−1, 1 ],
[ 1,−1, 1, 2, 1, 1,−1, 2 ],
[ 1,−1, 1, 2, 2, 1,−1, 3 ],
[ −1, 0, −1, −1, −2, 0, 1, −2 ],
[ −1, 0, −1, −1, −1, 0, 1, −2 ],
[ −1, 0, −1, 0, −1, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, −1, −1, −1, 1, −2 ],
[ −1, 0, 0, −1, −1, 0, 0, −1 ],
[ −1, 0, 0, −1, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 1, −2, −1, −2, 0, 1, −2 ],
[ −1, 1, −1, −1, −2, 0, 1, −2 ],
[ −1, 1, −1, −1, −1, 0, 0, −2 ],
[ −1, 1, −1, 0, −1, 0, 0, −1 ],
[ −1, 1, 0, −2, −1, −1, 0, −2 ],
[ −1, 1, 0, −1, −1, −1, 0, −2 ],
[ −1, 1, 0, −1, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 1, 0, 1, −1, 0 ],
[ 0, −1, 0, 1, 1, 0, −1, 0 ],
[ 0, −1, 0, 1, 1, 1, −1, 0 ],
[ 0, −1, 0, 2, 1, 1, −1, 1 ],
[ 0, −1, 1, 0, 1, 0, −1, 0 ],
[ 0, −1, 1, 1, 1, 0, −1, 0 ],
[ 0, −1, 1, 1, 1, 1, −1, 1 ],
[ 0, 0, −1, 0, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, 1, 0, 1, −1, 0 ],
[ 0, 0, 0, −1, −1, −1, 1, −1 ],
[ 0, 0, 0, −1, −1, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, −1, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 0, 1, 0, 1, −1, 0 ],
[ 0, 0, 0, 1, 1, 0, −1, 0 ],
[ 0, 0, 0, 1, 1, 1, −1, 1 ],
[ 0, 0, 1, −1, 0, −1, 1, 0 ],
[ 0, 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, −1, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, −1, −1, −1, −1, 1, −1 ],
[ 0, 1, −1, −1, −1, 0, 1, 0 ],
[ 0, 1, −1, 0, −1, 0, 1, 0 ],
[ 0, 1, 0, −2, −1, −1, 1, −1 ],
[ 0, 1, 0, −1, −1, −1, 1, 0 ],
[ 0, 1, 0, −1, −1, 0, 1, 0 ],
[ 0, 1, 0, −1, 0, −1, 1, 0 ],
[ 0, 1, 0, 0, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
194
[ −1, 1,−1,−2,−2,−1, 1,−2 ],
[ −1, 1,−1,−1,−2,−1, 1,−2 ],
[ −1, 2,−1,−2,−2,−1, 1,−2 ],
[ 1,−1, 1, 1, 1, 1,−1, 2 ],
[ 1,−1, 1, 2, 2, 1,−2, 2 ],
[ 2,−1, 1, 2, 2, 1,−1, 3 ],
[ −1, 0, −1, −1, −1, −1, 1, −2 ],
[ −1, 0, −1, −1, −1, 0, 1, −1 ],
[ −1, 0, −1, 0, −1, 0, 1, −1 ],
[ −1, 0, 0, −2, −1, −1, 1, −2 ],
[ −1, 0, 0, −1, −1, −1, 1, −1 ],
[ −1, 0, 0, −1, −1, 0, 1, −1 ],
[ −1, 0, 0, −1, 0, −1, 1, −1 ],
[ −1, 0, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, −1, −2, −2, 0, 1, −2 ],
[ −1, 1, −1, −1, −2, 0, 1, −1 ],
[ −1, 1, −1, −1, −1, 0, 0, −1 ],
[ −1, 1, 0, −2, −2, −1, 1, −2 ],
[ −1, 1, 0, −2, −1, −1, 1, −2 ],
[ −1, 1, 0, −1, −1, −1, 0, −1 ],
[ −1, 1, 0, −1, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ 0, −1, 0, 1, 0, 1, 0, 0 ],
[ 0, −1, 0, 1, 1, 0, 0, 0 ],
[ 0, −1, 0, 1, 1, 1, −1, 1 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, 0, 1, 0, 0, 0 ],
[ 0, −1, 1, 1, 1, 0, −1, 1 ],
[ 0, −1, 1, 1, 2, 0, −1, 1 ],
[ 0, 0, −1, 0, −1, 0, 1, −1 ],
[ 0, 0, −1, 0, −1, 1, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 1, −1, 1, 0, 0 ],
[ 0, 0, −1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, −1, 1 ],
[ 0, 0, 0, 1, 1, 0, −1, 1 ],
[ 0, 0, 1, −1, 0, −1, 0, −1 ],
[ 0, 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 0, 1, 0, 1, −1, −1, 0 ],
[ 0, 0, 1, 0, 1, 0, −1, 0 ],
[ 0, 0, 1, 1, 1, 0, −1, 1 ],
[ 0, 1, −1, −1, −1, 0, 0, −1 ],
[ 0, 1, −1, 0, −1, 0, 0, −1 ],
[ 0, 1, −1, 0, −1, 1, 0, 0 ],
[ 0, 1, 0, −1, −1, −1, 0, −1 ],
[ 0, 1, 0, −1, −1, 0, 0, −1 ],
[ 0, 1, 0, −1, 0, −1, 0, −1 ],
[ 0, 1, 0, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, −1, 0 ],
[ 0, 1, 1, −1, 0, −1, 0, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
1, −1,
1, −1,
1, −1,
1, −1,
1, −1,
1, −1,
1, −1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
0,
0,
0,
0,
1,
1,
1,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
2,
2,
1,
1,
2,
0,
0,
1,
1,
1,
2,
0,
1,
1,
0,
1,
1,
2,
1,
2,
2,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1, 0,
1, 0,
1, −1,
1, −1,
0, 0,
0, −1,
0, −1,
0, 0,
1, 0,
1, −1,
0, −1,
1, −1,
1, −1,
0, −1,
0, −1,
1, −1,
1 ],
1 ],
2 ],
2 ],
1 ],
1 ],
2 ],
0 ],
1 ],
1 ],
1 ],
1 ],
2 ],
1 ],
1 ],
2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
1, −1,
1, −1,
1, −1,
1, −1,
1, −1,
1, −1,
1, −1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
0,
0,
0,
1,
1,
1,
2,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
2,
0,
1,
1,
1,
0,
0,
1,
1,
1,
0,
0,
1,
1,
1,
1,
1,
1,
1,
2,
2,
0,
1,
0,
1,
1,
0,
1,
1,
2,
0, 0,
1, 0,
1, 0,
0, 0,
0, 0,
0, −1,
0, −1,
0, 0,
0, 0,
1, 0,
0, 0,
1, −1,
0, 0,
0, 0,
0, −1,
0, −1,
1 ],
2 ],
2 ],
1 ],
2 ],
2 ],
2 ],
1 ],
1 ],
1 ],
1 ],
2 ],
1 ],
1 ],
2 ],
2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
1, −1, 0,
1, −1, 0,
1, −1, 0,
1, −1, 1,
1, −1, 1,
1, −1, 1,
1, 0, −1,
1, 0, 0,
1, 0, 0,
1, 0, 0,
1, 0, 0,
1, 0, 0,
1, 0, 1,
1, 0, 1,
1, 0, 1,
1, 1, 0,
1,
2,
2,
1,
1,
1,
1,
0,
1,
1,
1,
1,
0,
0,
1,
0,
1, 1, −1,
1, 1, −1,
1, 2, −1,
1, 0, −1,
1, 1, 0,
2, 0, 0,
0, 1, 0,
0, 0, 1,
0, 0, 0,
0, 1, 0,
1, 0, 0,
1, 1, 0,
1, −1, 0,
1, 0, 0,
1, 0, 0,
0, 0, 0,
1
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1 ],
1 ],
2 ],
1 ],
2 ],
2 ],
1 ],
1 ],
1 ],
2 ],
2 ],
2 ],
1 ],
2 ],
2 ],
1]
∗
• I ≡ P103 :
7
5
6
4
2
3
1





CI =








b I =
Cox




0
0
1
0
0
1
0
−1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
−1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
−1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
















b
CI =



1
1
1
1
1
1
1
−1
















BI =



0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
−1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
−1
0
−1
0
0
0
0
−1
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
1
0
0
1
0
−1











−1
−1
0
−1
−1
0
−1
1
1
0
1
0
0
0
0
−1
Number of sincere Tits roots of poset I sI = 18.
Table of roots of qbI
[ −2, 1, 1, 2, 2, 1, 1, 3 ],
[ −1, 1, 1, 1, 2, 1, 1, 3 ],
[ −1, 1, 1, 2, 2, 1, 1, 4 ],
[ 1,−1,−2,−2,−2,−1,−1,−4 ],
[ 1,−1,−1,−2,−2,−1,−1,−3 ],
[ 1,−1,−1,−1,−1,−1,−1,−3 ],
[ −1, −1, 0, 0, 1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 0, 1, 1 ],
[ −1, 0, 1, 1, 1, 0, 1, 2 ],
[ −1, 1, 1, 1, 1, 1, 1, 2 ],
[ −1, 1, 1, 2, 1, 1, 1, 3 ],
[ −1, 1, 1, 2, 2, 2, 1, 4 ],
[ 1,−1,−1,−2,−2,−2,−1,−4 ],
[ 1,−1,−1,−2,−1,−1,−1,−3 ],
[ 1,−1,−1,−1,−1,−1,−1,−2 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 2 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 1, 2 ],
195
[ −1, 1, 1, 1, 1, 1, 1, 3 ],
[ −1, 1, 1, 2, 2, 1, 1, 3 ],
[ −1, 1, 2, 2, 2, 1, 1, 4 ],
[ 1,−1,−1,−2,−2,−1,−1,−4 ],
[ 1,−1,−1,−1,−2,−1,−1,−3 ],
[ 2,−1,−1,−2,−2,−1,−1,−3 ],
[ −1, 0, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 1, 1 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 2, 1, 1, 2 ],
[ −1, 0, 1, 1, 1, 0, 1, 1 ],
[ −1, 0, 1, 1, 2, 0, 1, 2 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, 1, 1, 2, 1, 1, 2 ],
−1, 0, 1, 2, 2, 1, 1, 3 ],
−1, 1, 0, 1, 0, 0, 0, 0 ],
−1, 1, 0, 1, 1, 0, 0, 1 ],
−1, 1, 0, 1, 1, 1, 1, 2 ],
−1, 1, 1, 1, 1, 0, 0, 1 ],
−1, 1, 1, 1, 1, 1, 0, 2 ],
−1, 1, 1, 2, 1, 1, 0, 3 ],
0, −1, −1, −2, −1, −1, 0, −3 ],
0, −1, −1, −1, −1, −1, 0, −2 ],
0, −1, −1, −1, 0, 0, 0, −2 ],
0, −1, −1, 0, 0, 0, 0, −1 ],
0, −1, 0, −1, 0, −1, 0, −1 ],
0, −1, 0, −1, 0, 0, 1, −1 ],
0, −1, 0, 0, 0, −1, 0, −1 ],
0, −1, 0, 0, 0, 0, 1, 0 ],
0, −1, 0, 0, 1, 0, 1, 1 ],
0, 0, −1, −1, −2, −1, −1, −3 ],
0, 0, −1, −1, −1, −1, 0, −2 ],
0, 0, −1, −1, −1, 0, 0, −1 ],
0, 0, −1, 0, −1, 0, −1, −2 ],
0, 0, −1, 0, 0, 0, −1, −1 ],
0, 0, −1, 0, 0, 1, 0, 0 ],
0, 0, 0, −1, −1, −1, 0, −1 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, 0, −1, −1, −1, −2 ],
0, 0, 0, 0, −1, 0, −1, −1 ],
0, 0, 0, 0, 0, −1, −1, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 0, 1, 1, 0, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 0, 1, 0, 1, 0, 1 ],
0, 0, 0, 1, 1, 1, 0, 2 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 0, 1, 0, 1, 1, 1, 2 ],
0, 0, 1, 1, 1, 0, 0, 2 ],
0, 0, 1, 1, 1, 1, 1, 2 ],
0, 1, −1, 0, −1, 0, −1, −1 ],
0, 1, 0, 0, −1, 0, −1, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 1, −1, 0, −1, 0 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
0, 1, 0, 1, 0, 1, 0, 2 ],
0, 1, 1, 1, 0, 0, −1, 1 ],
0, 1, 1, 1, 0, 1, 0, 2 ],
0, 1, 1, 1, 1, 1, 0, 3 ],
1, −2, −1, −2, −1, −1, 0, −3 ],
1, −1, −1, −2, −1, −1, 0, −2 ],
1, −1, −1, −1, −1, 0, −1, −2 ],
1, −1, −1, −1, 0, 0, 0, −1 ],
1, −1, 0, −1, −1, −1, 0, −2 ],
1, −1, 0, −1, 0, −1, 0, −1 ],
1, −1, 0, −1, 0, 0, 1, 0 ],
1, 0, −1, −1, −2, −1, −2, −3 ],
1, 0, −1, −1, −2, 0, −1, −2 ],
1, 0, −1, −1, −1, 0, −1, −1 ],
1, 0, 0, −1, −2, −1, −1, −2 ],
1, 0, 0, −1, −1, −1, 0, −1 ],
1, 0, 0, −1, −1, 0, 0, 0 ],
1, 0, 0, 0, −1, 0, −1, −1 ],
1, 0, 0, 0, 0, 0, −1, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, 1, 1, 2, 1, 1, 3 ],
−1, 1, 0, 0, 0, 0, 0, 0 ],
−1, 1, 0, 1, 0, 0, 0, 1 ],
−1, 1, 0, 1, 1, 1, 0, 1 ],
−1, 1, 0, 2, 1, 1, 0, 2 ],
−1, 1, 1, 1, 1, 0, 0, 2 ],
−1, 1, 1, 2, 1, 0, 0, 2 ],
−1, 1, 1, 2, 2, 1, 0, 3 ],
0, −1, −1, −1, −1, −1, −1, −3 ],
0, −1, −1, −1, −1, 0, 0, −2 ],
0, −1, −1, −1, 0, 0, 0, −1 ],
0, −1, 0, −1, −1, −1, 0, −2 ],
0, −1, 0, −1, 0, −1, 1, −1 ],
0, −1, 0, −1, 0, 0, 1, 0 ],
0, −1, 0, 0, 0, 0, 0, −1 ],
0, −1, 0, 0, 1, 0, 0, 0 ],
0, −1, 0, 0, 1, 1, 1, 1 ],
0, 0, −1, −1, −1, −1, −1, −3 ],
0, 0, −1, −1, −1, 0, −1, −2 ],
0, 0, −1, −1, 0, 0, 0, −1 ],
0, 0, −1, 0, −1, 0, −1, −1 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, 0, −1, −1, −1, −1, −2 ],
0, 0, 0, −1, −1, 0, 0, −1 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, 0, −1, −1, −1, −1 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 0, 1, 1, 1, 1 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 0, 1, 1, 0, 0, 1 ],
0, 0, 0, 1, 1, 1, 1, 2 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 1, 0, 1, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 0, 1, 1, 1, 0, 1, 2 ],
0, 0, 1, 1, 1, 1, 1, 3 ],
0, 1, 0, 0, −1, −1, −1, −1 ],
0, 1, 0, 0, −1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 1, 0, 0, −1, 0 ],
0, 1, 0, 1, 0, 1, −1, 1 ],
0, 1, 0, 1, 1, 1, 0, 2 ],
0, 1, 1, 1, 0, 0, 0, 1 ],
0, 1, 1, 1, 1, 0, 0, 2 ],
0, 1, 1, 1, 1, 1, 1, 3 ],
1, −1, −1, −2, −2, −1, 0, −3 ],
1, −1, −1, −2, −1, 0, 0, −2 ],
1, −1, −1, −1, −1, 0, 0, −2 ],
1, −1, 0, −2, −1, −1, 0, −2 ],
1, −1, 0, −1, −1, −1, 0, −1 ],
1, −1, 0, −1, 0, 0, 0, −1 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, −1, −1, −2, −1, −1, −3 ],
1, 0, −1, −1, −1, −1, −1, −2 ],
1, 0, −1, −1, −1, 0, 0, −1 ],
1, 0, 0, −1, −1, −1, −1, −2 ],
1, 0, 0, −1, −1, 0, −1, −1 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, −1, 0, −1, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
196
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, 1, 1, 2, 1, 2, 3 ],
−1, 1, 0, 1, 0, 0, −1, 0 ],
−1, 1, 0, 1, 0, 1, 0, 1 ],
−1, 1, 0, 1, 1, 1, 0, 2 ],
−1, 1, 1, 1, 0, 0, 0, 1 ],
−1, 1, 1, 1, 1, 0, 1, 2 ],
−1, 1, 1, 2, 1, 1, 0, 2 ],
−1, 2, 1, 2, 1, 1, 0, 3 ],
0, −1, −1, −1, −1, −1, 0, −3 ],
0, −1, −1, −1, 0, −1, 0, −2 ],
0, −1, −1, −1, 0, 0, 1, −1 ],
0, −1, 0, −1, 0, −1, 0, −2 ],
0, −1, 0, −1, 0, 0, 0, −1 ],
0, −1, 0, −1, 1, 0, 1, 0 ],
0, −1, 0, 0, 0, 0, 0, 0 ],
0, −1, 0, 0, 1, 0, 1, 0 ],
0, −1, 1, 0, 1, 0, 1, 1 ],
0, 0, −1, −1, −1, −1, −1, −2 ],
0, 0, −1, −1, −1, 0, 0, −2 ],
0, 0, −1, 0, −1, −1, −1, −2 ],
0, 0, −1, 0, −1, 0, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, 0, −1, −1, −1, 0, −2 ],
0, 0, 0, −1, 0, −1, 0, −1 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, −1, 0, −1 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 1, 1 ],
0, 0, 0, 0, 1, 0, 1, 1 ],
0, 0, 0, 0, 1, 1, 1, 2 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 1, 1, 0, 1 ],
0, 0, 1, 0, 0, −1, 0, 0 ],
0, 0, 1, 0, 0, 0, 1, 1 ],
0, 0, 1, 0, 1, 0, 1, 2 ],
0, 0, 1, 1, 1, 0, 0, 1 ],
0, 0, 1, 1, 1, 1, 0, 2 ],
0, 0, 1, 1, 2, 1, 1, 3 ],
0, 1, 0, 0, −1, 0, −1, −1 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 0, 0, 0, 1, 0, 1 ],
0, 1, 0, 1, 0, 0, −1, 1 ],
0, 1, 0, 1, 0, 1, 0, 1 ],
0, 1, 1, 0, 0, 0, 0, 1 ],
0, 1, 1, 1, 0, 0, 0, 2 ],
0, 1, 1, 1, 1, 1, 0, 2 ],
0, 1, 1, 2, 1, 1, 0, 3 ],
1, −1, −1, −2, −1, −1, 0, −3 ],
1, −1, −1, −1, −1, −1, 0, −2 ],
1, −1, −1, −1, −1, 0, 0, −1 ],
1, −1, 0, −1, −1, −1, −1, −2 ],
1, −1, 0, −1, −1, 0, 0, −1 ],
1, −1, 0, −1, 0, 0, 0, 0 ],
1, 0, −1, −2, −2, −1, −1, −3 ],
1, 0, −1, −1, −2, −1, −1, −2 ],
1, 0, −1, −1, −1, 0, −1, −2 ],
1, 0, −1, 0, −1, 0, −1, −1 ],
1, 0, 0, −1, −1, −1, −1, −1 ],
1, 0, 0, −1, −1, 0, 0, −1 ],
1, 0, 0, 0, −1, −1, −1, −1 ],
1, 0, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 1, 0, 0, −1, 0, −1, 0 ]
∗
7
• I ≡ P104 :
6
5
4
3
2
1





CI =








b
CoxI =



0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
−1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
−1
0
0
0
0
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
1
1
1
1
1
1
1
0
















BI =



0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
−1
−1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
−1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
1
1
1
0
0
−1
−1
−1
−1
−1
−1
−1
−1
1
1
1
0
1
0
0
0
0











0
−1
0
−1
0
0
0
0
1
1
1
1
0
1
0
−1
Number of sincere Tits roots of poset I sI = 16.
Table of roots of qbI
[ −2,−1, 1, 2, 2, 1,−1, 1 ],
[ −1,−1, 1, 1, 2, 1,−1, 1 ],
[ −1,−1, 1, 2, 2, 1,−1, 1 ],
[ 1, 1,−1,−2,−2,−1, 1,−1 ],
[ 1, 1,−1,−1,−2,−1, 1,−1 ],
[ 2, 1,−1,−2,−2,−1, 1,−1 ],
[ −1, −1, 0, 1, 1, 1, −1, 0 ],
[ −1, −1, 0, 1, 2, 1, −1, 0 ],
[ −1, −1, 0, 1, 2, 2, −1, 1 ],
[ −1, −1, 1, 1, 1, 0, −1, 0 ],
[ −1, −1, 1, 1, 1, 1, −1, 0 ],
[ −1, −1, 1, 2, 1, 0, −1, 1 ],
[ −1, −1, 2, 2, 1, 0, −1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, −1, 1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, −1, 1 ],
[ −1, 0, 1, 2, 1, 0, −1, 1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 0, 0 ],
[ 0, −1, 0, 1, 1, 0, −1, 0 ],
[ 0, −1, 0, 1, 1, 1, −1, 0 ],
[ −1,−2, 1, 2, 2, 1,−1, 1 ],
[ −1,−1, 1, 2, 1, 1,−1, 1 ],
[ −1,−1, 1, 2, 2, 1,−1, 2 ],
[ 1, 1,−1,−2,−2,−1, 2,−1 ],
[ 1, 1,−1,−1,−1,−1, 1,−1 ],
[ −1, −1, 0, 0, 1, 1, 0, 0 ],
[ −1, −1, 0, 1, 1, 1, 0, 0 ],
[ −1, −1, 0, 1, 2, 1, −1, 1 ],
[ −1, −1, 0, 2, 2, 1, −1, 1 ],
[ −1, −1, 1, 1, 1, 0, 0, 0 ],
[ −1, −1, 1, 1, 1, 1, 0, 1 ],
[ −1, −1, 1, 2, 1, 0, 0, 1 ],
[ −1, 0, −1, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 1, 1, −1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 1, 1, 0, −1, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 0, 1 ],
[ 0, −1, 0, 1, 1, 0, 0, 0 ],
[ 0, −1, 0, 1, 1, 1, −1, 1 ],
197
[ −1,−1, 1, 1, 1, 1,−1, 1 ],
[ −1,−1, 1, 2, 2, 1,−2, 1 ],
[ 1, 1,−1,−2,−2,−1, 1,−2 ],
[ 1, 1,−1,−2,−1,−1, 1,−1 ],
[ 1, 2,−1,−2,−2,−1, 1,−1 ],
[ −1, −1, 0, 1, 1, 0, 0, 0 ],
[ −1, −1, 0, 1, 1, 1, 0, 1 ],
[ −1, −1, 0, 1, 2, 1, 0, 1 ],
[ −1, −1, 1, 1, 0, 0, 0, 0 ],
[ −1, −1, 1, 1, 1, 0, 0, 1 ],
[ −1, −1, 1, 2, 1, 0, −1, 0 ],
[ −1, −1, 1, 2, 2, 0, −1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, −1, 0 ],
[ −1, 0, 0, 1, 1, 1, −1, 0 ],
[ −1, 0, 0, 1, 2, 1, −1, 1 ],
[ −1, 0, 1, 1, 0, 0, −1, 0 ],
[ −1, 0, 1, 1, 1, 0, −1, 0 ],
[ −1, 0, 1, 1, 1, 1, −1, 1 ],
[ 0, −1, −1, 0, 1, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, 1, 1, −1, 0 ],
[ 0, −1, 0, 1, 0, 0, 0, 0 ],
[ 0, −1, 0, 1, 1, 0, 0, 1 ],
[ 0, −1, 0, 1, 1, 1, 0, 1 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 0, 1, 2, 1, −1, 1 ],
0, −1, 1, 1, 0, 0, −1, 0 ],
0, −1, 1, 1, 1, 0, −1, 0 ],
0, −1, 1, 1, 1, 1, −1, 1 ],
0, 0, −1, −1, 0, 0, 0, −1 ],
0, 0, −1, −1, 0, 1, 0, −1 ],
0, 0, −1, −1, 1, 1, 0, 0 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, −1, 0, 1, 1, −1, 0 ],
0, 0, 0, −1, −1, −1, 1, −1 ],
0, 0, 0, −1, −1, 0, 1, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, −1, 1, −1 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 0, 1, 1, −1, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 0, 1, 1, 0, −1, 0 ],
0, 0, 0, 1, 1, 1, −1, 1 ],
0, 0, 1, 0, −1, −1, 1, 0 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 0, 1, 1, −1, −1, 0, 0 ],
0, 0, 1, 1, 0, −1, 0, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 1, −1, −1, −1, −1, 1, −1 ],
0, 1, −1, −1, −1, 0, 1, 0 ],
0, 1, −1, −1, 0, 0, 1, 0 ],
0, 1, 0, −1, −2, −1, 1, −1 ],
0, 1, 0, −1, −1, −1, 1, 0 ],
0, 1, 0, −1, −1, 0, 1, 0 ],
0, 1, 0, 0, −1, −1, 0, 0 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
1, 0, −1, −2, −1, 0, 1, −1 ],
1, 0, −1, −1, −1, 0, 1, −1 ],
1, 0, −1, −1, 0, 0, 0, 0 ],
1, 0, −1, 0, 0, 0, 0, 0 ],
1, 0, 0, −1, −1, −1, 1, −1 ],
1, 0, 0, −1, −1, 0, 0, 0 ],
1, 0, 0, 0, −1, −1, 0, −1 ],
1, 0, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 1, −2, −2, −1, 0, 1, −1 ],
1, 1, −1, −2, −1, 0, 1, −1 ],
1, 1, −1, −1, −1, −1, 1, 0 ],
1, 1, −1, −1, −1, 0, 1, 0 ],
1, 1, 0, −1, −2, −2, 1, −1 ],
1, 1, 0, −1, −2, −1, 1, 0 ],
1, 1, 0, −1, −1, −1, 1, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 1, 0, 0, 0, 0, 0 ],
0, −1, 1, 1, 0, 0, 0, 0 ],
0, −1, 1, 1, 1, 0, −1, 1 ],
0, −1, 1, 2, 1, 0, −1, 1 ],
0, 0, −1, −1, 0, 0, 1, −1 ],
0, 0, −1, −1, 0, 1, 0, 0 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 1, 0, 0 ],
0, 0, −1, 0, 1, 1, 0, 0 ],
0, 0, 0, −1, −1, 0, 0, −1 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 1, 0, 0 ],
0, 0, 0, 0, −1, −1, 1, 0 ],
0, 0, 0, 0, −1, 0, 1, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 0, 1, 1, 0, 1 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 0, 1, 1, 0, −1, 1 ],
0, 0, 1, 0, −1, −1, 0, −1 ],
0, 0, 1, 0, −1, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 1, 0, −1, −1, 0 ],
0, 0, 1, 1, 0, 0, −1, 0 ],
0, 0, 1, 1, 1, 0, −1, 1 ],
0, 1, −1, −1, −1, 0, 0, −1 ],
0, 1, −1, −1, 0, 0, 0, −1 ],
0, 1, −1, −1, 0, 1, 0, 0 ],
0, 1, 0, −1, −1, −1, 0, −1 ],
0, 1, 0, −1, −1, 0, 0, −1 ],
0, 1, 0, −1, 0, 0, 0, 0 ],
0, 1, 0, 0, −1, −1, 1, 0 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 1, 0, −1, −1, 0, 0 ],
1, 0, −1, −1, −1, −1, 1, −1 ],
1, 0, −1, −1, −1, 0, 1, 0 ],
1, 0, −1, −1, 0, 0, 1, 0 ],
1, 0, 0, −1, −2, −1, 1, −1 ],
1, 0, 0, −1, −1, −1, 1, 0 ],
1, 0, 0, −1, −1, 0, 1, 0 ],
1, 0, 0, 0, −1, −1, 0, 0 ],
1, 0, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 1, −1, −2, −2, 0, 1, −1 ],
1, 1, −1, −2, −1, 0, 1, 0 ],
1, 1, −1, −1, −1, 0, 0, −1 ],
1, 1, −1, −1, 0, 0, 0, 0 ],
1, 1, 0, −1, −2, −1, 0, −1 ],
1, 1, 0, −1, −1, −1, 0, −1 ],
1, 1, 0, −1, −1, 0, 0, 0 ],
∗
• I ≡ P105 :
7
6
4
3
5
2
1
198
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 1, 1, 0, −1, 0, 0 ],
0, −1, 1, 1, 0, 0, 0, 1 ],
0, −1, 1, 1, 1, 0, 0, 1 ],
0, 0, −1, −1, −1, 0, 1, −1 ],
0, 0, −1, −1, 0, 0, 1, 0 ],
0, 0, −1, −1, 0, 1, 1, 0 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, −1, 0, 1, 0, 0, 0 ],
0, 0, −1, 0, 1, 1, 0, 1 ],
0, 0, 0, −1, −1, 0, 1, −1 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, 0, −1, −1, 0, −1 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 0, 1, 1, −1, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 1, 0, 0, 1 ],
0, 0, 1, 0, −1, −1, 0, 0 ],
0, 0, 1, 0, 0, −1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 1, 0, −1, 0, 0 ],
0, 0, 1, 1, 0, 0, −1, 1 ],
0, 1, −1, −2, −1, 0, 1, −1 ],
0, 1, −1, −1, −1, 0, 1, −1 ],
0, 1, −1, −1, 0, 0, 0, 0 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, 0, −1, −1, −1, 1, −1 ],
0, 1, 0, −1, −1, 0, 0, 0 ],
0, 1, 0, 0, −1, −1, 0, −1 ],
0, 1, 0, 0, −1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, −1, −1, −1, 0, 0, −1 ],
1, 0, −1, −1, 0, 0, 0, −1 ],
1, 0, −1, −1, 0, 1, 0, 0 ],
1, 0, 0, −1, −1, −1, 0, −1 ],
1, 0, 0, −1, −1, 0, 0, −1 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, −1, −1, 1, 0 ],
1, 0, 0, 0, 0, 0, −1, 0 ],
1, 0, 1, 0, −1, −1, 0, 0 ],
1, 1, −1, −2, −1, 0, 0, −1 ],
1, 1, −1, −1, −1, −1, 0, −1 ],
1, 1, −1, −1, −1, 0, 0, 0 ],
1, 1, 0, −2, −2, −1, 1, −1 ],
1, 1, 0, −1, −2, −1, 1, −1 ],
1, 1, 0, −1, −1, −1, 0, 0 ],
1, 1, 0, 0, −1, −1, 0, 0 ]





CI =








b I =
Cox




0
0
0
0
1
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
−1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
−1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
















BI =



1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
−1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
−1
0
0
0
−1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
−1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
−1
−1
0
0
−1
0
0











0
−1
0
−1
0
0
0
0
0
0
0
0
0
0
0
−1
Number of sincere Tits roots of poset I sI = 18.
Table of roots of qbI
[ −2,−1, 1, 2, 1, 2, 1, 2 ],
[ −1,−1, 1, 1, 1, 1, 1, 2 ],
[ −1,−1, 1, 2, 1, 2, 1, 2 ],
[ 1, 1,−1,−2,−2,−2,−1,−3 ],
[ 1, 1,−1,−2,−1,−1,−1,−2 ],
[ 1, 1,−1,−1,−1,−1,−1,−1 ],
[ −1, −1, 0, 0, 0, 1, 1, 0 ],
[ −1, −1, 0, 1, 0, 1, 1, 1 ],
[ −1, −1, 0, 1, 1, 2, 1, 1 ],
[ −1, −1, 0, 2, 1, 2, 1, 2 ],
[ −1, −1, 1, 1, 0, 1, 0, 1 ],
[ −1, −1, 1, 2, 0, 1, 0, 1 ],
[ −1, −1, 1, 2, 1, 2, 0, 2 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 2, 1, 2 ],
[ −1, 0, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 1, 2 ],
[ 0, −1, −1, 0, 0, 1, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 1, 1, 0 ],
[ 0, −1, 0, 1, 0, 0, 0, 0 ],
[ 0, −1, 0, 1, 0, 1, 1, 1 ],
[ 0, −1, 0, 1, 1, 1, 1, 2 ],
[ 0, −1, 1, 1, 0, 0, −1, 0 ],
[ 0, −1, 1, 1, 0, 1, 0, 1 ],
[ 0, −1, 1, 1, 1, 1, 0, 2 ],
[ 0, 0, −1, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, −1, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, 1, 1, 1, 1 ],
[ 0, 0, 0, −1, −1, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1, −2 ],
[ 0, 0, 0, 0, −1, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ −1,−2, 1, 2, 1, 2, 1, 2 ],
[ −1,−1, 1, 1, 1, 2, 1, 2 ],
[ −1,−1, 1, 2, 1, 2, 1, 3 ],
[ 1, 1,−1,−2,−1,−2,−1,−3 ],
[ 1, 1,−1,−1,−1,−2,−1,−2 ],
[ 1, 2,−1,−2,−1,−2,−1,−2 ],
[ −1, −1, 0, 1, 0, 1, 0, 0 ],
[ −1, −1, 0, 1, 0, 2, 1, 1 ],
[ −1, −1, 0, 1, 1, 2, 1, 2 ],
[ −1, −1, 1, 1, 0, 0, 0, 0 ],
[ −1, −1, 1, 1, 0, 1, 1, 1 ],
[ −1, −1, 1, 2, 1, 1, 0, 1 ],
[ −1, −1, 2, 2, 1, 1, 0, 2 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 1, 0, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 0, 1 ],
[ −1, 0, 1, 2, 1, 1, 0, 2 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 1, 1, 1 ],
[ 0, −1, 0, 1, 0, 1, 0, 0 ],
[ 0, −1, 0, 1, 1, 1, 0, 1 ],
[ 0, −1, 0, 1, 1, 2, 1, 2 ],
[ 0, −1, 1, 1, 0, 0, 0, 0 ],
[ 0, −1, 1, 1, 1, 0, 0, 1 ],
[ 0, −1, 1, 1, 1, 1, 1, 2 ],
[ 0, 0, −1, −1, −1, 0, 0, −2 ],
[ 0, 0, −1, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, −1, 0, 1, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 1, 1, 0 ],
[ 0, 0, 0, −1, −1, −1, −1, −2 ],
[ 0, 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, −1, −1, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
199
[ −1,−1, 1, 1, 1, 1, 1, 1 ],
[ −1,−1, 1, 2, 1, 1, 1, 2 ],
[ −1,−1, 1, 2, 2, 2, 1, 3 ],
[ 1, 1,−1,−2,−1,−2,−1,−2 ],
[ 1, 1,−1,−1,−1,−1,−1,−2 ],
[ 2, 1,−1,−2,−1,−2,−1,−2 ],
[ −1, −1, 0, 1, 0, 1, 1, 0 ],
[ −1, −1, 0, 1, 1, 1, 1, 1 ],
[ −1, −1, 0, 1, 1, 2, 2, 2 ],
[ −1, −1, 1, 1, 0, 1, 0, 0 ],
[ −1, −1, 1, 1, 1, 1, 0, 1 ],
[ −1, −1, 1, 2, 1, 1, 0, 2 ],
[ −1, 0, −1, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 2 ],
[ −1, 0, 1, 1, 0, 0, −1, 0 ],
[ −1, 0, 1, 1, 0, 1, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 0, 2 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 1, 1 ],
[ 0, −1, 0, 1, 0, 1, 0, 1 ],
[ 0, −1, 0, 1, 1, 1, 1, 1 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, 1, 0, 0, 0, 1 ],
[ 0, −1, 1, 1, 1, 1, 0, 1 ],
[ 0, −1, 1, 2, 1, 1, 0, 2 ],
[ 0, 0, −1, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, −1, 0, 0, 1, −1 ],
[ 0, 0, −1, 0, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, −1, −1, −1, 0, −2 ],
[ 0, 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 0, 1, 1, 0, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 0, 1, 0, 1, 0, 1 ],
0, 0, 0, 1, 1, 1, 0, 2 ],
0, 0, 1, 0, 0, −1, −1, −1 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 0, 1, 1, 0, 0, −1, 1 ],
0, 0, 1, 1, 1, 0, 0, 1 ],
0, 1, −1, −2, −1, −1, 0, −2 ],
0, 1, −1, −1, −1, −1, 0, −1 ],
0, 1, −1, −1, 0, 0, 0, −1 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, 0, −1, −1, −1, −1, −1 ],
0, 1, 0, −1, 0, −1, 0, −1 ],
0, 1, 0, 0, −1, −1, −1, −1 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, −1, −1, −1, −1, 0, −2 ],
1, 0, −1, −1, 0, −1, 0, −1 ],
1, 0, −1, −1, 0, 0, 1, 0 ],
1, 0, 0, −1, −1, −1, −1, −2 ],
1, 0, 0, −1, 0, −1, −1, −1 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, −1, −1, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 1, 0, 0, −1, −1, 0 ],
1, 1, −1, −2, −1, −1, 0, −2 ],
1, 1, −1, −1, −1, −1, 0, −1 ],
1, 1, −1, −1, 0, −1, 0, 0 ],
1, 1, 0, −1, −1, −2, −2, −2 ],
1, 1, 0, −1, −1, −1, −1, −1 ],
1, 1, 0, −1, 0, −1, −1, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 1, 1, 1 ],
0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 1, 0, 0, 1 ],
0, 0, 1, 1, 1, 1, 2 ],
0, 1, 0, 0, −1, −1, 0 ],
0, 1, 0, 0, 0, 0, 0 ],
0, 1, 1, 0, −1, −1, 0 ],
0, 1, 1, 0, 0, 0, 1 ],
0, 1, 1, 1, 0, 0, 2 ],
1, −1, −1, −1, −1, −1, −2 ],
1, −1, −1, −1, 0, 0, −1 ],
1, −1, −1, 0, 0, 0, 0 ],
1, 0, −1, −1, −2, −1, −2 ],
1, 0, −1, −1, −1, 0, −1 ],
1, 0, −1, 0, −1, 0, 0 ],
1, 0, 0, 0, −1, −1, −1 ],
1, 0, 0, 0, 0, −1, 0 ],
1, 0, 0, 1, 0, 0, 1 ],
0, −1, −2, −1, −1, 0, −2 ],
0, −1, −1, −1, −1, 0, −1 ],
0, −1, −1, 0, 0, 0, −1 ],
0, −1, 0, 0, 0, 0, 0 ],
0, 0, −1, −1, −1, −1, −1 ],
0, 0, −1, 0, −1, 0, −1 ],
0, 0, 0, −1, −1, −1, −1 ],
0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, 1 ],
1, −2, −2, −1, −1, 0, −2 ],
1, −1, −2, −1, −1, 0, −1 ],
1, −1, −1, 0, −1, −1, −1 ],
1, −1, −1, 0, 0, 0, 0 ],
1, 0, −1, −1, −2, −1, −2 ],
1, 0, −1, 0, −2, −1, −1 ],
1, 0, −1, 0, −1, 0, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, 0, 0, 0, 1, 1, 1 ],
0, 0, 0, 1, 0, 1, 1 ],
0, 0, 0, 1, 1, 1, 2 ],
0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 1, 1, 0, 1 ],
0, 1, 0, −1, −1, −1, −1 ],
0, 1, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 1 ],
0, 1, 1, 0, 0, −1, 0 ],
0, 1, 1, 1, 0, −1, 1 ],
0, 1, 1, 1, 1, 0, 2 ],
1, −1, −1, −1, −1, 0, −2 ],
1, −1, −1, 0, −1, 0, −1 ],
1, −1, −1, 0, 0, 1, 0 ],
1, 0, −1, −1, −1, −1, −2 ],
1, 0, −1, 0, −1, −1, −1 ],
1, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, −1, −1, 0 ],
1, 0, 0, 0, 0, 0, 0 ],
1, 1, 0, 0, −1, −1, 0 ],
0, −1, −1, −1, −1, −1, −2 ],
0, −1, −1, −1, 0, 0, −1 ],
0, −1, −1, 0, 0, 0, 0 ],
0, 0, −1, −1, −2, −1, −2 ],
0, 0, −1, −1, −1, 0, −1 ],
0, 0, −1, 0, −1, 0, 0 ],
0, 0, 0, 0, −1, −1, −1 ],
0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 1, 0, 0, 1 ],
1, −1, −2, −1, −2, 0, −2 ],
1, −1, −2, 0, −1, 0, −1 ],
1, −1, −1, 0, −1, 0, −1 ],
1, 0, −2, −1, −2, −1, −2 ],
1, 0, −1, −1, −2, −1, −1 ],
1, 0, −1, 0, −1, −1, −1 ],
1, 0, 0, 0, −1, −1, 0 ]
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
∗
7
6
5
4
• I ≡ P106 :
3
2
1





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
















bI =
C




200
1
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
−1
0
0
0
0
0
1
1
1
1
1
1
1
−1











0
 0

 −1

BI = −10

 0
 0
0
0
−1
−1
0
−1
0
0
0

−1
−1
−1
−1
0
−1
0
0
0
1
1
1
0
1
0
0
1
1
2
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
−1
1
1
1
1
1
1
0
−1
Number of sincere Tits roots of poset I sI = 16.
Table of roots of qbI
[ −2,−1,−1, 1, 2, 2, 1, 1 ],
[ −1,−1,−1, 1, 1, 1, 1, 1 ],
[ −1,−1,−1, 1, 2, 2, 1, 1 ],
[ 1, 1, 1,−1,−2,−2,−1,−1 ],
[ 1, 1, 1,−1,−1,−1,−1,−1 ],
[ 2, 1, 1,−1,−2,−2,−1,−1 ],
[ −1, −1, −1, 0, 1, 2, 1, 1 ],
[ −1, −1, −1, 1, 1, 1, 0, 0 ],
[ −1, −1, −1, 1, 2, 1, 0, 1 ],
[ −1, −1, 0, 0, 0, 1, 1, 0 ],
[ −1, −1, 0, 0, 1, 1, 1, 1 ],
[ −1, −1, 0, 1, 1, 1, 0, 0 ],
[ −1, −1, 0, 1, 2, 1, 0, 1 ],
[ −1, 0, −1, 0, 1, 1, 1, 0 ],
[ −1, 0, −1, 1, 1, 0, 0, 0 ],
[ −1, 0, −1, 1, 1, 1, 1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, 0, 1, 1, 0, 0 ],
[ 0, −1, −1, 0, 1, 2, 1, 1 ],
[ 0, −1, −1, 1, 1, 1, 0, 1 ],
[ 0, −1, 0, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 1, 1, 1 ],
[ 0, −1, 0, 0, 1, 1, 0, 1 ],
[ 0, −1, 0, 1, 1, 0, −1, 0 ],
[ 0, −1, 0, 1, 1, 1, 0, 1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 1, 1, 1 ],
[ 0, 0, −1, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, −1, 1, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, −1, −1, −1 ],
[ 0, 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 0, 1, 1, −1, −1, 0 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, −1, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, −1, −1, −1, −1 ],
[ 0, 0, 1, 0, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ −1,−2,−1, 1, 2, 2, 1, 1 ],
[ −1,−1,−1, 1, 1, 2, 1, 1 ],
[ −1,−1,−1, 1, 2, 2, 1, 2 ],
[ 1, 1, 1,−1,−2,−1,−1,−1 ],
[ 1, 1, 2,−1,−2,−2,−1,−1 ],
[ −1, −1, −1, 0, 1, 1, 1, 0 ],
[ −1, −1, −1, 0, 1, 2, 2, 1 ],
[ −1, −1, −1, 1, 1, 1, 1, 0 ],
[ −1, −1, −1, 1, 2, 2, 0, 1 ],
[ −1, −1, 0, 0, 1, 1, 0, 0 ],
[ −1, −1, 0, 0, 1, 2, 1, 1 ],
[ −1, −1, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, −1, 0, 0, 1, 1, 0 ],
[ −1, 0, −1, 0, 1, 1, 1, 1 ],
[ −1, 0, −1, 1, 1, 1, 0, 0 ],
[ −1, 0, −1, 1, 2, 1, 0, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, 0, 1, 1, 1, 0 ],
[ 0, −1, −1, 1, 1, 0, 0, 0 ],
[ 0, −1, −1, 1, 1, 1, 1, 1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 1, 1 ],
[ 0, −1, 0, 1, 1, 0, 0, 0 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 1, 1, 0 ],
[ 0, 0, −1, 0, 1, 1, 0, 0 ],
[ 0, 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, 1, 1, 0, 0, 1 ],
[ 0, 0, 0, −1, −1, 0, 1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, −1, −1, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, −1, 0 ],
[ 0, 0, 1, −1, −1, −1, 0, −1 ],
[ 0, 0, 1, −1, −1, 0, 1, 0 ],
[ 0, 0, 1, 0, −1, −1, 0, −1 ],
[ 0, 0, 1, 0, 0, −1, −1, −1 ],
[ 0, 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 0, 1, 1, 0, −1, −1, 0 ],
201
[ −1,−1,−2, 1, 2, 2, 1, 1 ],
[ −1,−1,−1, 1, 2, 1, 1, 1 ],
[ 1, 1, 1,−1,−2,−2,−1,−2 ],
[ 1, 1, 1,−1,−1,−2,−1,−1 ],
[ 1, 2, 1,−1,−2,−2,−1,−1 ],
[ −1, −1, −1, 0, 1, 2, 1, 0 ],
[ −1, −1, −1, 0, 2, 2, 1, 1 ],
[ −1, −1, −1, 1, 2, 1, 0, 0 ],
[ −1, −1, −1, 2, 2, 1, 0, 1 ],
[ −1, −1, 0, 0, 1, 1, 1, 0 ],
[ −1, −1, 0, 1, 1, 0, 0, 0 ],
[ −1, −1, 0, 1, 1, 1, 1, 1 ],
[ −1, 0, −1, 0, 1, 1, 0, 0 ],
[ −1, 0, −1, 0, 1, 2, 1, 1 ],
[ −1, 0, −1, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, −1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 0, −1, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ 0, −1, −1, 0, 0, 1, 1, 0 ],
[ 0, −1, −1, 0, 1, 1, 1, 1 ],
[ 0, −1, −1, 1, 1, 1, 0, 0 ],
[ 0, −1, −1, 1, 2, 1, 0, 1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 1, 1, 0 ],
[ 0, −1, 0, 0, 1, 1, 0, 0 ],
[ 0, −1, 0, 1, 0, 0, 0, 0 ],
[ 0, −1, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, −1, −1, 0, 1, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 1, 1, 1 ],
[ 0, 0, −1, 0, 1, 1, 0, 1 ],
[ 0, 0, −1, 1, 1, 0, −1, 0 ],
[ 0, 0, −1, 1, 1, 1, 0, 1 ],
[ 0, 0, 0, −1, −1, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 1, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, −1, 1 ],
[ 0, 0, 1, −1, −1, 0, 0, −1 ],
[ 0, 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, −1, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, −1, −1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, −1, 0, 0, 0, 0, 0 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1, 0, −1, −1, −1, 0, −1 ],
1, 0, −1, −1, 0, 1, 0 ],
1, 0, 0, −1, −1, 0, −1 ],
1, 0, 0, 0, −1, −1, −1 ],
1, 0, 0, 0, 0, −1, 0 ],
1, 0, 1, 0, −1, −1, 0 ],
1, 1, −1, −1, −1, 0, −1 ],
1, 1, 0, −1, −2, −1, −1 ],
1, 1, 0, −1, −1, 0, 0 ],
0, −1, 0, 0, 0, 0, 0 ],
0, 0, −1, −1, 0, 0, 0 ],
0, 0, 0, −1, −1, −1, −1 ],
0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, 1 ],
0, 1, −1, −1, −1, −1, −1 ],
0, 1, −1, −1, 0, 0, 0 ],
0, 1, 0, −1, −1, −1, 0 ],
1, 0, −1, −2, −1, 0, −1 ],
1, 0, −1, −1, −1, 0, 0 ],
1, 0, 0, −1, −1, −1, −1 ],
1, 0, 0, 0, −1, −1, 0 ],
1, 1, −1, −2, −1, 0, −1 ],
1, 1, −1, −1, −1, 0, 0 ],
1, 1, 0, −1, −2, −1, −1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, −1, −1, 0, 0, −1 ],
0, −1, 0, 0, 0, 0 ],
0, 0, −1, −1, 0, 0 ],
0, 0, 0, −1, −1, 0 ],
0, 0, 0, 0, 0, 0 ],
1, −1, −2, −1, 0, −1 ],
1, −1, −1, −1, 0, 0 ],
1, 0, −1, −1, −1, −1 ],
1, 0, 0, −1, −1, 0 ],
0, −1, −1, −1, 0, −1 ],
0, −1, −1, 0, 1, 0 ],
0, 0, −1, −1, 0, −1 ],
0, 0, 0, −1, −1, −1 ],
0, 0, 0, 0, −1, 0 ],
0, 1, 0, −1, −1, 0 ],
1, −1, −1, −1, 0, −1 ],
1, 0, −1, −2, −1, −1 ],
1, 0, −1, −1, 0, 0 ],
0, −1, −1, −1, −1, −1 ],
0, −1, −1, 0, 0, 0 ],
0, 0, −1, −1, −1, 0 ],
1, −2, −2, −1, 0, −1 ],
1, −1, −2, −1, 0, 0 ],
1, 0, −2, −2, −1, −1 ],
1, 0, −1, −2, −1, 0 ],
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
1, −1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
0, −1, −1, 0, 0, 0 ],
0, 0, −1, −1, −1, −1 ],
0, 0, −1, 0, 0, 0 ],
0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 1 ],
1, −1, −1, −1, −1, −1 ],
1, −1, −1, 0, 0, 0 ],
1, 0, −1, −1, −1, 0 ],
0, 0, 0, 0, 0, 0 ],
0, −1, −1, 0, 0, −1 ],
0, −1, 0, 0, 0, 0 ],
0, 0, −1, −1, 0, 0 ],
0, 0, 0, −1, −1, 0 ],
0, 0, 0, 0, 0, 0 ],
1, −1, −2, −1, 0, −1 ],
1, −1, −1, −1, 0, 0 ],
1, 0, −1, −1, −1, −1 ],
1, 0, 0, −1, −1, 0 ],
0, −1, −1, −1, 0, −1 ],
0, 0, −1, −2, −1, −1 ],
0, 0, −1, −1, 0, 0 ],
1, −1, −2, −2, 0, −1 ],
1, −1, −1, −1, −1, 0 ],
1, 0, −1, −2, −2, −1 ],
1, 0, −1, −1, −1, 0 ]
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
0
















BI =



1
1
1
1
1
1
1
−1
∗
7
• I ≡ P107 :
2
6
1
5
4
3





CI =








b
CoxI =



0
0
1
1
1
0
0
−1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
−1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
−1
−1
0
0
0
1
1
1
1
1
1
1
1
0
−1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
0
0
0
1
1
1
1
0
0
−1
0
0
0
0
−1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
−1
−1
−1
−1
−1
0











0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
−1
Number of sincere Tits roots of poset I sI = 18.
Table of roots of qbI
[ −2,−1,−2,−1,−1, 1, 2,−2 ],
[ −2,−1,−1,−2,−1, 1, 2,−2 ],
202
[ −2,−1,−1,−1,−2, 1, 2,−2 ],











[ −2,−1,−1,−1,−1, 1, 1,−2 ],
[ −1,−1,−1,−1,−1, 1, 1,−2 ],
[ 1, 1, 1, 1, 1,−1,−2, 1 ],
[ 2, 1, 1, 1, 1,−1,−2, 1 ],
[ 2, 1, 1, 1, 2,−1,−2, 2 ],
[ −2, −1, −1, −1, −1, 0, 2, −2 ],
[ −2, 0, −1, −1, −1, 1, 2, −1 ],
[ −2, 0, −1, 0, −1, 1, 1, −1 ],
[ −1, −1, −1, −1, −1, 0, 1, −2 ],
[ −1, −1, −1, −1, 0, 0, 1, −2 ],
[ −1, −1, −1, −1, 0, 1, 1, −1 ],
[ −1, −1, −1, 0, −1, 0, 2, −1 ],
[ −1, −1, 0, −1, −1, 0, 1, −2 ],
[ −1, −1, 0, −1, −1, 1, 1, −1 ],
[ −1, 0, −1, −1, −1, 1, 1, −1 ],
[ −1, 0, −1, −1, 0, 1, 1, −1 ],
[ −1, 0, −1, 0, −1, 1, 0, −1 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, 1, 0, −1 ],
[ −1, 0, 0, −1, −1, 0, 1, −1 ],
[ −1, 0, 0, −1, −1, 1, 1, 0 ],
[ −1, 0, 0, −1, 0, 0, 1, 0 ],
[ −1, 0, 0, −1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, −1, 0, 1, 0 ],
[ −1, 0, 0, 0, −1, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 1, 0, −1, 0, 1, 0, 0 ],
[ −1, 1, 0, 0, 0, 1, −1, 0 ],
[ 0, −1, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, −1, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 1, −1, 0 ],
[ 0, 1, 0, 0, 1, 0, −1, 0 ],
[ 0, 1, 0, 0, 1, 1, −1, 1 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 1, 0, 0, 1, −1, 1 ],
[ 1, −1, 0, 0, 0, −1, 0, −1 ],
[ 1, −1, 0, 0, 0, 0, 0, 0 ],
[ 1, −1, 1, 0, 0, −1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, −1, 0, 0 ],
[ 1, 0, 0, 0, 1, 0, −1, 1 ],
[ 1, 0, 0, 1, 0, −1, 0, 0 ],
[ 1, 0, 0, 1, 0, 0, −1, 1 ],
[ 1, 0, 0, 1, 1, −1, −1, 1 ],
[ 1, 0, 1, 0, 0, −1, −1, 0 ],
[ 1, 0, 1, 0, 0, 0, −1, 0 ],
[ 1, 0, 1, 0, 1, −1, −1, 0 ],
[ 1, 0, 1, 0, 1, 0, −1, 1 ],
[ 1, 0, 1, 1, 0, −1, 0, 1 ],
[ 1, 1, 0, 0, 1, 0, −1, 1 ],
[ 1, 1, 0, 1, 1, 0, −2, 1 ],
[ −2,−1,−1,−1,−1, 1, 2,−2 ],
[ −1,−1,−1,−1,−1, 1, 1,−1 ],
[ 1, 1, 1, 1, 1,−1,−1, 1 ],
[ 2, 1, 1, 1, 1,−1,−2, 2 ],
[ 2, 1, 1, 2, 1,−1,−2, 2 ],
[ −2, 0, −1, −1, −1, 1, 1, −2 ],
[ −2, 0, −1, −1, −1, 2, 1, −1 ],
[ −2, 0, 0, −1, −1, 1, 1, −1 ],
[ −1, −1, −1, −1, −1, 0, 2, −2 ],
[ −1, −1, −1, −1, 0, 0, 1, −1 ],
[ −1, −1, −1, 0, −1, 0, 1, −2 ],
[ −1, −1, −1, 0, −1, 1, 1, −1 ],
[ −1, −1, 0, −1, −1, 0, 1, −1 ],
[ −1, −1, 0, −1, 0, 0, 1, −1 ],
[ −1, 0, −1, −1, 0, 0, 1, −1 ],
[ −1, 0, −1, −1, 0, 1, 1, 0 ],
[ −1, 0, −1, 0, −1, 1, 1, −1 ],
[ −1, 0, −1, 0, 0, 0, 1, −1 ],
[ −1, 0, −1, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, −1, −1, 1, 0, −1 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, −1, 0, 1, 0, −1 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, −1, 1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 0, −1, 1, 0, 0 ],
[ −1, 1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, −1, 0, −1, 0, 1, −1 ],
[ 0, −1, −1, 0, 0, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, −1, 1, −1 ],
[ 0, −1, 0, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, −1, 0, 1, −1 ],
[ 0, −1, 0, 0, 0, −1, 1, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 0, 1, −1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, −1, 1 ],
[ 0, 1, 0, 0, 1, 0, −1, 1 ],
[ 0, 1, 0, 1, 0, 0, −1, 0 ],
[ 0, 1, 0, 1, 0, 1, −1, 1 ],
[ 0, 1, 1, 0, 0, 0, −1, 1 ],
[ 0, 1, 1, 0, 1, 0, −1, 1 ],
[ 1, −1, 0, 0, 0, −1, 0, 0 ],
[ 1, −1, 0, 0, 1, −1, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 1, −1, 0, 1 ],
[ 1, 0, 0, 0, 1, 0, 0, 1 ],
[ 1, 0, 0, 1, 0, −1, 0, 1 ],
[ 1, 0, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 0, 1, 1, −1, 0, 1 ],
[ 1, 0, 1, 0, 0, −1, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, −1, 1 ],
[ 1, 0, 1, 0, 1, −1, −1, 1 ],
[ 1, 0, 1, 1, 0, −1, −1, 0 ],
[ 1, 0, 1, 1, 0, 0, −1, 1 ],
[ 1, 1, 0, 1, 0, 0, −1, 1 ],
[ 1, 1, 0, 1, 1, 0, −1, 1 ],
203
[ −2,−1,−1,−1,−1, 1, 2,−1 ],
[ −1,−1,−1,−1,−1, 1, 2,−1 ],
[ 1, 1, 1, 1, 1,−1,−1, 2 ],
[ 2, 1, 1, 1, 1,−1,−1, 2 ],
[ 2, 1, 2, 1, 1,−1,−2, 2 ],
[ −2, 0, −1, −1, −1, 1, 1, −1 ],
[ −2, 0, −1, −1, 0, 1, 1, −1 ],
[ −1, −2, −1, −1, −1, 0, 2, −2 ],
[ −1, −1, −1, −1, −1, 0, 2, −1 ],
[ −1, −1, −1, −1, 0, 0, 2, −1 ],
[ −1, −1, −1, 0, −1, 0, 1, −1 ],
[ −1, −1, −1, 0, 0, 0, 1, −1 ],
[ −1, −1, 0, −1, −1, 0, 2, −1 ],
[ −1, −1, 0, 0, −1, 0, 1, −1 ],
[ −1, 0, −1, −1, 0, 1, 0, −1 ],
[ −1, 0, −1, 0, −1, 0, 1, −1 ],
[ −1, 0, −1, 0, −1, 1, 1, 0 ],
[ −1, 0, −1, 0, 0, 0, 1, 0 ],
[ −1, 0, −1, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, −1, −1, 1, 1, −1 ],
[ −1, 0, 0, −1, 0, 0, 1, −1 ],
[ −1, 0, 0, −1, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, −1, 0, 1, −1 ],
[ −1, 0, 0, 0, −1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, −1, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 1, 0, 1 ],
[ 0, −1, −1, 0, 0, −1, 1, −1 ],
[ 0, −1, −1, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, −1, −1, 1, −1 ],
[ 0, −1, 0, 0, −1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, −1, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 0, −1, 1 ],
[ 0, 1, 0, 1, 1, 0, −1, 1 ],
[ 0, 1, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 0, 0, −1, 1 ],
[ 1, −1, 0, 0, 0, −1, 1, 0 ],
[ 1, −1, 0, 1, 0, −1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, −1, 0 ],
[ 1, 0, 0, 0, 1, −1, −1, 0 ],
[ 1, 0, 0, 0, 1, 0, −1, 0 ],
[ 1, 0, 0, 1, 0, −1, −1, 0 ],
[ 1, 0, 0, 1, 0, 0, −1, 0 ],
[ 1, 0, 0, 1, 1, −1, −1, 0 ],
[ 1, 0, 0, 1, 1, 0, −1, 1 ],
[ 1, 0, 1, 0, 0, −1, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0, 1, −1, 0, 1 ],
[ 1, 0, 1, 1, 0, −1, −1, 1 ],
[ 1, 0, 1, 1, 1, −1, −1, 1 ],
[ 1, 1, 0, 1, 1, −1, −1, 1 ],
[ 1, 1, 0, 1, 1, 0, −1, 2 ],
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
2,
2,
1,
1,
1,
1,
2,
0,
0,
1,
1,
1,
1,
1,
1,
1,
0,
0,
1,
1,
1,
1,
1,
0, 0, −1,
1, 0, −1,
0, 0, −2,
1, 0, −2,
1, 0, −2,
0, −1, −1,
1, −1, −1,
1 ],
1 ],
1 ],
1 ],
2 ],
1 ],
1 ],
[
[
[
[
[
[
[
1,
1,
1,
1,
2,
2,
2,
1,
1,
1,
1,
0,
0,
0,
1,
1,
1,
1,
0,
1,
1,
0,
0,
1,
1,
1,
1,
1,
1, −1, −1,
1, 0, −1,
0, 0, −1,
1, 0, −2,
1, −1, −1,
1, −2, −1,
1, −1, −1,
1 ],
2 ],
1 ],
2 ],
1 ],
1 ],
2 ],
[
[
[
[
[
[
[
1,
1,
1,
1,
2,
2,
2,
1,
1,
1,
1,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
0,
1,
1,
1,
0,
1,
1,
1, 0, −2,
0, −1, −1,
0, 0, −1,
1, 0, −1,
1, −1, −1,
1, −1, −2,
1, 0, −2,
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1 ],
1 ],
2 ],
2 ],
1 ],
1 ],
2]
∗
• I ≡ P108 :
3
7
2
6
1
5
4





CI =








b I =
Cox




0
1
1
1
1
1
1
−1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
−1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
−1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
−1
0
0
−1
−1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
















BI =



0
1
0
1
0
0
0
−1
1
0
0
1
0
0
−1
−1
0
1
1
0
0
0
0
−1
1
1
0
0
0
0
0
−1
0
0
0
1
1
1
0
−1
−1
−1
−1
−1
−1
−1
−1
1











0
0
0
0
0
−1
−1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
−1
−2
Number of sincere Tits roots of poset I sI = 18.
Table of roots of qbI
[ −2,−2,−1,−2,−1,−1, 1,−4 ],
[ −2,−2,−1,−1,−1,−1, 1,−4 ],
[ −1,−2,−1,−1,−1,−1, 1,−3 ],
[ 1, 1, 1, 1, 1, 1,−1, 2 ],
[ 2, 1, 1, 1, 1, 1,−1, 3 ],
[ 2, 2, 1, 1, 1, 2,−1, 4 ],
[ −2, −2, −1, −1, −1, −1, 0, −4 ],
[ −2, −1, −1, −1, −1, −1, 0, −4 ],
[ −2, −1, −1, −1, 0, −1, 0, −3 ],
[ −1, −2, 0, −1, −1, −1, 1, −2 ],
[ −1, −2, 0, −1, 0, −1, 1, −2 ],
[ −1, −1, −1, −1, −1, 0, 0, −3 ],
[ −1, −1, −1, −1, 0, −1, 0, −3 ],
[ −1, −1, −1, −1, 0, 0, 0, −2 ],
[ −1, −1, −1, 0, −1, −1, 1, −2 ],
[ −1, −1, 0, −1, −1, −1, 1, −2 ],
[ −1, −1, 0, −1, −1, 0, 1, −1 ],
[ −1, −1, 0, −1, 0, −1, 1, −1 ],
[ −1, −1, 0, −1, 0, 0, 1, −1 ],
[ −1, −1, 0, 0, −1, −1, 1, −1 ],
[ −2,−2,−1,−1,−2,−1, 1,−4 ],
[ −2,−2,−1,−1,−1,−1, 1,−3 ],
[ −1,−1,−1,−1,−1,−1, 1,−3 ],
[ 1, 1, 1, 1, 1, 1,−1, 3 ],
[ 2, 2, 1, 1, 1, 1,−1, 3 ],
[ 2, 2, 1, 1, 2, 1,−1, 4 ],
[ −2, −2, 0, −1, −1, −1, 1, −3 ],
[ −2, −1, −1, −1, −1, −1, 0, −3 ],
[ −2, −1, −1, 0, −1, −1, 0, −3 ],
[ −1, −2, 0, −1, −1, −1, 2, −2 ],
[ −1, −2, 0, 0, −1, −1, 1, −2 ],
[ −1, −1, −1, −1, −1, 0, 0, −2 ],
[ −1, −1, −1, −1, 0, −1, 0, −2 ],
[ −1, −1, −1, 0, −1, −1, 0, −3 ],
[ −1, −1, −1, 0, −1, 0, 0, −2 ],
[ −1, −1, 0, −1, −1, 0, 0, −2 ],
[ −1, −1, 0, −1, 0, −1, 0, −2 ],
[ −1, −1, 0, −1, 0, 0, 0, −2 ],
[ −1, −1, 0, 0, −1, −1, 0, −2 ],
[ −1, −1, 0, 0, −1, 0, 0, −2 ],
204
[ −2,−2,−1,−1,−1,−2, 1,−4 ],
[ −2,−1,−1,−1,−1,−1, 1,−3 ],
[ −1,−1,−1,−1,−1,−1, 1,−2 ],
[ 1, 2, 1, 1, 1, 1,−1, 3 ],
[ 2, 2, 1, 1, 1, 1,−1, 4 ],
[ 2, 2, 1, 2, 1, 1,−1, 4 ],
[ −2, −1, −2, −1, −1, −1, 0, −4 ],
[ −2, −1, −1, −1, −1, 0, 0, −3 ],
[ −1, −2, 0, −1, −1, −1, 1, −3 ],
[ −1, −2, 0, −1, −1, 0, 1, −2 ],
[ −1, −1, −1, −1, −1, −1, 0, −3 ],
[ −1, −1, −1, −1, −1, 0, 1, −2 ],
[ −1, −1, −1, −1, 0, −1, 1, −2 ],
[ −1, −1, −1, 0, −1, −1, 0, −2 ],
[ −1, −1, −1, 0, 0, −1, 0, −2 ],
[ −1, −1, 0, −1, −1, 0, 1, −2 ],
[ −1, −1, 0, −1, 0, −1, 1, −2 ],
[ −1, −1, 0, −1, 0, 0, 0, −1 ],
[ −1, −1, 0, 0, −1, −1, 1, −2 ],
[ −1, −1, 0, 0, −1, 0, 0, −1 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, −1, 0, 0, −1, 0, 1, −1 ],
−1, −1, 0, 0, 0, −1, 1, −1 ],
−1, 0, −1, −1, 0, −1, 0, −2 ],
−1, 0, −1, −1, 0, 0, 0, −1 ],
−1, 0, −1, 0, −1, 0, 0, −2 ],
−1, 0, −1, 0, 0, −1, 0, −2 ],
−1, 0, −1, 0, 0, 0, −1, −1 ],
−1, 0, 0, 0, −1, 0, 0, −1 ],
−1, 0, 0, 0, 0, 0, 0, −1 ],
0, −1, 0, −1, −1, 0, 1, −1 ],
0, −1, 0, −1, 0, 0, 1, −1 ],
0, −1, 0, 0, −1, 0, 0, −1 ],
0, −1, 0, 0, 0, −1, 0, −1 ],
0, −1, 0, 0, 0, 0, 0, −1 ],
0, −1, 1, −1, 0, 0, 1, 0 ],
0, −1, 1, 0, 0, 0, 0, 0 ],
0, 0, −1, −1, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 0, −1, −1 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 1, 0, 0 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1, −1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 1, 0, 1 ],
0, 1, −1, 0, 0, 0, −1, −1 ],
0, 1, −1, 0, 0, 1, −1, 0 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 0, 0, 0, 1, −1, 0 ],
0, 1, 0, 0, 1, 0, −1, 0 ],
0, 1, 0, 0, 1, 1, −1, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
1, −1, 1, 0, 0, 0, 1, 1 ],
1, 0, 0, 0, 0, 0, 1, 1 ],
1, 0, 0, 1, 0, 0, 0, 1 ],
1, 0, 1, 0, 0, 0, 1, 2 ],
1, 0, 1, 0, 0, 1, 1, 2 ],
1, 0, 1, 0, 1, 0, 1, 2 ],
1, 0, 1, 1, 0, 0, 0, 2 ],
1, 0, 1, 1, 1, 0, 0, 2 ],
1, 1, 0, 0, 0, 1, 0, 1 ],
1, 1, 0, 0, 1, 0, 0, 1 ],
1, 1, 0, 0, 1, 1, −1, 2 ],
1, 1, 0, 1, 0, 0, 0, 1 ],
1, 1, 0, 1, 0, 1, −1, 2 ],
1, 1, 0, 1, 1, 0, −1, 2 ],
1, 1, 1, 0, 0, 1, 0, 2 ],
1, 1, 1, 0, 1, 1, 0, 2 ],
1, 1, 1, 1, 0, 1, −1, 2 ],
1, 1, 1, 1, 1, 0, −1, 2 ],
1, 1, 1, 1, 1, 1, 0, 3 ],
1, 2, 0, 1, 1, 0, −1, 2 ],
1, 2, 0, 1, 1, 1, −1, 3 ],
2, 1, 1, 1, 1, 0, 0, 3 ],
2, 1, 2, 1, 1, 1, 0, 4 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, −1, 0, 0, 0, −1, 0, −2 ],
−1, −1, 0, 0, 0, 0, 0, −1 ],
−1, 0, −1, −1, 0, 0, −1, −2 ],
−1, 0, −1, 0, −1, −1, 0, −2 ],
−1, 0, −1, 0, −1, 0, 0, −1 ],
−1, 0, −1, 0, 0, −1, 0, −1 ],
−1, 0, −1, 0, 0, 0, 0, −1 ],
−1, 0, 0, 0, 0, −1, 0, −1 ],
−1, 0, 0, 0, 0, 0, 0, 0 ],
0, −1, 0, −1, 0, −1, 1, −1 ],
0, −1, 0, −1, 0, 0, 1, 0 ],
0, −1, 0, 0, −1, 0, 1, −1 ],
0, −1, 0, 0, 0, −1, 1, −1 ],
0, −1, 0, 0, 0, 0, 0, 0 ],
0, −1, 1, 0, −1, 0, 1, 0 ],
0, −1, 1, 0, 0, 0, 1, 0 ],
0, 0, −1, 0, −1, 0, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, −1, 1, 0, 0, 0 ],
0, 0, 0, 0, −1, 0, 1, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 1, −1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 1, −1, 0, 0, 0, −1, 0 ],
0, 1, −1, 0, 1, 0, −1, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 1, −1, 1 ],
0, 1, 0, 0, 1, 0, −1, 1 ],
0, 1, 0, 1, 0, 0, −1, 0 ],
0, 1, 0, 1, 0, 1, −1, 1 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 0, 1, 0, 0, 1, 0, 1 ],
1, 0, 1, 0, 1, 0, 0, 1 ],
1, 0, 1, 0, 1, 1, 0, 2 ],
1, 0, 1, 1, 0, 0, 1, 2 ],
1, 1, 0, 0, 0, 0, 0, 1 ],
1, 1, 0, 0, 0, 1, 0, 2 ],
1, 1, 0, 0, 1, 0, 0, 2 ],
1, 1, 0, 0, 1, 1, 0, 2 ],
1, 1, 0, 1, 0, 0, 0, 2 ],
1, 1, 0, 1, 0, 1, 0, 2 ],
1, 1, 0, 1, 1, 0, 0, 2 ],
1, 1, 1, 0, 1, 0, 0, 2 ],
1, 1, 1, 0, 1, 1, 0, 3 ],
1, 1, 1, 1, 0, 1, 0, 2 ],
1, 1, 1, 1, 1, 0, 0, 2 ],
1, 2, 0, 0, 1, 1, −1, 2 ],
1, 2, 0, 1, 1, 1, −2, 2 ],
2, 1, 1, 0, 1, 1, 0, 3 ],
2, 1, 1, 1, 1, 1, 0, 3 ],
2, 2, 0, 1, 1, 1, −1, 3 ],
205
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, −1, 0, 0, 0, −1, 0, −1 ],
−1, 0, −1, −1, −1, 0, 0, −2 ],
−1, 0, −1, −1, 0, 0, 0, −2 ],
−1, 0, −1, 0, −1, 0, −1, −2 ],
−1, 0, −1, 0, 0, −1, −1, −2 ],
−1, 0, −1, 0, 0, 0, −1, −2 ],
−1, 0, 0, −1, 0, 0, 0, −1 ],
−1, 0, 0, 0, 0, 0, −1, −1 ],
−1, 1, −1, 0, 0, 0, −1, −1 ],
0, −1, 0, −1, 0, 0, 0, −1 ],
0, −1, 0, 0, −1, −1, 1, −1 ],
0, −1, 0, 0, −1, 0, 1, 0 ],
0, −1, 0, 0, 0, −1, 1, 0 ],
0, −1, 0, 0, 0, 0, 1, 0 ],
0, −1, 1, 0, 0, −1, 1, 0 ],
0, −1, 1, 0, 0, 0, 1, 1 ],
0, 0, −1, 0, 0, −1, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, −1, 1, 0, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, 0, 1, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, −1, 1, 0, 0, −1, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 0, 1, 0, 1 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
0, 1, 0, 1, 0, 0, −1, 1 ],
0, 1, 0, 1, 1, 0, −1, 1 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 0, 1, 0, 0, 1 ],
1, 0, 1, 0, 0, 0, 1, 1 ],
1, 0, 1, 0, 0, 1, 0, 2 ],
1, 0, 1, 0, 1, 0, 0, 2 ],
1, 0, 1, 1, 0, 0, 0, 1 ],
1, 0, 1, 1, 0, 1, 0, 2 ],
1, 1, 0, 0, 0, 1, −1, 1 ],
1, 1, 0, 0, 1, 0, −1, 1 ],
1, 1, 0, 0, 1, 1, −1, 1 ],
1, 1, 0, 1, 0, 0, −1, 1 ],
1, 1, 0, 1, 0, 1, −1, 1 ],
1, 1, 0, 1, 1, 0, −1, 1 ],
1, 1, 0, 1, 1, 1, −1, 2 ],
1, 1, 1, 0, 1, 1, −1, 2 ],
1, 1, 1, 1, 0, 0, 0, 2 ],
1, 1, 1, 1, 0, 1, 0, 3 ],
1, 1, 1, 1, 1, 0, 0, 3 ],
1, 2, 0, 1, 0, 1, −1, 2 ],
1, 2, 0, 1, 1, 1, −1, 2 ],
2, 1, 1, 1, 0, 1, 0, 3 ],
2, 1, 1, 1, 1, 1, 0, 4 ],
2, 2, 1, 1, 1, 1, 0, 4 ]
∗
7
6
• I ≡ P109 :
4
5
2
3
1





CI =








b
CoxI =



0
0
1
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
−1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
−1
−1
0
−1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
















BI =



1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
−1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
−1
0
0
0
0
1
0
1
0
0
0
0
−1
0
−1
−1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
−1
−1
−1
0
−1
−1
−1
−1
−1
−1
−1
1

1
0
0
0
0
0
0
0
−1
0
0
0
0
1
1
0










1
0
0
0
0
0
−1
−1
Number of sincere Tits roots of poset I sI = 18.
Table of roots of qbI
[ −1, 1, 1, 1, 1, 1,−2, 1 ],
[ −1, 1, 1, 1, 2, 1,−2, 1 ],
[ −1, 1, 1, 1, 2, 2,−2, 2 ],
[ 1,−2,−1,−1,−2,−1, 2,−2 ],
[ 1,−1,−1,−1,−2,−1, 1,−2 ],
[ 1,−1,−1,−1,−1,−1, 1,−2 ],
[ −2, 1, 0, 1, 2, 1, −1, 1 ],
[ −1, 0, −1, 0, 0, −1, 1, −1 ],
[ −1, 0, −1, 0, 0, 0, 1, 0 ],
[ −1, 0, −1, 0, 1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, −1, 0 ],
[ −1, 0, 0, 1, 1, 1, −1, 0 ],
[ −1, 0, 0, 1, 2, 1, −1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 0, 1 ],
[ −1, 1, 0, 0, 1, 1, 0, 1 ],
[ −1, 1, 0, 1, 1, 0, −1, 1 ],
[ −1, 1, 0, 1, 2, 0, −1, 1 ],
[ −1, 1, 0, 1, 2, 1, −1, 2 ],
[ 0, −1, −2, −1, −1, −1, 2, −2 ],
[ 0, −1, −1, −1, −1, −1, 2, −2 ],
[ 0, −1, −1, −1, −1, 0, 1, −1 ],
[ 0, −1, −1, 0, −1, −1, 1, −2 ],
[ 0, −1, −1, 0, −1, 0, 1, −1 ],
[ −1, 1, 1, 1, 1, 1,−1, 1 ],
[ −1, 1, 1, 1, 2, 1,−2, 2 ],
[ −1, 1, 1, 2, 2, 1,−2, 2 ],
[ 1,−1,−1,−2,−2,−1, 2,−2 ],
[ 1,−1,−1,−1,−2,−1, 2,−2 ],
[ 1,−1,−1,−1,−1,−1, 1,−1 ],
[ −1, −1, −1, 0, 0, 0, 1, −1 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, −1, 0, 1, 0, 0, −1 ],
[ −1, 0, −1, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, −1, 1 ],
[ −1, 0, 1, 1, 1, 1, −1, 1 ],
[ −1, 1, 0, 0, 1, 0, −1, 0 ],
[ −1, 1, 0, 0, 1, 1, −1, 0 ],
[ −1, 1, 0, 0, 2, 1, −1, 1 ],
[ −1, 1, 0, 1, 1, 0, 0, 1 ],
[ −1, 1, 0, 1, 2, 1, −2, 1 ],
[ −1, 1, 1, 0, 1, 1, −1, 1 ],
[ 0, −1, −1, −1, −2, −1, 2, −2 ],
[ 0, −1, −1, −1, −1, −1, 2, −1 ],
[ 0, −1, −1, −1, −1, 0, 2, −1 ],
[ 0, −1, −1, 0, −1, −1, 1, −1 ],
[ 0, −1, −1, 0, 0, −1, 1, −1 ],
206
[ −1, 1, 1, 1, 1, 1,−1, 2 ],
[ −1, 1, 1, 1, 2, 1,−1, 2 ],
[ −1, 2, 1, 1, 2, 1,−2, 2 ],
[ 1,−1,−1,−1,−2,−2, 2,−2 ],
[ 1,−1,−1,−1,−2,−1, 2,−1 ],
[ 1,−1,−1,−1,−1,−1, 2,−1 ],
[ −1, 0, −1, −1, 0, 0, 1, −1 ],
[ −1, 0, −1, 0, 0, 0, 1, −1 ],
[ −1, 0, −1, 0, 1, 0, 0, 0 ],
[ −1, 0, −1, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 1, 1, −1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 1, −1, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 1, 1, −1, 1 ],
[ −1, 1, 0, 1, 1, 0, −1, 0 ],
[ −1, 1, 0, 1, 1, 1, −1, 1 ],
[ −1, 1, 0, 1, 2, 1, −1, 1 ],
[ −1, 1, 1, 1, 1, 0, −1, 1 ],
[ 0, −1, −1, −1, −1, −1, 1, −2 ],
[ 0, −1, −1, −1, −1, 0, 1, −2 ],
[ 0, −1, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, −1, 0, −1, −1, 2, −1 ],
[ 0, −1, −1, 0, 0, 0, 0, −1 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, −1, 0, 0, 0, 1, −1 ],
0, −1, 0, 0, −1, −1, 1, −1 ],
0, −1, 0, 0, −1, 0, 1, 0 ],
0, −1, 0, 0, 0, 0, 1, 0 ],
0, 0, −1, −1, −1, −1, 1, −2 ],
0, 0, −1, −1, −1, 0, 1, −1 ],
0, 0, −1, −1, 0, 0, 1, −1 ],
0, 0, −1, 0, 0, −1, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, −1, 0, 1, 0, 0, 0 ],
0, 0, 0, −1, −1, 0, 1, −1 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, 0, −1, −1, 0, −1 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 0, 1, 1, −1, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 1, 0, 0, 1 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 0, 1, 0, 0, 1, −1, 0 ],
0, 0, 1, 0, 1, 1, −1, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 0, 1, 1, 1, 1, −2, 1 ],
0, 1, 0, −1, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 1, 0, −1, 1 ],
0, 1, 0, 1, 1, 0, −1, 1 ],
0, 1, 1, 0, 0, 0, 0, 1 ],
0, 1, 1, 0, 1, 1, −2, 1 ],
0, 1, 1, 1, 0, 0, −1, 1 ],
0, 1, 1, 1, 1, 0, −1, 2 ],
0, 1, 1, 1, 1, 1, −1, 2 ],
1, −1, −1, −1, −1, 0, 1, −1 ],
1, −1, 0, −1, −2, −1, 1, −1 ],
1, −1, 0, −1, −1, −1, 1, −1 ],
1, −1, 0, −1, −1, 0, 1, 0 ],
1, −1, 0, 0, −1, −1, 1, −1 ],
1, −1, 0, 0, −1, 0, 0, 0 ],
1, −1, 1, 0, −1, 0, 0, 0 ],
1, 0, 0, −1, −1, −1, 0, −1 ],
1, 0, 0, −1, −1, 0, 0, −1 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, −1, −1, 1, 0 ],
1, 0, 0, 0, 0, 0, −1, 0 ],
1, 0, 1, −1, −1, 0, 0, 0 ],
1, 0, 1, 0, −1, 0, 0, 0 ],
1, 0, 1, 0, 0, 0, −1, 1 ],
1, 0, 1, 1, 0, 0, −1, 1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, −1, 0, 0, 0, 1, 0 ],
0, −1, 0, 0, −1, 0, 0, −1 ],
0, −1, 0, 0, 0, 0, 0, −1 ],
0, −1, 0, 0, 0, 1, 0, 0 ],
0, 0, −1, −1, −1, −1, 1, −1 ],
0, 0, −1, −1, 0, −1, 1, −1 ],
0, 0, −1, −1, 0, 0, 1, 0 ],
0, 0, −1, 0, 0, −1, 1, −1 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, 0, −1, −1, −1, 1, −1 ],
0, 0, 0, −1, −1, 0, 1, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, −1, 1, −1 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 0, 1, 1, −1, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 0, 1, 1, 0, −1, 0 ],
0, 0, 0, 1, 1, 1, −1, 1 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 1, −1, 1 ],
0, 0, 1, 1, 0, 0, −1, 0 ],
0, 0, 1, 1, 0, 1, −1, 1 ],
0, 0, 1, 1, 1, 1, −1, 1 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
0, 1, 1, 0, 0, 0, −1, 0 ],
0, 1, 1, 0, 0, 1, −1, 1 ],
0, 1, 1, 0, 1, 1, −1, 1 ],
0, 1, 1, 1, 1, 0, −2, 1 ],
0, 1, 1, 1, 1, 1, −2, 1 ],
0, 1, 1, 1, 2, 1, −2, 2 ],
1, −1, −1, 0, −1, −1, 1, −1 ],
1, −1, 0, −1, −2, −1, 2, −1 ],
1, −1, 0, −1, −1, 0, 0, −1 ],
1, −1, 0, 0, −2, −1, 1, −1 ],
1, −1, 0, 0, −1, −1, 1, 0 ],
1, −1, 0, 0, −1, 0, 1, 0 ],
1, 0, −1, −1, −1, −1, 1, −1 ],
1, 0, 0, −1, −1, −1, 1, −1 ],
1, 0, 0, −1, −1, 0, 0, 0 ],
1, 0, 0, 0, −1, −1, 0, −1 ],
1, 0, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 1, 0, −1, −1, 0, 0 ],
1, 0, 1, 0, −1, 0, 0, 1 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 1, 1, 0, 0, 0, −1, 1 ],
∗
• I ≡ P110 :
6
7
3
4
5
2
1
207
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 0, −1, −1, 0, 1, −1 ],
0, −1, 0, 0, −1, 0, 1, −1 ],
0, −1, 0, 0, 0, 0, 0, 0 ],
0, −1, 0, 1, 0, 0, 0, 0 ],
0, 0, −1, −1, −1, −1, 2, −1 ],
0, 0, −1, −1, 0, 0, 0, −1 ],
0, 0, −1, 0, −1, −1, 1, −1 ],
0, 0, −1, 0, 0, −1, 1, 0 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, 0, −1, −1, 0, 0, −1 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 1, 0, 0 ],
0, 0, 0, 0, −1, −1, 1, 0 ],
0, 0, 0, 0, −1, 0, 1, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 0, 1, 1, 0, 1 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 0, 1, 1, 0, −1, 1 ],
0, 0, 1, 0, −1, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, 1, 0, 1 ],
0, 0, 1, 1, 0, 0, −1, 1 ],
0, 0, 1, 1, 1, 0, −1, 1 ],
0, 0, 1, 1, 1, 1, −1, 2 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 0, 0, 1, 0, −1, 0 ],
0, 1, 0, 0, 1, 1, −1, 1 ],
0, 1, 1, 0, 0, 0, −1, 1 ],
0, 1, 1, 0, 1, 0, −1, 1 ],
0, 1, 1, 0, 1, 1, −1, 2 ],
0, 1, 1, 1, 1, 0, −1, 1 ],
0, 1, 1, 1, 1, 1, −2, 2 ],
0, 1, 2, 1, 1, 1, −2, 2 ],
1, −1, 0, −1, −2, −1, 1, −2 ],
1, −1, 0, −1, −2, 0, 1, −1 ],
1, −1, 0, −1, −1, 0, 1, −1 ],
1, −1, 0, 0, −1, −1, 0, −1 ],
1, −1, 0, 0, −1, 0, 0, −1 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, −1, −2, −1, 1, −1 ],
1, 0, 0, −1, −1, −1, 1, 0 ],
1, 0, 0, −1, −1, 0, 1, 0 ],
1, 0, 0, 0, −1, −1, 0, 0 ],
1, 0, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 1, 0, −1, 0, −1, 0 ],
1, 0, 1, 0, 0, 0, −1, 0 ],
1, 0, 1, 0, 0, 1, −1, 1 ],
2, −1, 0, −1, −2, −1, 1, −1 ]





CI =








b I =
Cox




0
0
1
0
1
0
0
−1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
−1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
−1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
−1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
−1
















bI =
C




1
1
0
1
0
1
1
0
















BI =



0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
−1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
−1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
−1
−1
−1
−1
−1
−1
−1
−1
1
1
0
1
0
0
1
0
−1











1
1
0
1
0
0
1
−1
2
2
1
1
1
0
0
−2
Number of sincere Tits roots of poset I sI = 18.
Table of roots of qbI
[ −1, 1, 1, 1, 1, 1, 1, 2 ],
[ −1, 1, 1, 1, 2, 1, 1, 3 ],
[ −1, 1, 1, 1, 2, 2, 2, 4 ],
[ 1,−2,−1,−1,−2,−2,−1,−4 ],
[ 1,−1,−1,−1,−2,−2,−1,−4 ],
[ 1,−1,−1,−1,−1,−2,−1,−3 ],
[ −2, 1, 0, 1, 1, 2, 1, 2 ],
[ −1, 0, −1, 0, −1, 0, −1, −2 ],
[ −1, 0, −1, 0, −1, 1, 0, −1 ],
[ −1, 0, −1, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 2, 1, 2 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 1, 1, 1 ],
[ −1, 1, 0, 0, 1, 1, 1, 2 ],
[ −1, 1, 0, 1, 1, 1, 0, 1 ],
[ −1, 1, 0, 1, 1, 2, 0, 2 ],
[ −1, 1, 0, 1, 2, 2, 1, 3 ],
[ 0, −1, −2, −1, −2, −1, −1, −4 ],
[ 0, −1, −1, −1, −2, −1, −1, −3 ],
[ 0, −1, −1, −1, −1, −1, 0, −3 ],
[ 0, −1, −1, 0, −2, −1, −1, −3 ],
[ 0, −1, −1, 0, −1, −1, 0, −2 ],
[ 0, −1, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, −1, −1, −1, −2 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, −2, −1, −1, −3 ],
[ 0, 0, −1, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 0, −1, −2 ],
[ 0, 0, −1, 0, 0, 0, −1, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, −1, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1, −2 ],
[ 0, 0, 0, 0, −1, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ −1, 1, 1, 1, 1, 1, 1, 3 ],
[ −1, 1, 1, 1, 2, 2, 1, 3 ],
[ −1, 1, 1, 2, 2, 2, 1, 4 ],
[ 1,−1,−1,−2,−2,−2,−1,−4 ],
[ 1,−1,−1,−1,−2,−2,−1,−3 ],
[ 1,−1,−1,−1,−1,−1,−1,−3 ],
[ −1, −1, −1, 0, −1, 0, 0, −2 ],
[ −1, 0, −1, 0, −1, 0, 0, −2 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 1, 0, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 1 ],
[ −1, 0, 1, 1, 1, 1, 1, 2 ],
[ −1, 1, 0, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 0, 1, 1, 0, 1 ],
[ −1, 1, 0, 0, 1, 2, 1, 2 ],
[ −1, 1, 0, 1, 1, 1, 0, 2 ],
[ −1, 1, 0, 1, 1, 2, 1, 2 ],
[ −1, 1, 1, 0, 1, 1, 1, 2 ],
[ 0, −1, −1, −1, −2, −2, −1, −4 ],
[ 0, −1, −1, −1, −2, −1, 0, −3 ],
[ 0, −1, −1, −1, −1, −1, 0, −2 ],
[ 0, −1, −1, 0, −1, −1, −1, −3 ],
[ 0, −1, −1, 0, −1, 0, −1, −2 ],
[ 0, −1, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, −1, −1, 0, −2 ],
[ 0, −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, −1, −1, −1, −1, −3 ],
[ 0, 0, −1, −1, −1, 0, −1, −2 ],
[ 0, 0, −1, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 0, −1, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, −1, −1, −1, −2 ],
[ 0, 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, −1, −1, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
208
[ −1, 1, 1, 1, 1, 2, 1, 3 ],
[ −1, 1, 1, 1, 2, 2, 1, 4 ],
[ −1, 2, 1, 1, 2, 2, 1, 4 ],
[ 1,−1,−1,−1,−2,−2,−2,−4 ],
[ 1,−1,−1,−1,−2,−1,−1,−3 ],
[ 1,−1,−1,−1,−1,−1,−1,−2 ],
[ −1, 0, −1, −1, −1, 0, 0, −2 ],
[ −1, 0, −1, 0, −1, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, 1, 0, −1 ],
[ −1, 0, −1, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 2 ],
[ −1, 1, −1, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 0, 0, 1, 0, 1 ],
[ −1, 1, 0, 0, 1, 1, 1, 1 ],
[ −1, 1, 0, 1, 0, 1, 0, 1 ],
[ −1, 1, 0, 1, 1, 1, 1, 2 ],
[ −1, 1, 0, 1, 1, 2, 1, 3 ],
[ −1, 1, 1, 1, 1, 1, 0, 2 ],
[ 0, −1, −1, −1, −2, −1, −1, −4 ],
[ 0, −1, −1, −1, −1, −1, −1, −3 ],
[ 0, −1, −1, −1, −1, 0, 0, −2 ],
[ 0, −1, −1, 0, −1, −1, −1, −2 ],
[ 0, −1, −1, 0, −1, 0, 0, −2 ],
[ 0, −1, 0, −1, −1, −1, 0, −2 ],
[ 0, −1, 0, 0, −1, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, −1, −1, −1, −2 ],
[ 0, 0, −1, −1, −1, 0, 0, −2 ],
[ 0, 0, −1, 0, −1, −1, −1, −2 ],
[ 0, 0, −1, 0, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, −1, 0, −2 ],
[ 0, 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 0, 1, 1, 0, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 0, 1, 0, 1, 0, 1 ],
0, 0, 0, 1, 1, 1, 0, 2 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 0, 1, 0, 1, 1, 1, 2 ],
0, 0, 1, 1, 1, 0, 0, 2 ],
0, 0, 1, 1, 1, 1, 1, 2 ],
0, 1, 0, −1, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 1, 1, 0, 1 ],
0, 1, 0, 1, 1, 1, 0, 2 ],
0, 1, 1, 0, 1, 0, 0, 2 ],
0, 1, 1, 0, 1, 1, 1, 2 ],
0, 1, 1, 1, 1, 0, 0, 2 ],
0, 1, 1, 1, 1, 1, 1, 3 ],
0, 1, 1, 1, 2, 1, 1, 4 ],
1, −1, −1, −1, −1, −1, 0, −2 ],
1, −1, 0, −1, −1, −2, −1, −3 ],
1, −1, 0, −1, −1, −1, −1, −2 ],
1, −1, 0, −1, 0, −1, 0, −1 ],
1, −1, 0, 0, −1, −1, −1, −1 ],
1, −1, 0, 0, 0, −1, 0, −1 ],
1, −1, 1, 0, 0, −1, 0, 0 ],
1, 0, 0, −1, −1, −1, −1, −2 ],
1, 0, 0, −1, 0, −1, −1, −1 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, −1, −1, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 1, −1, 0, −1, 0, 0 ],
1, 0, 1, 0, 0, −1, 0, 1 ],
1, 0, 1, 0, 1, 0, 0, 1 ],
1, 0, 1, 1, 1, 0, 0, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 0, 1, 1, 1, 1 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 0, 1, 1, 0, 0, 1 ],
0, 0, 0, 1, 1, 1, 1, 2 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 1, 0, 1, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 0, 1, 1, 1, 0, 1, 2 ],
0, 0, 1, 1, 1, 1, 1, 3 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 0, 0, 0, 1, 0, 1 ],
0, 1, 0, 0, 1, 1, 0, 2 ],
0, 1, 1, 0, 0, 0, 0, 1 ],
0, 1, 1, 0, 1, 0, 1, 2 ],
0, 1, 1, 0, 1, 1, 1, 3 ],
0, 1, 1, 1, 1, 1, 0, 2 ],
0, 1, 1, 1, 2, 1, 0, 3 ],
0, 1, 1, 1, 2, 2, 1, 4 ],
1, −1, −1, 0, −1, −1, −1, −2 ],
1, −1, 0, −1, −1, −2, −1, −2 ],
1, −1, 0, −1, −1, −1, 0, −2 ],
1, −1, 0, 0, −1, −2, −1, −2 ],
1, −1, 0, 0, −1, −1, 0, −1 ],
1, −1, 0, 0, 0, −1, 0, 0 ],
1, 0, −1, −1, −1, −1, −1, −2 ],
1, 0, 0, −1, −1, −1, −1, −1 ],
1, 0, 0, −1, 0, −1, 0, −1 ],
1, 0, 0, 0, −1, −1, −1, −1 ],
1, 0, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 1, 0, 0, −1, −1, 0 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 0, 1, 0, 1, 0, 0, 2 ],
1, 1, 1, 0, 1, 0, 0, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
1, −1,
1, −1,
1, −1,
1, −1,
1, −1,
1, −1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
2, −1,
0, 0, 0, 1, 1, 1 ],
0, 0, 1, 0, 1, 1 ],
0, 0, 1, 1, 1, 2 ],
0, 1, 0, 0, 0, 1 ],
0, 1, 1, 1, 0, 1 ],
1, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 1, 1 ],
1, 0, 1, 0, 1, 2 ],
1, 1, 1, 0, 0, 1 ],
1, 1, 1, 1, 0, 2 ],
1, 1, 2, 1, 1, 3 ],
0, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 1 ],
0, 0, 1, 1, 1, 2 ],
1, 0, 1, 0, 0, 1 ],
1, 0, 1, 1, 0, 2 ],
1, 0, 2, 1, 1, 3 ],
1, 1, 1, 1, 0, 3 ],
1, 1, 2, 1, 1, 3 ],
2, 1, 2, 1, 1, 4 ],
0, −1, −2, −2, −1, −3 ],
0, −1, −1, −2, 0, −2 ],
0, −1, −1, −1, 0, −1 ],
0, 0, −1, −1, −1, −2 ],
0, 0, 0, −1, −1, −1 ],
0, 0, 0, 0, 0, 0 ],
0, −1, −1, −2, −1, −2 ],
0, −1, −1, −1, 0, −1 ],
0, −1, 0, −1, 0, 0 ],
0, 0, 0, −1, −1, −1 ],
0, 0, 0, 0, −1, 0 ],
0, 0, 1, 0, 0, 1 ],
1, 0, 0, −1, 0, 0 ],
1, 0, 1, −1, 0, 1 ],
1, 0, 1, 0, 1, 2 ],
0, −1, −1, −2, −1, −2 ]
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
∗
3
7
2
6
• I ≡ P111 :
5
4
1





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
















bI =
C




209
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
0
0
0
0
0
−1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
−1
0
0
−1
−1
0
0
0
1
1
1
1
1
1
1
−1
















BI =



−1
0
0
0
0
0
1
0
1
0
0
1
0
0
−1
0
1
1
1
0
0
0
0
−1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
−1
0
0
0
0
0
−1
−1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
−1
Number of sincere Tits roots of poset I sI = 18.
Table of roots of qbI
[ −2, 1, 1, 1, 1, 1,−1, 1 ],
[ −2, 2, 1, 1, 1, 2,−1, 2 ],
[ −1, 1, 1, 1, 1, 1,−1, 1 ],
[ 1,−2,−1,−1,−1,−1, 1,−2 ],
[ 2,−2,−1,−2,−1,−1, 1,−2 ],
[ 2,−2,−1,−1,−1,−1, 1,−2 ],
[ −2, 1, 1, 0, 1, 1, 0, 1 ],
[ −2, 1, 1, 1, 1, 1, 0, 1 ],
[ −2, 2, 0, 1, 1, 1, −1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 1, 0, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 1, 0, 1 ],
[ −1, 1, 0, 0, 1, 0, 0, 1 ],
[ −1, 1, 0, 0, 1, 1, 0, 1 ],
[ −1, 1, 0, 1, 0, 0, 0, 1 ],
[ −1, 1, 0, 1, 0, 1, 0, 1 ],
[ −1, 1, 0, 1, 1, 0, 0, 1 ],
[ −1, 1, 1, 0, 1, 0, 0, 1 ],
[ −1, 1, 1, 0, 1, 1, 0, 2 ],
[ −1, 1, 1, 1, 0, 1, 0, 1 ],
[ −1, 1, 1, 1, 1, 0, 0, 1 ],
[ −1, 2, 0, 0, 1, 1, −1, 1 ],
[ −1, 2, 0, 1, 1, 1, −2, 1 ],
[ 0, −1, 0, −1, −1, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 1, −1, 0, 0, 1, 0 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, −1, 0, 0, 0, −1, −1 ],
[ 0, 1, −1, 0, 0, 1, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 1, −1, 0 ],
[ 0, 1, 0, 0, 1, 0, −1, 0 ],
[ −2, 2, 1, 1, 1, 1,−1, 1 ],
[ −2, 2, 1, 1, 2, 1,−1, 2 ],
[ −1, 1, 1, 1, 1, 1,−1, 2 ],
[ 1,−1,−1,−1,−1,−1, 1,−2 ],
[ 2,−2,−1,−1,−2,−1, 1,−2 ],
[ 2,−2,−1,−1,−1,−1, 1,−1 ],
[ −2, 1, 1, 1, 0, 1, 0, 1 ],
[ −2, 1, 1, 1, 1, 1, 0, 2 ],
[ −2, 2, 1, 1, 1, 1, 0, 2 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 1, 0, 1 ],
[ −1, 0, 1, 0, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 1, 0, 1 ],
[ −1, 1, 0, 0, 0, 1, −1, 0 ],
[ −1, 1, 0, 0, 1, 0, −1, 0 ],
[ −1, 1, 0, 0, 1, 1, −1, 0 ],
[ −1, 1, 0, 1, 0, 0, −1, 0 ],
[ −1, 1, 0, 1, 0, 1, −1, 0 ],
[ −1, 1, 0, 1, 1, 0, −1, 0 ],
[ −1, 1, 0, 1, 1, 1, −1, 1 ],
[ −1, 1, 1, 0, 1, 1, −1, 1 ],
[ −1, 1, 1, 1, 0, 0, 0, 1 ],
[ −1, 1, 1, 1, 0, 1, 0, 2 ],
[ −1, 1, 1, 1, 1, 0, 0, 2 ],
[ −1, 2, 0, 1, 0, 1, −1, 1 ],
[ −1, 2, 0, 1, 1, 1, −1, 1 ],
[ 0, −1, 0, −1, 0, −1, 1, −1 ],
[ 0, −1, 0, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, −1, 0, 1, −1 ],
[ 0, −1, 0, 0, 0, −1, 1, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, 0, −1, 0, 1, 0 ],
[ 0, −1, 1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 0, 1, −1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, −1, 0, 0, 0, −1, 0 ],
[ 0, 1, −1, 0, 1, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, −1, 1 ],
[ 0, 1, 0, 0, 1, 0, −1, 1 ],
210
[ −2, 2, 1, 1, 1, 1,−1, 2 ],
[ −2, 2, 1, 2, 1, 1,−1, 2 ],
[ −1, 2, 1, 1, 1, 1,−1, 2 ],
[ 1,−1,−1,−1,−1,−1, 1,−1 ],
[ 2,−2,−1,−1,−1,−2, 1,−2 ],
[ 2,−1,−1,−1,−1,−1, 1,−1 ],
[ −2, 1, 1, 1, 1, 0, 0, 1 ],
[ −2, 1, 2, 1, 1, 1, 0, 2 ],
[ −1, −1, 1, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 1, 1 ],
[ −1, 0, 1, 0, 0, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 0, 1, 1 ],
[ −1, 0, 1, 1, 0, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ −1, 1, 0, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 1, 1, −1, 1 ],
[ −1, 1, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 1, −1, 1 ],
[ −1, 1, 0, 1, 1, 0, −1, 1 ],
[ −1, 1, 1, 0, 0, 1, 0, 1 ],
[ −1, 1, 1, 0, 1, 1, 0, 1 ],
[ −1, 1, 1, 1, 0, 1, −1, 1 ],
[ −1, 1, 1, 1, 1, 0, −1, 1 ],
[ −1, 1, 1, 1, 1, 1, 0, 2 ],
[ −1, 2, 0, 1, 1, 0, −1, 1 ],
[ −1, 2, 0, 1, 1, 1, −1, 2 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, −1, −1, 1, −1 ],
[ 0, −1, 0, 0, −1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, −1, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 1, 0, 0, −1, 1, 0 ],
[ 0, −1, 1, 0, 0, 0, 1, 1 ],
[ 0, 0, −1, 0, 0, −1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, −1, 0, 0, 0, 0, 0 ],
[ 0, 1, −1, 1, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 1, 0, 0, 1, 1, −1, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
1, −2, 0, −1, −1, −1, 1, −2 ],
1, −2, 0, −1, −1, 0, 1, −1 ],
1, −1, −1, −1, −1, −1, 0, −2 ],
1, −1, −1, −1, −1, 0, 1, −1 ],
1, −1, −1, −1, 0, −1, 1, −1 ],
1, −1, −1, 0, −1, −1, 0, −1 ],
1, −1, −1, 0, 0, −1, 0, −1 ],
1, −1, 0, −1, −1, 0, 1, −1 ],
1, −1, 0, −1, 0, −1, 1, −1 ],
1, −1, 0, −1, 0, 0, 0, 0 ],
1, −1, 0, 0, −1, −1, 1, −1 ],
1, −1, 0, 0, −1, 0, 0, 0 ],
1, −1, 0, 0, 0, −1, 0, 0 ],
1, 0, −1, −1, −1, 0, 0, −1 ],
1, 0, −1, −1, 0, 0, 0, −1 ],
1, 0, −1, 0, −1, 0, −1, −1 ],
1, 0, −1, 0, 0, −1, −1, −1 ],
1, 0, −1, 0, 0, 0, −1, −1 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, −1, 0 ],
1, 1, −1, 0, 0, 0, −1, 0 ],
2, −1, −2, −1, −1, −1, 0, −2 ],
2, −1, −1, −1, −1, 0, 0, −1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 1, 0, 1, 0, 0, −1, 0 ],
0, 1, 0, 1, 0, 1, −1, 1 ],
1, −2, 0, −1, −1, −1, 1, −1 ],
1, −2, 0, −1, 0, −1, 1, −1 ],
1, −1, −1, −1, −1, 0, 0, −2 ],
1, −1, −1, −1, 0, −1, 0, −2 ],
1, −1, −1, −1, 0, 0, 0, −1 ],
1, −1, −1, 0, −1, −1, 1, −1 ],
1, −1, 0, −1, −1, −1, 1, −1 ],
1, −1, 0, −1, −1, 0, 1, 0 ],
1, −1, 0, −1, 0, −1, 1, 0 ],
1, −1, 0, −1, 0, 0, 1, 0 ],
1, −1, 0, 0, −1, −1, 1, 0 ],
1, −1, 0, 0, −1, 0, 1, 0 ],
1, −1, 0, 0, 0, −1, 1, 0 ],
1, 0, −1, −1, 0, −1, 0, −1 ],
1, 0, −1, −1, 0, 0, 0, 0 ],
1, 0, −1, 0, −1, 0, 0, −1 ],
1, 0, −1, 0, 0, −1, 0, −1 ],
1, 0, −1, 0, 0, 0, −1, 0 ],
1, 0, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
2, −2, −1, −1, −1, −1, 0, −2 ],
2, −1, −1, −1, −1, −1, 0, −2 ],
2, −1, −1, −1, 0, −1, 0, −1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 1, 0, 1, 0, 0, −1, 1 ],
0, 1, 0, 1, 1, 0, −1, 1 ],
1, −2, 0, −1, −1, −1, 2, −1 ],
1, −2, 0, 0, −1, −1, 1, −1 ],
1, −1, −1, −1, −1, 0, 0, −1 ],
1, −1, −1, −1, 0, −1, 0, −1 ],
1, −1, −1, 0, −1, −1, 0, −2 ],
1, −1, −1, 0, −1, 0, 0, −1 ],
1, −1, 0, −1, −1, 0, 0, −1 ],
1, −1, 0, −1, 0, −1, 0, −1 ],
1, −1, 0, −1, 0, 0, 0, −1 ],
1, −1, 0, 0, −1, −1, 0, −1 ],
1, −1, 0, 0, −1, 0, 0, −1 ],
1, −1, 0, 0, 0, −1, 0, −1 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, −1, −1, 0, 0, −1, −1 ],
1, 0, −1, 0, −1, −1, 0, −1 ],
1, 0, −1, 0, −1, 0, 0, 0 ],
1, 0, −1, 0, 0, −1, 0, 0 ],
1, 0, −1, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
2, −2, 0, −1, −1, −1, 1, −1 ],
2, −1, −1, −1, −1, −1, 0, −1 ],
2, −1, −1, 0, −1, −1, 0, −1 ]
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
−1
∗
6
7
4
5
• I ≡ P112 :
3
2
1





CI =








b
CoxI =



0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
−1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
−1
















bI =
C




1
1
1
1
1
1
1
0
















BI =



−1
−1
−1
−1
−1
−1
−1
1











1
1
1
0
1
0
1
−1
1
1
1
1
1
0
0
−1











Number of sincere Tits roots of poset I sI = 18.
Table of roots of qbI
[ −2,−1, 1, 1, 1, 1, 1, 1 ],
[ −2,−1, 1, 1, 1, 2, 1, 1 ],
211
[ −2,−1, 1, 1, 1, 2, 1, 2 ],
[ −2,−1, 1, 1, 1, 2, 2, 2 ],
[ −1,−1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1,−1,−1,−1,−2,−1,−2 ],
[ 2, 1,−2,−1,−1,−2,−1,−2 ],
[ 2, 1,−1,−1,−1,−2,−1,−2 ],
[ −2, −1, 1, 0, 1, 2, 1, 1 ],
[ −2, 0, 1, 1, 1, 1, 0, 1 ],
[ −2, 0, 1, 1, 1, 2, 1, 2 ],
[ −1, −1, 0, 0, 0, 1, 1, 0 ],
[ −1, −1, 0, 0, 1, 1, 1, 1 ],
[ −1, −1, 1, 0, 0, 1, 0, 0 ],
[ −1, −1, 1, 0, 0, 2, 1, 1 ],
[ −1, −1, 1, 0, 1, 1, 1, 1 ],
[ −1, −1, 1, 0, 1, 2, 1, 2 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 1, 0, 0, 1, 1 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 1 ],
[ −1, 0, 1, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 1, 0, 0, 1, 1 ],
[ −1, 0, 1, 1, 0, 1, 1, 2 ],
[ −1, 0, 1, 1, 1, 1, 0, 2 ],
[ −1, 1, 0, 1, 0, −1, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 1, 1 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 1, 1, 0 ],
[ 0, −1, 0, 0, 1, 1, 0, 0 ],
[ 0, −1, 1, −1, 0, 1, 0, 0 ],
[ 0, −1, 1, 0, 0, 1, 0, 1 ],
[ 0, 0, −1, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, −1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, −1, 0, −1, −1, 0, −1 ],
[ 0, 1, −1, 0, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, −1, −1, −1, −1 ],
[ 0, 1, 0, 0, −1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, −1, 0, 0 ],
[ 1, −1, −1, −1, 0, 0, 0, −1 ],
[ 1, −1, 0, −1, 0, 0, 0, −1 ],
[ 1, −1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, −1, −1, −1, −1, 0, −1 ],
[ 1, 0, −1, −1, 0, −1, −1, −1 ],
[ 1, 0, −1, −1, 0, 0, 0, −1 ],
[ 1, 0, −1, 0, 0, −1, −1, −1 ],
[ 1, 0, −1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, −1, −1, −1, 0, −1 ],
[ 1, 0, 0, −1, −1, 0, 0, 0 ],
[ 1, 0, 0, −1, 0, 0, −1, 0 ],
[ 1, 0, 0, 0, −1, −1, 0, −1 ],
[ 1, 0, 0, 0, 0, −1, −1, −1 ],
[ 1, 0, 0, 0, 0, 0, −1, 0 ],
[ 1, 1, −1, −1, −1, −1, 0, −1 ],
[ 1, 1, −1, 0, −1, −2, −1, −1 ],
[ −2,−1, 1, 1, 2, 2, 1, 2 ],
[ −1,−1, 1, 1, 1, 1, 1, 2 ],
[ 1, 1,−1,−1,−1,−1,−1,−2 ],
[ 2, 1,−1,−1,−2,−2,−1,−2 ],
[ 2, 1,−1,−1,−1,−2,−1,−1 ],
[ −2, 0, 0, 1, 1, 1, 1, 1 ],
[ −2, 0, 1, 1, 1, 1, 1, 1 ],
[ −2, 0, 1, 2, 1, 1, 1, 2 ],
[ −1, −1, 0, 0, 1, 1, 0, 0 ],
[ −1, −1, 0, 0, 1, 2, 1, 1 ],
[ −1, −1, 1, 0, 0, 1, 1, 0 ],
[ −1, −1, 1, 0, 1, 1, 0, 0 ],
[ −1, −1, 1, 0, 1, 2, 0, 1 ],
[ −1, −1, 1, 1, 0, 1, 1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 0, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 2 ],
[ −1, 0, 1, 0, 0, 1, 0, 1 ],
[ −1, 0, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 1, 0, 1 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 1, 2 ],
[ −1, 1, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 1, 0, 0, 1 ],
[ 0, −1, 0, −1, 0, 1, 0, −1 ],
[ 0, −1, 0, −1, 1, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 1, 1, 1 ],
[ 0, −1, 0, 0, 1, 1, 0, 1 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, 0, 0, 1, 1, 1 ],
[ 0, 0, −1, 0, 0, −1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, −1, −1 ],
[ 0, 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 1, −1, 0, 0, −1, −1, −1 ],
[ 0, 1, −1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, −1, −1, 0, −1 ],
[ 0, 1, 0, 0, 0, −1, −1, −1 ],
[ 0, 1, 0, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 1, −1, −1, 0, 0 ],
[ 0, 1, 0, 1, 0, −1, 0, 1 ],
[ 1, −1, 0, −1, −1, 0, 0, −1 ],
[ 1, −1, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, −1, −1, −1, −1, −1, −2 ],
[ 1, 0, −1, −1, −1, 0, 0, −1 ],
[ 1, 0, −1, −1, 0, −1, 0, −1 ],
[ 1, 0, −1, −1, 0, 0, 0, 0 ],
[ 1, 0, −1, 0, 0, −1, 0, −1 ],
[ 1, 0, 0, −1, −1, −1, −1, −2 ],
[ 1, 0, 0, −1, −1, 0, −1, −1 ],
[ 1, 0, 0, −1, 0, −1, −1, −1 ],
[ 1, 0, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, −1, −1, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, −1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, −1, −1, 0, −1, −1, −1 ],
[ 1, 1, −1, 0, −1, −2, 0, −1 ],
212
[ −2,−1, 2, 1, 1, 2, 1, 2 ],
[ −1,−1, 1, 1, 1, 2, 1, 2 ],
[ 1, 1,−1,−1,−1,−1,−1,−1 ],
[ 2, 1,−1,−1,−1,−2,−2,−2 ],
[ 2, 1,−1,−1,−1,−1,−1,−1 ],
[ −2, 0, 1, 1, 0, 1, 1, 1 ],
[ −2, 0, 1, 1, 1, 1, 1, 2 ],
[ −1, −2, 1, 0, 1, 2, 1, 1 ],
[ −1, −1, 0, 0, 1, 1, 1, 0 ],
[ −1, −1, 0, 1, 1, 1, 1, 1 ],
[ −1, −1, 1, 0, 0, 1, 1, 1 ],
[ −1, −1, 1, 0, 1, 1, 0, 1 ],
[ −1, −1, 1, 0, 1, 2, 1, 1 ],
[ −1, −1, 1, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 1, 1, 1 ],
[ −1, 0, 1, 1, 0, 0, 0, 1 ],
[ −1, 0, 1, 1, 0, 1, 1, 1 ],
[ −1, 0, 1, 1, 1, 1, 0, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 0, 1 ],
[ −1, 1, 1, 1, 0, 0, 0, 1 ],
[ 0, −1, 0, −1, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 1, 1 ],
[ 0, −1, 1, 0, 0, 1, 0, 0 ],
[ 0, −1, 1, 0, 1, 1, 0, 1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, −1, 0, 0, −1, 0, −1 ],
[ 0, 1, −1, 1, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, −1, −1, 0, 0 ],
[ 0, 1, 0, 0, 0, −1, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, −1, −1, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 1, −1, 0, −1, 0, 0, −1, −1 ],
[ 1, −1, 0, −1, 0, 1, 0, 0 ],
[ 1, 0, −1, −1, −1, −1, 0, −2 ],
[ 1, 0, −1, −1, 0, −1, −1, −2 ],
[ 1, 0, −1, −1, 0, 0, −1, −1 ],
[ 1, 0, −1, 0, −1, −1, 0, −1 ],
[ 1, 0, −1, 0, 0, −1, 0, 0 ],
[ 1, 0, 0, −1, −1, −1, −1, −1 ],
[ 1, 0, 0, −1, −1, 0, 0, −1 ],
[ 1, 0, 0, −1, 0, 0, −1, −1 ],
[ 1, 0, 0, 0, −1, −1, −1, −1 ],
[ 1, 0, 0, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 1, −1, 0, −1, −2, −1, −2 ],
[ 1, 1, −1, 0, −1, −1, −1, −1 ],
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
2,
2,
1, −1, 0, −1, −1, 0, −1 ],
1, −1, 0, 0, −1, −1, −1 ],
1, 0, −1, −1, −1, −1, −1 ],
1, 0, 0, −1, −1, −1, 0 ],
2, −1, 0, −1, −2, −1, −1 ],
0, −1, −1, −1, −1, −1, −2 ],
0, −1, −1, 0, −1, −1, −1 ],
[
[
[
[
[
[
[
1, −1, 0, −1, −1, 0, 0 ],
1, −1, 0, 0, −1, −1, 0 ],
1, 0, 0, −1, −2, −1, −1 ],
1, 0, 0, −1, −1, 0, 0 ],
0, −1, −2, −1, −1, −1, −2 ],
0, −1, −1, −1, −1, −1, −1 ],
0, 0, −1, −1, −1, −1, −1 ],
1,
1,
1,
1,
2,
2,
2,
[
[
[
[
[
[
[
1,
1,
1,
1,
2,
2,
2,
1, −1, 0, 0, −2, −1, −1 ],
1, −1, 0, 0, −1, 0, 0 ],
1, 0, 0, −1, −1, −1, −1 ],
1, 0, 0, 0, −1, −1, 0 ],
0, −1, −1, −1, −2, −1, −2 ],
0, −1, −1, −1, −1, 0, −1 ],
1, −1, 0, −1, −2, −1, −1 ]
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
∗
7
6
• I ≡ P113 :
5
2
4
1
3





CI =








b I =
Cox




0
0
1
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
−1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
−1
0
0
−1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
1
0
0
















b
CI =



1
1
1
1
1
1
1
−1











1
1
0
1
1
1
1
0
−1
 0

 0

BI = −10

 0
 0
0

1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
−1
−1
−1
−1
−1
−1
−1
1
0
0
1
0
0
0
0
−1











0
0
−1
−1
−1
−1
−1
0
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 2, 1,
[ −1,−1,−2,
[ −1,−1,−1,
[ −1,−1,−1,
[ −1, 0,−1,
[ −1, 0,−1,
[ −1, 0,−1,
[ −1, 0,−1,
[ −1, 0,−1,
[ −1, 0, 0,
[ −1, 0, 0,
[ −1, 1,−1,
[ −1, 1,−1,
[ −1, 1, 0,
[ −1, 1, 0,
[ −1, 1, 0,
[ −1, 1, 0,
[ −1, 1, 0,
1,
0,
0,
0,
0,
0,
0,
1,
1,
0,
1,
1,
1,
0,
1,
1,
1,
1,
1,−1,−1, 1 ],
0, 1, 1,−1 ],
0, 0, 1,−1 ],
0, 1, 1, 0 ],
0, 0, 1, 0 ],
0, 1, 1, 0 ],
1, 0, 1, 0 ],
0, 0, 0, 0 ],
1, 0, 0, 0 ],
0, 0, 1, 0 ],
0, 0, 0, 0 ],
1, −1, 0, 0 ],
1, 0, 0, 1 ],
1, 0, −1, 0 ],
0, −1, 0, 0 ],
0, 0, 0, 1 ],
1, −1, 0, 1 ],
1, 0, 0, 1 ],
[ 1,−2,−1,−1,−1, 1, 1,−1 ],
[ −1, −1, −1, −1, 0, 1, 1, −1 ],
[ −1, −1, −1, 0, 0, 1, 0, −1 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, 1, 0, −1 ],
[ −1, 0, −1, 0, 1, 0, 0, −1 ],
[ −1, 0, −1, 0, 1, 1, 0, 0 ],
[ −1, 0, −1, 1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 1, −1, 0, 1, 0, 0, 0 ],
[ −1, 1, −1, 1, 1, 0,−1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0,−1, 0 ],
[ −1, 1, 0, 1, 1,−1,−1, 0 ],
[ −1, 1, 0, 1, 1, 0,−1, 0 ],
[ −1, 2, 0, 1, 1,−1,−1, 0 ],
213
[ −2, 1,−1,
[ −1,−1,−1,
[ −1,−1,−1,
[ −1, 0,−1,
[ −1, 0,−1,
[ −1, 0,−1,
[ −1, 0,−1,
[ −1, 0,−1,
[ −1, 0, 0,
[ −1, 0, 0,
[ −1, 1,−1,
[ −1, 1,−1,
[ −1, 1, 0,
[ −1, 1, 0,
[ −1, 1, 0,
[ −1, 1, 0,
[ −1, 1, 0,
[ −1, 2, 0,
1, 1, 0, 0, 0 ],
0,−1, 1, 1,−1 ],
0, 0, 1, 1,−1 ],
0, 0, 0, 1,−1 ],
0, 0, 1, 0, 0 ],
0, 1, 0, 0, 0 ],
1, 0, 0, 0,−1 ],
1, 0, 1, 0, 0 ],
0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0 ],
1, 0, 0, 0, 0 ],
1, 1, 0, 0, 0 ],
0, 1,−1, 0, 0 ],
0, 1, 0, 0, 1 ],
1, 0, 0, 0, 0 ],
1, 1,−1, 0, 0 ],
1, 1, 0,−1, 1 ],
1, 1,−1,−1, 1 ],
0
0
0
0
1
0
0
0











[ −1, 2, 0, 1, 1, −1, 0, 1 ],
[ −1, 2, 0, 2, 1, −1, −1, 1 ],
[ 0,−2,−1,−1,−1, 1, 2,−1 ],
[ 0,−2,−1, 0,−1, 1, 1,−1 ],
[ 0,−1,−1,−1, 0, 0, 1,−1 ],
[ 0,−1,−1,−1, 0, 1, 1, 0 ],
[ 0,−1,−1, 0,−1, 1, 1,−1 ],
[ 0,−1,−1, 0, 0, 0, 1,−1 ],
[ 0,−1,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 0,−1,−1, 1, 0,−1 ],
[ 0,−1, 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 0, 1, 0,−1 ],
[ 0,−1, 0, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0,−1, 1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, −1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, −1, 0, 0 ],
[ 0, 1, 0, 0, 1, 0, −1, 1 ],
[ 0, 1, 0, 1, 0, −1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, −1, 1 ],
[ 0, 1, 0, 1, 1, −1, −1, 1 ],
[ 0, 1, 1, 0, 0, −1, −1, 0 ],
[ 0, 1, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 1, 0, 1, −1, −1, 0 ],
[ 0, 1, 1, 0, 1, 0, −1, 1 ],
[ 0, 1, 1, 1, 0, −1, 0, 1 ],
[ 0, 2, 0, 1, 1, −1, −1, 1 ],
[ 0, 2, 1, 1, 1, −2, −1, 1 ],
[ 0, 2, 1, 1, 1, −1, −1, 2 ],
[ 1,−2, 0,−1,−1, 0, 1,−1 ],
[ 1,−2, 0,−1,−1, 1, 1, 0 ],
[ 1,−1, 0,−1,−1, 0, 1, 0 ],
[ 1,−1, 0,−1,−1, 1, 1, 0 ],
[ 1,−1, 0,−1, 0, 0, 1, 0 ],
[ 1,−1, 0, 0,−1, 0, 0, 0 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1,−1, 1,−1,−1, 0, 1, 0 ],
[ 1,−1, 1, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, −1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1,−1, 0, 0, −1, 0 ],
[ 1, 0, 1, 0,−1, −1, 0, 0 ],
[ 1, 0, 1, 0,−1, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, −1, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 1, 0, 0, −1, 0, 1 ],
[ 1, 1, 1, 1, 0, −1, −1, 1 ],
[ −1, 2, 0, 1, 1, 0,−1, 1 ],
[ 0, −2, −1, −1, −1, 1, 1, −2 ],
[ 0, −2, −1, −1, −1, 2, 1, −1 ],
[ 0, −2, 0, −1, −1, 1, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 0, −1 ],
[ 0, −1, −1, 0, −1, 0, 1, −1 ],
[ 0, −1, −1, 0, −1, 1, 1, 0 ],
[ 0, −1, −1, 0, 0, 0, 1, 0 ],
[ 0, −1, −1, 0, 0, 1, 1, 0 ],
[ 0, −1, 0, −1, −1, 1, 1, −1 ],
[ 0, −1, 0, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, −1, 0, 1, −1 ],
[ 0, −1, 0, 0, −1, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0,−1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1,−1, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 1, 0,−1, 0, 1 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 1,−1, 0, 1 ],
[ 0, 1, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 1, 0, 0, 0,−1, 1 ],
[ 0, 1, 1, 0, 1,−1,−1, 1 ],
[ 0, 1, 1, 1, 0,−1,−1, 0 ],
[ 0, 1, 1, 1, 0, 0,−1, 1 ],
[ 0, 2, 1, 0, 1,−1,−1, 1 ],
[ 0, 2, 1, 1, 1,−1,−2, 1 ],
[ 1, −2, 0, −2, −1, 1, 1, −1 ],
[ 1, −2, 0, −1, −1, 1, 0, −1 ],
[ 1, −1, 0, −1, −1, 0, 0, −1 ],
[ 1, −1, 0, −1, −1, 1, 0, −1 ],
[ 1, −1, 0, −1, 0, 0, 0, −1 ],
[ 1, −1, 0, −1, 0, 1, 0, 0 ],
[ 1, −1, 0, 0, −1, 0, 1, 0 ],
[ 1, −1, 1, −1, −1, 0, 0, −1 ],
[ 1, −1, 1, −1, −1, 1, 0, 0 ],
[ 1, 0, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 1, −1, −1, 0, 0, 0 ],
[ 1, 0, 1, −1, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, −1, 0,−1, 0 ],
[ 1, 0, 1, 0, 0,−1,−1, 0 ],
[ 1, 0, 1, 0, 0, 0,−1, 0 ],
[ 1, 1, 1, 0, 0,−1,−1, 0 ],
[ 1, 1, 1, 0, 0, 0,−1, 1 ],
[ 1, 1, 2, 0, 0,−1,−1, 1 ],
214
[ −1, 2, 0, 1, 2,−1,−1, 1 ],
[ 0,−2,−1,−1,−1, 1, 1,−1 ],
[ 0,−2,−1,−1, 0, 1, 1,−1 ],
[ 0,−1,−1,−1,−1, 1, 1,−1 ],
[ 0,−1,−1,−1, 0, 1, 1,−1 ],
[ 0,−1,−1, 0,−1, 1, 0,−1 ],
[ 0,−1,−1, 0, 0, 0, 0,−1 ],
[ 0,−1,−1, 0, 0, 1, 0,−1 ],
[ 0,−1, 0,−1,−1, 0, 1,−1 ],
[ 0,−1, 0,−1,−1, 1, 1, 0 ],
[ 0,−1, 0,−1, 0, 0, 1, 0 ],
[ 0,−1, 0,−1, 0, 1, 1, 0 ],
[ 0,−1, 0, 0,−1, 0, 1, 0 ],
[ 0,−1, 0, 0,−1, 1, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 1,−1,−1, 0 ],
[ 0, 1, 0, 0, 1, 0,−1, 0 ],
[ 0, 1, 0, 1, 0,−1,−1, 0 ],
[ 0, 1, 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0, 1, 1,−1,−1, 0 ],
[ 0, 1, 0, 1, 1, 0,−1, 1 ],
[ 0, 1, 1, 0, 0,−1, 0, 1 ],
[ 0, 1, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 1,−1, 0, 1 ],
[ 0, 1, 1, 1, 0,−1,−1, 1 ],
[ 0, 1, 1, 1, 1,−1,−1, 1 ],
[ 0, 2, 1, 1, 0,−1,−1, 1 ],
[ 0, 2, 1, 1, 1,−1,−1, 1 ],
[ 1,−2, 0,−1,−2, 1, 1,−1 ],
[ 1,−2, 0,−1,−1, 1, 1,−1 ],
[ 1,−1, 0,−1,−1, 0, 1,−1 ],
[ 1,−1, 0,−1,−1, 1, 0, 0 ],
[ 1,−1, 0,−1, 0, 0, 0, 0 ],
[ 1,−1, 0, 0,−1, 0, 0,−1 ],
[ 1,−1, 0, 0,−1, 1, 0, 0 ],
[ 1,−1, 1,−1,−1, 0, 0, 0 ],
[ 1,−1, 1,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1,−1, 0,−1, 0, 0 ],
[ 1, 0, 1,−1, 0, 0, 0, 1 ],
[ 1, 0, 1, 0,−1, 0, 0, 0 ],
[ 1, 0, 1, 0, 0,−1, 0, 0 ],
[ 1, 0, 1, 0, 0, 0,−1, 1 ],
[ 1, 1, 1, 0, 0,−1,−1, 1 ],
[ 1, 1, 1, 0, 1,−1,−1, 1 ],
[ 2,−1, 1,−1,−1, 0, 0, 0 ]
∗
7
• I ≡ P114 :
1
6
3
5
2
4





CI =








b I =
Cox




0
1
1
1
1
1
1
−1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
−1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
−1
0
0
0
1
0
0
0
0
−1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
−1
0
0
−1
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
















BI =



1
0
0
0
0
0
0
−1
















b
CI =



1
1
1
1
1
1
1
−1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
−1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
−1
0
0
−1
−1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
−1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
−1
−1
−1
−1
−1
−1
1











0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 1,−2,−1,−1,−1, 1,−2 ],
[ −1,−1, −1, −2, 0, 0, 1, −2 ],
[ −1,−1, −1, −1, 0, 0, 0, −2 ],
[ −1,−1, 0, −1, 0, 0, 0, −2 ],
[ −1,−1, 0, −1, 0, 1, 0, −1 ],
[ −1, 0, −2, −1, −1, −1, 1, −3 ],
[ −1, 0, −2, −1, −1, 0, 1, −2 ],
[ −1, 0, −1, −1, −1, −1, 1, −2 ],
[ −1, 0, −1, −1, −1, 0, 1, −1 ],
[ −1, 0, −1, −1, 0, −1, 1, −1 ],
[ −1, 0, −1, −1, 0, 0, 1, −1 ],
[ −1, 0, −1, 0, −1, −1, 1, −1 ],
[ −1, 0, −1, 0, −1, 0, 1, −1 ],
[ −1, 0, −1, 0, 0, −1, 1, −1 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 1, −2, 0, −1, −2, 1, −2 ],
[ −1, 1, −2, 0, −1, −1, 1, −1 ],
[ −1, 1, −1, 0, −1, −1, 1, −1 ],
[ −1, 1, −1, 1, −1, −1, 0, −1 ],
[ 0,−1, 0, −1, 0, 0, 0, −1 ],
[ 0,−1, 0, −1, 0, 1, 0, −1 ],
[ 0,−1, 0, −1, 1, 0, 0, −1 ],
[ 0,−1, 0, −1, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 1, −1, 0, 1, 0, 0 ],
[ 0,−1, 1, −1, 1, 1, 0, 0 ],
[ 0,−1, 1, 0, 0, 1,−1, 0 ],
[ 0,−1, 1, 0, 1, 0,−1, 0 ],
[ 0,−1, 1, 0, 1, 1,−1, 0 ],
[ 1,−1, 2, 1, 1, 1,−1, 2 ],
[ −1, −1,−1,−1,−1, 0, 1,−2 ],
[ −1, −1,−1,−1, 0, 0, 1,−2 ],
[ −1, −1, 0,−1, 0, 0, 0,−1 ],
[ −1, −1, 0,−1, 1, 0, 0,−1 ],
[ −1, 0,−2,−1,−1,−1, 1,−2 ],
[ −1, 0,−2,−1, 0,−1, 1,−2 ],
[ −1, 0,−1,−1,−1, 0, 0,−2 ],
[ −1, 0,−1,−1, 0,−1, 0,−2 ],
[ −1, 0,−1,−1, 0, 0, 0,−2 ],
[ −1, 0,−1, 0,−1,−1, 0,−2 ],
[ −1, 0,−1, 0,−1, 0, 0,−2 ],
[ −1, 0,−1, 0, 0,−1, 0,−2 ],
[ −1, 0,−1, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 1,−2, 0,−1,−1, 0,−2 ],
[ −1, 1,−1, 0,−1,−1, 0,−2 ],
[ −1, 1,−1, 0,−1, 0, 0,−1 ],
[ 0, −2, 1,−1, 1, 1, 0, 0 ],
[ 0, −1, 0,−1, 0, 0, 1,−1 ],
[ 0, −1, 0,−1, 0, 1, 0, 0 ],
[ 0, −1, 0,−1, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0,−1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 1,−1, 1, 0, 0, 0 ],
[ 0, −1, 1,−1, 1, 1, 0, 1 ],
[ 0, −1, 1, 0, 0, 1, 0, 0 ],
[ 0, −1, 1, 0, 1, 0, 0, 0 ],
[ 0, −1, 1, 0, 1, 1, −1, 1 ],
215
[ −2, 0,−2,−1,−1,−1, 1,−3 ],
[ −1,−1,−1,−1, 0,−1, 1,−2 ],
[ −1,−1,−1,−1, 0, 0, 1,−1 ],
[ −1,−1, 0,−1, 0, 0, 1,−1 ],
[ −1,−1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0,−2,−1,−1,−1, 2,−2 ],
[ −1, 0,−2, 0,−1,−1, 1,−2 ],
[ −1, 0,−1,−1,−1, 0, 1,−2 ],
[ −1, 0,−1,−1, 0,−1, 1,−2 ],
[ −1, 0,−1,−1, 0, 0, 0,−1 ],
[ −1, 0,−1, 0,−1,−1, 1,−2 ],
[ −1, 0,−1, 0,−1, 0, 0,−1 ],
[ −1, 0,−1, 0, 0,−1, 0,−1 ],
[ −1, 0, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 1,−2, 0,−2,−1, 1,−2 ],
[ −1, 1,−2, 0,−1,−1, 1,−2 ],
[ −1, 1,−1, 0,−1,−1, 0,−1 ],
[ −1, 1,−1, 0, 0,−1, 0,−1 ],
[ 0,−1,−1,−1, 0, 0, 1,−1 ],
[ 0,−1, 0,−1, 0, 0, 1, 0 ],
[ 0,−1, 0,−1, 0, 1, 1, 0 ],
[ 0,−1, 0,−1, 1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 1,−1, 1, 1,−1, 0 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 0, 1, 0, 1 ],
[ 0,−1, 1, 0, 1, 0, 0, 1 ],
[ 0,−1, 1, 0, 1, 1, 0, 1 ],
0
0
0
0
0
0
0
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,−1, 2, 0, 1, 1,−1, 1 ],
0, 0, −1, −1, 0, 0, 0, −1 ],
0, 0, −1, 0, −1, −1, 1, −1 ],
0, 0, −1, 0, −1, 0, 1, 0 ],
0, 0, −1, 0, 0, −1, 1, 0 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, −1, 1, 0, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, 1, 0, 1 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 0, 1, 1, 0, 0,−1, 1 ],
0, 0, 1, 1, 1, 0,−1, 1 ],
0, 1, −1, 0, −1, −1, 1, −1 ],
0, 1, −1, 0, −1, 0, 0, 0 ],
0, 1, −1, 0, 0, −1, 0, 0 ],
0, 1, −1, 1, −1, −1, 0, −1 ],
0, 1, −1, 1, −1, 0, 0, 0 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 1, −1, 0, 0, 0 ],
0, 1, 0, 1, 0, −1, 0, 0 ],
0, 1, 0, 1, 0, 0,−1, 1 ],
0, 2, −1, 1, −1, −1, 0, 0 ],
1,−1, 1, 0, 1, 0, 0, 1 ],
1,−1, 1, 0, 1, 1, 0, 2 ],
1,−1, 2, 0, 1, 1, 0, 2 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 0, 1, 0, 0, 1, 0, 2 ],
1, 0, 1, 0, 1, 0, 0, 2 ],
1, 0, 1, 0, 1, 1, 0, 2 ],
1, 0, 1, 1, 0, 0, 0, 2 ],
1, 0, 1, 1, 0, 1, 0, 2 ],
1, 0, 1, 1, 1, 0, 0, 2 ],
1, 0, 2, 1, 0, 1,−1, 2 ],
1, 0, 2, 1, 1, 1,−1, 2 ],
1, 1, 0, 1, −1, 0, 0, 1 ],
1, 1, 0, 1, 0, 0, 0, 1 ],
1, 1, 1, 1, 0, 0,−1, 2 ],
1, 1, 1, 1, 1, 0,−1, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0,−1,−1,−1, 0, 1,−1 ],
0, 0,−1,−1, 0, 0, 1,−1 ],
0, 0,−1, 0,−1, 0, 0,−1 ],
0, 0,−1, 0, 0,−1, 0,−1 ],
0, 0,−1, 0, 0, 0, 0,−1 ],
0, 0, 0,−1, 0, 0, 0,−1 ],
0, 0, 0,−1, 0, 1, 0, 0 ],
0, 0, 0, 0,−1, 0, 0, 0 ],
0, 0, 0, 0, 0,−1, 0,−1 ],
0, 0, 0, 0, 0, 0, −1,−1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1,−1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 0, 1, 0, 0, 1, −1, 0 ],
0, 0, 1, 0, 1, 0, −1, 0 ],
0, 0, 1, 0, 1, 1, −1, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 1,−2, 0,−1,−1, 1,−1 ],
0, 1,−1, 0,−1,−1, 1, 0 ],
0, 1,−1, 0,−1, 0, 1, 0 ],
0, 1,−1, 0, 0,−1, 1, 0 ],
0, 1,−1, 1,−1,−1, 0, 0 ],
0, 1,−1, 1, 0,−1, 0, 0 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 0, 1,−1,−1, 0, 0 ],
0, 1, 0, 1,−1, 0, 0, 1 ],
0, 1, 0, 1, 0,−1, 0, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
1, −1, 1,−1, 1, 1, 0, 1 ],
1, −1, 1, 0, 1, 1, −1, 1 ],
1, −1, 2, 0, 1, 1, −1, 1 ],
1, −1, 2, 0, 1, 2, −1, 2 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 0, 1, 0, 0, 1 ],
1, 0, 1, 0, 0, 1, −1, 1 ],
1, 0, 1, 0, 1, 0, −1, 1 ],
1, 0, 1, 0, 1, 1, −1, 1 ],
1, 0, 1, 1, 0, 0, −1, 1 ],
1, 0, 1, 1, 0, 1, −1, 1 ],
1, 0, 1, 1, 1, 0, −1, 1 ],
1, 0, 1, 1, 1, 1, −1, 2 ],
1, 0, 2, 1, 1, 0, −1, 2 ],
1, 0, 2, 1, 1, 1, −1, 3 ],
1, 1, 0, 1, 0,−1, 0, 1 ],
1, 1, 0, 1, 0, 0, 0, 2 ],
1, 1, 1, 1, 0, 0, 0, 2 ],
1, 1, 1, 2, 0, 0, −1, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0,−1,−1, 0,−1, 1,−1 ],
0, 0,−1,−1, 0, 0, 1, 0 ],
0, 0,−1, 0,−1, 0, 1,−1 ],
0, 0,−1, 0, 0,−1, 1,−1 ],
0, 0,−1, 0, 0, 0, 0, 0 ],
0, 0, 0,−1, 0, 0, 0, 0 ],
0, 0, 0,−1, 1, 0, 0, 0 ],
0, 0, 0, 0,−1, 0, 1, 0 ],
0, 0, 0, 0, 0,−1, 0, 0 ],
0, 0, 0, 0, 0, 0,−1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0,−1, 0 ],
0, 0, 0, 1,−1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 1,−1, 1 ],
0, 0, 1, 0, 1, 0,−1, 1 ],
0, 0, 1, 1, 0, 0,−1, 0 ],
0, 0, 1, 1, 0, 1,−1, 1 ],
0, 1,−1, 0,−1,−1, 0,−1 ],
0, 1,−1, 0,−1, 0, 0,−1 ],
0, 1,−1, 0, 0,−1, 0,−1 ],
0, 1,−1, 0, 0, 0, 0, 0 ],
0, 1,−1, 1,−1,−1, 1, 0 ],
0, 1, 0, 0,−1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 1,−1, 0,−1, 0 ],
0, 1, 0, 1, 0,−1,−1, 0 ],
0, 1, 0, 1, 0, 0,−1, 0 ],
0, 1, 1, 1, 0, 0,−1, 1 ],
1,−1, 1, 0, 0, 1, 0, 1 ],
1,−1, 1, 0, 1, 1, 0, 1 ],
1,−1, 2, 0, 1, 1,−1, 2 ],
1,−1, 2, 0, 2, 1,−1, 2 ],
1, 0, 0, 0, 0, 0, 1, 1 ],
1, 0, 0, 1, 0, 0, 0, 1 ],
1, 0, 1, 0, 0, 1, 0, 1 ],
1, 0, 1, 0, 1, 0, 0, 1 ],
1, 0, 1, 0, 1, 1,−1, 2 ],
1, 0, 1, 1, 0, 0, 0, 1 ],
1, 0, 1, 1, 0, 1,−1, 2 ],
1, 0, 1, 1, 1, 0,−1, 2 ],
1, 0, 2, 0, 1, 1,−1, 2 ],
1, 0, 2, 1, 1, 1,−2, 2 ],
1, 1, 0, 0, 0, 0, 0, 1 ],
1, 1, 0, 1, 0, 0,−1, 1 ],
1, 1, 1, 1, 0, 0,−1, 1 ],
1, 1, 1, 1, 0, 1,−1, 2 ],
2, 0, 2, 1, 1, 1,−1, 3 ]
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
∗
• I ≡ P115 :
7
2
4
6
1
3
5





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
















b
CI =



216
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
1
1
1
1
1
−1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
−1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
−1
−1
−1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1











0
 0

 0

BI = 00

 −1
 0
0

1
1
0
0
0
0
0
−1
1
0
1
0
1
1
1
−1
0
0
−1
0
0
−1
−1
0
1
0
1
1
0
0
0
−1
−1
0
0
0
0
0
0
0
0
0
−1
−1
−1
−1
−1
1
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1, 1,−2,−1,−1,−1,−3 ],
[ −1, −2, 0, −2, −1, −1, −1, −4 ],
[ −1, −1,−1, −1, −1, 0, −1, −3 ],
[ −1, −1,−1, 0, −1, 0, 0, −2 ],
[ −1, −1, 0, −2, −1, −1, 0, −3 ],
[ −1, −1, 0, −1, −1, −1, −1, −3 ],
[ −1, −1, 0, −1, −1, 0, −1, −3 ],
[ −1, −1, 0, −1, 0, −1, −1, −3 ],
[ −1, −1, 0, −1, 0, 0, −1, −2 ],
[ −1, −1, 1, −2, 0, −1, −1, −3 ],
[ −1, 0,−1, −1, −1, 0, 0, −2 ],
[ −1, 0,−1, 0, −1, 0, 1, −1 ],
[ −1, 0, 0, −1, −1, −1, 0, −2 ],
[ −1, 0, 0, −1, −1, 0, 0, −1 ],
[ −1, 0, 0, −1, 0, −1, 0, −1 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1, −1 ],
[ −1, 0, 1, −2, 0, −1, −1, −2 ],
[ −1, 0, 1, −1, 0, −1, 0, −1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1,−1, 0, −1, 0, 0, −1 ],
[ 0, −1,−1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, −1, 0, 0, −2 ],
[ 0, −1, 0, −1, 0, −1, 0, −2 ],
[ 0, −1, 0, −1, 0, 0, −1, −1 ],
[ 0, −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, −1, 0, −1, −1, −1 ],
[ 0, −1, 1, −1, 1, −1, −1, −1 ],
[ 0, 0,−1, 0, −1, 0, 1, −1 ],
[ 0, 0,−1, 0, −1, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 1, −1, 0, 1, 0 ],
[ 0, 0,−1, 1, −1, 1, 1, 1 ],
[ 0, 0,−1, 1, 0, 0, 1, 1 ],
[ 0, 0,−1, 1, 0, 1, 1, 1 ],
[ 0, 0, 0, −1, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, −1, 0, −1, 0, 0 ],
[ 0, 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 0, 1, −1, 1, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 0, 1, 0, 1, −1, −1, 0 ],
[ 0, 0, 1, 0, 1, 0, −1, 0 ],
[ 0, 0, 2, −1, 1, −1, −1, 0 ],
[ 0, 1,−1, 1, 0, 1, 0, 1 ],
[ 0, 1,−1, 2, 0, 1, 1, 2 ],
[ 1, 1,−1, 2, 1, 1, 1, 3 ],
[ −1,−1, −1,−1,−2, 0, 0,−3 ],
[ −1,−1, −1,−1,−1, 0, 0,−3 ],
[ −1,−1, 0,−2,−1,−1,−1,−4 ],
[ −1,−1, 0,−2,−1, 0,−1,−3 ],
[ −1,−1, 0,−1,−1,−1, 0,−3 ],
[ −1,−1, 0,−1,−1, 0,−1,−2 ],
[ −1,−1, 0,−1, 0,−1,−1,−2 ],
[ −1,−1, 1,−2, 0,−2,−1,−3 ],
[ −1,−1, 1,−2, 0,−1,−1,−2 ],
[ −1, 0, −1, 0,−1, 0, 0,−2 ],
[ −1, 0, −1, 0,−1, 1, 0,−1 ],
[ −1, 0, 0,−1,−1, 0,−1,−2 ],
[ −1, 0, 0,−1, 0,−1,−1,−2 ],
[ −1, 0, 0,−1, 0, 0,−1,−2 ],
[ −1, 0, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 1,−1, 0,−1,−1,−2 ],
[ −1, 0, 1,−1, 0, 0,−1,−1 ],
[ 0,−1, −1,−1,−1, 0, 0,−2 ],
[ 0,−1, −1, 0,−1, 0, 1,−1 ],
[ 0,−1, 0,−1,−1,−1, 0,−2 ],
[ 0,−1, 0,−1,−1, 0, 0,−1 ],
[ 0,−1, 0,−1, 0,−1, 0,−1 ],
[ 0,−1, 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 1,−2, 0,−1,−1,−2 ],
[ 0,−1, 1,−1, 0,−1, 0,−1 ],
[ 0, 0, −2, 1,−1, 1, 1, 0 ],
[ 0, 0, −1, 0,−1, 0, 1, 0 ],
[ 0, 0, −1, 0,−1, 1, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 1,−1, 1, 0, 0 ],
[ 0, 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1,−1, 0,−1,−1,−1 ],
[ 0, 0, 1,−1, 0, 0,−1,−1 ],
[ 0, 0, 1,−1, 1,−1,−1,−1 ],
[ 0, 0, 1,−1, 1, 0,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1,−1, 0, 0 ],
[ 0, 0, 1, 0, 1, 0,−1, 1 ],
[ 0, 1, −1, 1,−1, 1, 1, 1 ],
[ 0, 1, −1, 1, 0, 1, 1, 1 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
217
[ −2,−1, 0,−2,−1,−1,−1,−4 ],
[ −1,−1,−1,−1,−1,−1, 0,−3 ],
[ −1,−1,−1,−1,−1, 0, 0,−2 ],
[ −1,−1, 0,−2,−1,−1,−1,−3 ],
[ −1,−1, 0,−2, 0,−1,−1,−3 ],
[ −1,−1, 0,−1,−1,−1, 0,−2 ],
[ −1,−1, 0,−1,−1, 0, 0,−2 ],
[ −1,−1, 0,−1, 0,−1, 0,−2 ],
[ −1,−1, 1,−2, 0,−1,−2,−3 ],
[ −1,−1, 1,−1, 0,−1,−1,−2 ],
[ −1, 0,−1, 0,−1, 0, 0,−1 ],
[ −1, 0,−1, 0, 0, 0, 0,−1 ],
[ −1, 0, 0,−1,−1, 0, 0,−2 ],
[ −1, 0, 0,−1, 0,−1, 0,−2 ],
[ −1, 0, 0,−1, 0, 0,−1,−1 ],
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1,−1, 0,−1,−1,−1 ],
[ −1, 0, 1,−1, 1,−1,−1,−1 ],
[ 0,−1,−1, 0,−1, 0, 0,−2 ],
[ 0,−1,−1, 0,−1, 1, 0,−1 ],
[ 0,−1, 0,−1,−1, 0,−1,−2 ],
[ 0,−1, 0,−1, 0,−1,−1,−2 ],
[ 0,−1, 0,−1, 0, 0,−1,−2 ],
[ 0,−1, 0, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 1,−1, 0,−1,−1,−2 ],
[ 0,−1, 1,−1, 0, 0,−1,−1 ],
[ 0, 0,−1, 0,−1, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 1,−1, 1, 1, 0 ],
[ 0, 0,−1, 1, 0, 0, 1, 0 ],
[ 0, 0,−1, 1, 0, 1, 0, 1 ],
[ 0, 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1,−1, 0,−1, 0,−1 ],
[ 0, 0, 1,−1, 0, 0,−1, 0 ],
[ 0, 0, 1,−1, 1,−1,−1, 0 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1,−1, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1,−1, 1, 0, 0, 1, 1 ],
[ 0, 1,−1, 1, 0, 1, 1, 2 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
1
0
0
0
0
−1
0
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
0,−1,
0,−1,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 1,
0, 1,
1,−1,
1,−1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
0,
1,
1,
1,
1,
0,
1,
1,
1,
0,
0,
1,
1,
1,
0,
0,
2,
2,
1,
1,
1,
2,
2,
1,
1,
0, 0, 1,
0, 0, 0,
0, 1, 0,
1, 0, 0,
1, 1, 0,
1, 0, −1,
1, 0, 0,
0, 0, 1,
0, 1, 1,
0, 0, 0,
1, 0, 0,
0, 0, 1,
0, 1, 1,
1, 0, 1,
1, −1, 0,
1, 0, 0,
0, 1, 1,
0, 2, 1,
0, 1, 1,
1, 0, 1,
1, 1, 0,
1, 0, 1,
1, 1, 1,
1, 0, 0,
2, 0, 0,
1 ],
1 ],
1 ],
1 ],
2 ],
1 ],
2 ],
1 ],
2 ],
1 ],
1 ],
2 ],
2 ],
2 ],
1 ],
2 ],
2 ],
3 ],
2 ],
2 ],
3 ],
3 ],
4 ],
3 ],
3 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 1, 0,
0, 1, 0,
0, 1, 0,
0, 1, 0,
0, 1, 1,
0, 1, 1,
1,−1, 0,
1, 0, −1,
1, 0, −1,
1, 0, 0,
1, 0, 0,
1, 0, 0,
1, 0, 0,
1, 0, 0,
1, 0, 1,
1, 0, 1,
1, 1, −1,
1, 1, 0,
1, 1, 0,
1, 1, 0,
1, 1, 0,
1, 1, 0,
1, 1, 1,
1, 1, 1,
1, 2, 0,
0,
1,
1,
1,
0,
0,
0,
1,
2,
0,
1,
1,
1,
1,
0,
1,
2,
1,
1,
1,
1,
2,
0,
1,
2,
0,
0,
0,
1,
0,
1,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1, 0,
0, 1,
1, 0,
0, 0,
0, 0,
0, 0,
0, 0,
1, 0,
1, 1,
0, 1,
0, 0,
1, 0,
0, 0,
1, 0,
0,−1,
0, 0,
1, 1,
0, 1,
1, 1,
0, 1,
1, 1,
1, 0,
0, 0,
0, 1,
1, 1,
1 ],
1 ],
2 ],
2 ],
1 ],
1 ],
0 ],
1 ],
2 ],
1 ],
1 ],
1 ],
1 ],
2 ],
1 ],
2 ],
3 ],
2 ],
3 ],
3 ],
3 ],
3 ],
2 ],
3 ],
4 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
0,−1,
0,−1,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 1,
0, 1,
1,−1,
1,−1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
1, 0,
0, 1, 0,
1, 0, 0,
1, 0, 1,
1, 1, 0,
0, 1,−1,
0, 1, 0,
1,−1, 1,
1, 0, 1,
0, 0, 0,
0, 0, 1,
1, 0, 0,
1, 0, 1,
1, 1, 0,
0, 0, 0,
0, 1, 0,
1, 0, 1,
2, 0, 1,
1, 0, 1,
1, 1, 0,
1, 1, 1,
2, 0, 1,
2, 1, 1,
1, 1, 0,
1, 1, 1,
2, 1, 1,
0,
1,
1,
1,
0,
0,
1,
1,
0,
0,
1,
0,
0,
0,
0,
1,
2,
0,
0,
0,
1,
1,
0,
0,
1,
1 ],
2 ],
2 ],
2 ],
1 ],
2 ],
1 ],
1 ],
0 ],
1 ],
1 ],
2 ],
2 ],
1 ],
1 ],
2 ],
3 ],
2 ],
2 ],
2 ],
3 ],
3 ],
2 ],
3 ],
4]
∗
7
6
• I ≡ P116 :
5
4
3
2
1





CI =








b
CoxI =



0
0
1
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
−1
0
1
0
0
1
0
0
0
−1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
−1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1
















bI =
C




















BI =



1
1
1
1
1
1
1
−1
0
0
0
0
0
0
−1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
−1
0
−1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
−1
0
−1
−1
0
0
0
0
0
0
0
1
0
0











0
−1
0
0
0
0
0
0
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−2,−1, 1, 1, 1,−1 ],
[ 1, 1, 2, 1,−1,−1,−1, 1 ],
218
[ −2,−1,−2, 0, 1, 1, 1,−1 ],
0
0
1
0
0
0
0
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, −2, −2, 0, 1, 1, 1, −1 ],
−1, −1, −2, −1, 0, 1, 2, −1 ],
−1, −1, −2, 0, 1, 0, 1, −1 ],
−1, −1, −2, 0, 1, 1, 1, 0 ],
−1, −1, −1, 0, 0, 1, 0, −1 ],
−1, −1, −1, 0, 1, 0, 0, −1 ],
−1, −1, −1, 0, 1, 1, 0, −1 ],
−1, −1, −1, 1, 1, 0, 0, −1 ],
−1, −1, −1, 1, 1, 1, 0, 0 ],
−1, 0, −2, −1, 0, 1, 1, −1 ],
−1, 0, −1, −1, 0, 1, 0, −1 ],
−1, 0, −1, 0, 0, 0, 0, −1 ],
−1, 0, −1, 0, 0, 1, 0, −1 ],
−1, 0, −1, 0, 1, 0, 0, −1 ],
−1, 0, −1, 0, 1, 1, 0, 0 ],
−1, 0, 0, 0, 0, 0, 0, 0 ],
−1, 0, 0, 0, 1, 0, 0, 0 ],
−1, 0, 0, 1, 1, 0,−1, 0 ],
−1, 1, 0, 0, 0, 0, 0, 0 ],
0, −1, −1, −1, 0, 0, 1, −1 ],
0, −1, −1, −1, 0, 1, 1, 0 ],
0, −1, −1, 0, 0, 0, 1, 0 ],
0, −1, −1, 0, 0, 1, 1, 0 ],
0, −1, −1, 0, 1, 0, 1, 0 ],
0, −1, 0, 0, 0, 0, 0, −1 ],
0, −1, 0, 0, 0, 1, 0, 0 ],
0, −1, 0, 1, 1,−1, 0, 0 ],
0, −1, 0, 1, 1, 0, 0, 1 ],
0, 0, −1, −1,−1, 1, 0, −1 ],
0, 0, −1, −1, 0, 0, 0, −1 ],
0, 0, −1, −1, 0, 1, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 1, 0, 0 ],
0, 0, 0, −1,−1, 0, 1, −1 ],
0, 0, 0, −1,−1, 1, 0, 0 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, 0,−1, 0, 0, −1 ],
0, 0, 0, 0,−1, 1, 0, 0 ],
0, 0, 0, 0, 0,−1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0,−1, 0 ],
0, 0, 0, 1, 1,−1,−1, 0 ],
0, 0, 0, 1, 1, 0,−1, 0 ],
0, 0, 1, 0,−1, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 1, 0,−1, 0, 0 ],
0, 0, 1, 1, 0, 0,−1, 1 ],
0, 0, 1, 1, 1,−1,−1, 1 ],
0, 0, 1, 2, 1,−1,−1, 1 ],
0, 1, 0, −1,−1, 0, 1, 0 ],
0, 1, 0, 0,−1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 1, 0,−1,−1, 0, 0 ],
0, 1, 1, 0,−1, 0, 0, 1 ],
0, 1, 1, 0, 0,−1, 0, 1 ],
0, 1, 1, 0, 0, 0, 0, 1 ],
0, 1, 1, 1, 0,−1, 0, 1 ],
0, 1, 2, 1, 0,−1,−1, 1 ],
1, 0, 0, −1,−1, 0, 0, 0 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 0,−1, 0 ],
1, 0, 1, −1,−1, 0, 0, 0 ],
1, 0, 1, 0,−1, 0, 0, 0 ],
1, 0, 1, 0, 0,−1, 0, 0 ],
1, 0, 1, 0, 0, 0,−1, 1 ],
1, 0, 1, 1, 0,−1,−1, 1 ],
1, 0, 1, 1, 1,−1,−1, 1 ],
1, 1, 1, −1,−2, 0, 0, 0 ],
1, 1, 1, −1,−1, 0, 0, 0 ],
[ −1,−1,−2,−1, 0, 1, 1,−2 ],
[ −1,−1,−2,−1, 0, 2, 1,−1 ],
[ −1,−1,−2, 0, 1, 1, 0,−1 ],
[ −1,−1,−1,−1, 0, 1, 1,−1 ],
[ −1,−1,−1, 0, 0, 1, 1,−1 ],
[ −1,−1,−1, 0, 1, 0, 1,−1 ],
[ −1,−1,−1, 0, 1, 1, 0, 0 ],
[ −1,−1,−1, 1, 1, 0, 0, 0 ],
[ −1,−1,−1, 1, 2, 0, 0, 0 ],
[ −1, 0,−1,−1, −1, 1, 1,−1 ],
[ −1, 0,−1,−1, 0, 1, 1,−1 ],
[ −1, 0,−1, 0, 0, 0, 1,−1 ],
[ −1, 0,−1, 0, 0, 1, 0, 0 ],
[ −1, 0,−1, 0, 1, 0, 0, 0 ],
[ −1, 0,−1, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ 0,−1,−2,−1, 0, 1, 1,−1 ],
[ 0,−1,−1,−1, 0, 1, 0,−1 ],
[ 0,−1,−1, 0, 0, 0, 0,−1 ],
[ 0,−1,−1, 0, 0, 1, 0,−1 ],
[ 0,−1,−1, 0, 1, 0, 0,−1 ],
[ 0,−1,−1, 0, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, −1, 0 ],
[ 0, 0,−1,−2, −1, 1, 1,−1 ],
[ 0, 0,−1,−1, −1, 1, 1,−1 ],
[ 0, 0,−1,−1, 0, 0, 1,−1 ],
[ 0, 0,−1,−1, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, −1, 0, 1, 0 ],
[ 0, 0, 0,−1, −1, 1, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, −1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, −1, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, −1, 1 ],
[ 0, 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, −1, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, −1, 0, 1 ],
[ 0, 1, 0,−1, −1, 0, 0,−1 ],
[ 0, 1, 0,−1, −1, 1, 0, 0 ],
[ 0, 1, 0, 0, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, −1, 0, −1, 0 ],
[ 0, 1, 1, 0, 0, −1, −1, 0 ],
[ 0, 1, 1, 0, 0, 0, −1, 0 ],
[ 0, 1, 1, 1, 0, −1, −1, 0 ],
[ 0, 1, 1, 1, 0, 0, −1, 1 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1, −1, 0, 1, 0 ],
[ 1, 0, 0, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, −1, −1, 0, 0 ],
[ 1, 0, 1, 0, −1, 0, 0, 1 ],
[ 1, 0, 1, 0, 0, −1, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 1, 0, −1, 0, 1 ],
[ 1, 0, 2, 1, 0, −1, −1, 1 ],
[ 1, 1, 1,−1, −1, −1, 0, 0 ],
[ 1, 1, 1,−1, −1, 0, 0, 1 ],
219
[ −1,−1,−2,−1, 0, 1, 1,−1 ],
[ −1,−1,−2, 0, 0, 1, 1,−1 ],
[ −1,−1,−2, 0, 1, 1, 1,−1 ],
[ −1,−1,−1, 0, 0, 0, 1,−1 ],
[ −1,−1,−1, 0, 0, 1, 1, 0 ],
[ −1,−1,−1, 0, 1, 0, 1, 0 ],
[ −1,−1,−1, 0, 1, 1, 1, 0 ],
[ −1,−1,−1, 1, 1, 0, 1, 0 ],
[ −1,−1, 0, 1, 1, 0, 0, 0 ],
[ −1, 0,−1,−1, 0, 0, 1,−1 ],
[ −1, 0,−1,−1, 0, 1, 1, 0 ],
[ −1, 0,−1, 0, 0, 0, 1, 0 ],
[ −1, 0,−1, 0, 0, 1, 1, 0 ],
[ −1, 0,−1, 0, 1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1,−1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ 0,−1,−1,−1,−1, 1, 1,−1 ],
[ 0,−1,−1,−1, 0, 1, 1,−1 ],
[ 0,−1,−1, 0, 0, 0, 1,−1 ],
[ 0,−1,−1, 0, 0, 1, 0, 0 ],
[ 0,−1,−1, 0, 1, 0, 0, 0 ],
[ 0,−1,−1, 1, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 0, 0 ],
[ 0, 0,−1,−1,−1, 0, 1,−1 ],
[ 0, 0,−1,−1,−1, 1, 1, 0 ],
[ 0, 0,−1,−1, 0, 0, 1, 0 ],
[ 0, 0,−1,−1, 0, 1, 1, 0 ],
[ 0, 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1,−1, 1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1,−1, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 0, 1, 1, 0,−1,−1, 0 ],
[ 0, 0, 1, 1, 0, 0,−1, 0 ],
[ 0, 0, 1, 1, 1,−1,−1, 0 ],
[ 0, 0, 1, 1, 1, 0,−1, 1 ],
[ 0, 1, 0,−1,−1, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0,−1, 0 ],
[ 0, 1, 1,−1,−1, 0, 0, 0 ],
[ 0, 1, 1, 0,−1, 0, 0, 0 ],
[ 0, 1, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 1, 0, 0, 0,−1, 1 ],
[ 0, 1, 1, 1, 0,−1,−1, 1 ],
[ 0, 1, 1, 1, 1,−1,−1, 1 ],
[ 1, 0, 0,−1,−1, 0, 0,−1 ],
[ 1, 0, 0,−1,−1, 1, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0,−1, 0,−1, 0 ],
[ 1, 0, 1, 0, 0,−1,−1, 0 ],
[ 1, 0, 1, 0, 0, 0,−1, 0 ],
[ 1, 0, 1, 1, 0,−1,−1, 0 ],
[ 1, 0, 1, 1, 0, 0,−1, 1 ],
[ 1, 1, 0,−1,−1, 0, 0, 0 ],
[ 1, 1, 1,−1,−1, 0,−1, 0 ],
[ 1, 1, 1, 0,−1,−1,−1, 0 ],
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
2,
2,
0,−1,−1, 0,
0,−1, 0,−1,
0, 0,−1,−1,
1, 0,−1,−1,
0,−1,−1, 0,
1, 0,−2,−1,
1, 0,−1,−1,
0 ],
1 ],
1 ],
1 ],
1 ],
1 ],
2 ],
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0, −1, −1, 0,
0, −1, 0, 0,
0, 0, −1, 0,
0, −1, −1, −1,
0, −1, 0, −1,
1, 0, −1, −2,
0, −1, −1, −1,
1,
1,
1,
2,
2,
2,
2,
1 ],
1 ],
1 ],
0 ],
1 ],
1 ],
1 ],
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
2,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
2,
2,
2,
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
−1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
−1
0,−1, 0,−1,
0, 0,−1,−1,
0, 0, 0,−1,
0,−1,−1,−1,
0, 0,−1,−1,
1, 0,−1,−1,
0,−1,−1,−1,
0 ],
0 ],
1 ],
1 ],
1 ],
1 ],
1]
∗
7
• I ≡ P117 :
5
4
3
2
6
1




CI =



1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
−1
1
1
0
1
0
1
0
−1






b I =
Cox




1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
−1
0
0
0
0
−1
0
1
1
1
1
1
1
0
1
−1
0
−1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
















BI =



0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
−1
0
0
0
0
0
0
1
0
0
−1
0
0
−1
0
0
0
−1
−1
−1
−1
−1
−1
−1
1
1
1
0
1
0
0
0
−1











−1
0
0
0
0
0
0
0
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−2,−1,
[ −1, −2, −2, 0,
[ −1, −1, −2, −1,
[ −1, −1, −2, 0,
[ −1, −1, −2, 0,
[ −1, −1, −1, 0,
[ −1, −1, −1, 0,
[ −1, −1, −1, 0,
[ −1, −1, −1, 1,
[ −1, −1, −1, 1,
[ −1, 0, −2, −1,
[ −1, 0, −1, −1,
[ −1, 0, −1, 0,
[ −1, 0, −1, 0,
[ −1, 0, −1, 0,
[ −1, 0, −1, 0,
[ −1, 0, 0, 0,
[ −1, 0, 0, 0,
[ −1, 0, 0, 1,
[ −1, 1, 0, 0,
1,−1,
1, −1,
0, −1,
1, −1,
1, 0,
0, −1,
1, −1,
1, 0,
1, −1,
1, 0,
0, −1,
0, −1,
0, −1,
0, 0,
1, −1,
1, 0,
0, 0,
1, 0,
1, 0,
0, 0,
1,−2 ],
1, −2 ],
1, −2 ],
0, −2 ],
1, −1 ],
1, −2 ],
0, −2 ],
0, −1 ],
0, −1 ],
1, 0 ],
1, −2 ],
1, −2 ],
0, −2 ],
0, −1 ],
0, −1 ],
1, 0 ],
0, −1 ],
0, 0 ],
0, 0 ],
0, 0 ],
[ 1, 1, 2, 1,−1, 1,−1, 2 ],
[ −1,−1,−2,−1, 0,−2, 1,−3 ],
[ −1,−1,−2,−1, 0,−1, 2,−2 ],
[ −1,−1,−2, 0, 1,−1, 1,−2 ],
[ −1,−1,−1,−1, 0,−1, 1,−2 ],
[ −1,−1,−1, 0, 0,−1, 1,−1 ],
[ −1,−1,−1, 0, 1,−1, 0,−1 ],
[ −1,−1,−1, 0, 1, 0, 1,−1 ],
[ −1,−1,−1, 1, 1, 0, 0,−1 ],
[ −1,−1,−1, 1, 2, 0, 0, 0 ],
[ −1, 0,−1,−1, −1,−1, 1,−2 ],
[ −1, 0,−1,−1, 0,−1, 1,−1 ],
[ −1, 0,−1, 0, 0,−1, 0,−1 ],
[ −1, 0,−1, 0, 0, 0, 1,−1 ],
[ −1, 0,−1, 0, 1, 0, 0,−1 ],
[ −1, 0,−1, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ 0,−1,−2,−1, 0,−1, 1,−2 ],
220
[ −2,−1,−2, 0, 1,−1, 1,−2 ],
[ −1,−1,−2,−1, 0,−1, 1,−3 ],
[ −1,−1,−2, 0, 0,−1, 1,−2 ],
[ −1,−1,−2, 0, 1,−1, 1,−1 ],
[ −1,−1,−1, 0, 0,−1, 0,−2 ],
[ −1,−1,−1, 0, 0, 0, 1,−1 ],
[ −1,−1,−1, 0, 1,−1, 1,−1 ],
[ −1,−1,−1, 0, 1, 0, 1, 0 ],
[ −1,−1,−1, 1, 1, 0, 0, 0 ],
[ −1,−1, 0, 1, 1, 0, 0, 0 ],
[ −1, 0,−1,−1, 0,−1, 0,−2 ],
[ −1, 0,−1,−1, 0, 0, 1,−1 ],
[ −1, 0,−1, 0, 0,−1, 1,−1 ],
[ −1, 0,−1, 0, 0, 0, 1, 0 ],
[ −1, 0,−1, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 0,−1, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ 0,−1,−1,−1,−1,−1, 1,−2 ],
1
1
0
0
0
0
−1
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, −1, −1, 0, −1, 0, −2 ],
0, −1, −1, −1, 0, 0, 1, −1 ],
0, −1, −1, 0, 0, −1, 1, −1 ],
0, −1, −1, 0, 0, 0, 1, 0 ],
0, −1, −1, 0, 1, 0, 0, 0 ],
0, −1, 0, 0, 0, −1, 0, −1 ],
0, −1, 0, 0, 0, 0, 1, 0 ],
0, −1, 0, 1, 1, 0,−1, 0 ],
0, −1, 0, 1, 1, 1, 0, 1 ],
0, 0, −1, −1,−1, −1, 1, −2 ],
0, 0, −1, −1, 0, −1, 0, −2 ],
0, 0, −1, −1, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, −1, 0, −1 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, 0, −1,−1, −1, 0, −1 ],
0, 0, 0, −1,−1, 0, 1, −1 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, 0,−1, −1, 0, −1 ],
0, 0, 0, 0,−1, 0, 1, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 1, 1 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 0, 1, 1, 0,−1, 0 ],
0, 0, 0, 1, 1, 1,−1, 1 ],
0, 0, 1, 0,−1, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 1, 0, 0,−1, 1 ],
0, 0, 1, 1, 0, 1, 0, 1 ],
0, 0, 1, 1, 1, 1,−1, 1 ],
0, 0, 1, 2, 1, 1,−1, 2 ],
0, 1, 0, −1,−1, 0, 0, 0 ],
0, 1, 0, 0,−1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 1, 0,−1, 0,−1, 0 ],
0, 1, 1, 0,−1, 1, 0, 1 ],
0, 1, 1, 0, 0, 0, 0, 1 ],
0, 1, 1, 0, 0, 1, 0, 2 ],
0, 1, 1, 1, 0, 1,−1, 2 ],
0, 1, 2, 1, 0, 1,−1, 2 ],
1, 0, 0, −1,−1, 0, 0, −1 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 1, −1,−1, 0, 0, 0 ],
1, 0, 1, 0,−1, 0, 0, 1 ],
1, 0, 1, 0, 0, 0,−1, 1 ],
1, 0, 1, 0, 0, 1, 0, 1 ],
1, 0, 1, 1, 0, 1,−1, 1 ],
1, 0, 1, 1, 1, 1,−1, 2 ],
1, 1, 1, −1,−2, 0, 0, 0 ],
1, 1, 1, −1,−1, 0, 0, 1 ],
1, 1, 1, 0,−1, 0,−1, 1 ],
1, 1, 1, 0,−1, 1, 0, 1 ],
1, 1, 1, 0, 0, 1,−1, 1 ],
1, 1, 1, 1, 0, 1,−1, 2 ],
1, 1, 2, 0,−1, 1,−1, 2 ],
1, 1, 2, 1, 0, 1,−2, 2 ],
1, 1, 2, 1, 0, 2,−1, 3 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,−1,−1,−1, 0,−1, 1,−2 ],
0,−1,−1, 0, 0,−1, 0,−2 ],
0,−1,−1, 0, 0, 0, 0,−1 ],
0,−1,−1, 0, 1,−1, 0,−1 ],
0,−1,−1, 0, 1, 0, 1, 0 ],
0,−1, 0, 0, 0, 0, 0,−1 ],
0,−1, 0, 0, 1, 0, 0, 0 ],
0,−1, 0, 1, 1, 0, 0, 0 ],
0, 0,−1,−2, −1,−1, 1,−2 ],
0, 0,−1,−1, −1,−1, 1,−1 ],
0, 0,−1,−1, 0,−1, 0,−1 ],
0, 0,−1,−1, 0, 0, 1,−1 ],
0, 0,−1, 0, 0, 0, 0,−1 ],
0, 0,−1, 0, 1, 0, 0, 0 ],
0, 0, 0,−1, −1,−1, 1,−1 ],
0, 0, 0,−1, −1, 0, 1, 0 ],
0, 0, 0,−1, 0, 0, 0, 0 ],
0, 0, 0, 0, −1, 0, 0,−1 ],
0, 0, 0, 0, 0,−1, −1,−1 ],
0, 0, 0, 0, 0, 0, −1,−1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 0, 1, 1, 0, 1 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 1, 0, −1, 1 ],
0, 0, 0, 1, 1, 1, 0, 1 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 0, 1, 0, 0, 1, 0, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 0, 1, 1, 0, 1, 0, 2 ],
0, 0, 1, 1, 1, 1, −1, 2 ],
0, 1, 0,−1, −1,−1, 0,−1 ],
0, 1, 0,−1, −1, 0, 1, 0 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 0, 0, 0, 1, 0, 1 ],
0, 1, 1, 0, −1, 0, 0, 0 ],
0, 1, 1, 0, 0, 0, −1, 0 ],
0, 1, 1, 0, 0, 1, −1, 1 ],
0, 1, 1, 1, 0, 0, −1, 1 ],
0, 1, 1, 1, 0, 1, 0, 2 ],
1,−1, 0, 0, 0, 0, 0, 0 ],
1, 0, 0,−1, −1, 0, 0, 0 ],
1, 0, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 1, 0, −1, 0, −1, 0 ],
1, 0, 1, 0, −1, 1, 0, 1 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 0, 1, 0, 0, 1, 0, 2 ],
1, 0, 1, 1, 0, 1, −1, 2 ],
1, 0, 2, 1, 0, 1, −1, 2 ],
1, 1, 1,−1, −1, 0, −1, 0 ],
1, 1, 1,−1, −1, 1, 0, 1 ],
1, 1, 1, 0, −1, 0, 0, 1 ],
1, 1, 1, 0, −1, 1, 0, 2 ],
1, 1, 1, 0, 0, 1, −1, 2 ],
1, 1, 2, 0, −1, 0, −1, 1 ],
1, 1, 2, 0, −1, 1, 0, 2 ],
1, 1, 2, 1, 0, 1, −1, 2 ],
1, 2, 2, 0, −1, 1, −1, 2 ],
∗
• I ≡ P118 :
7
5
6
4
2
3
1
221
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,−1,−1,−1, 0,−1, 1,−1 ],
0,−1,−1, 0, 0,−1, 0,−1 ],
0,−1,−1, 0, 0, 0, 1,−1 ],
0,−1,−1, 0, 1, 0, 0,−1 ],
0,−1,−1, 1, 1, 0, 0, 0 ],
0,−1, 0, 0, 0, 0, 0, 0 ],
0,−1, 0, 1, 0, 0, 0, 0 ],
0,−1, 0, 1, 1, 0, 0, 1 ],
0, 0,−1,−1,−1,−1, 0,−2 ],
0, 0,−1,−1,−1, 0, 1,−1 ],
0, 0,−1,−1, 0,−1, 1,−1 ],
0, 0,−1,−1, 0, 0, 1, 0 ],
0, 0,−1, 0, 0, 0, 0, 0 ],
0, 0, 0,−1,−1,−1, 0,−2 ],
0, 0, 0,−1,−1, 0, 0,−1 ],
0, 0, 0,−1, 0,−1, 0,−1 ],
0, 0, 0,−1, 0, 0, 1, 0 ],
0, 0, 0, 0,−1, 0, 0, 0 ],
0, 0, 0, 0, 0,−1, 0,−1 ],
0, 0, 0, 0, 0, 0,−1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0,−1, 0 ],
0, 0, 0, 1, 0, 1, 0, 1 ],
0, 0, 0, 1, 1, 0, 0, 1 ],
0, 0, 0, 1, 1, 1, 0, 2 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 1, 0, 0,−1, 0 ],
0, 0, 1, 1, 0, 1,−1, 1 ],
0, 0, 1, 1, 1, 0,−1, 1 ],
0, 0, 1, 1, 1, 1, 0, 2 ],
0, 1, 0,−1,−1, 0, 0,−1 ],
0, 1, 0,−1, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 1,−1,−1, 0, 0, 0 ],
0, 1, 1, 0,−1, 0, 0, 1 ],
0, 1, 1, 0, 0, 0,−1, 1 ],
0, 1, 1, 0, 0, 1, 0, 1 ],
0, 1, 1, 1, 0, 1,−1, 1 ],
0, 1, 1, 1, 1, 1,−1, 2 ],
1, 0, 0,−1,−1,−1, 0,−1 ],
1, 0, 0,−1,−1, 0, 1, 0 ],
1, 0, 0, 0, 0, 0,−1, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
1, 0, 1, 0,−1, 0, 0, 0 ],
1, 0, 1, 0, 0, 0,−1, 0 ],
1, 0, 1, 0, 0, 1,−1, 1 ],
1, 0, 1, 1, 0, 0,−1, 1 ],
1, 0, 1, 1, 0, 1, 0, 2 ],
1, 1, 0,−1,−1, 0, 0, 0 ],
1, 1, 1,−1,−1, 0, 0, 0 ],
1, 1, 1, 0,−1, 0,−1, 0 ],
1, 1, 1, 0,−1, 1,−1, 1 ],
1, 1, 1, 0, 0, 0,−1, 1 ],
1, 1, 1, 0, 0, 1, 0, 2 ],
1, 1, 2, 0,−1, 1,−1, 1 ],
1, 1, 2, 0, 0, 1,−1, 2 ],
1, 1, 2, 1, 0, 1,−1, 3 ],
2, 1, 2, 0,−1, 1,−1, 2 ]





CI =








b I =
Cox




0
0
1
1
0
1
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
−1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
−1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
−1
0
−1
0
0
−1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
















BI =



1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
−1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
−1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
−1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
1
1
0
0
1
0
0
−1
0
0
0
0
0
0
−1
0











0
0
0
0
0
−1
0
0
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−1,−2,−1,−1, 1,−3 ],
[ −1, −2, −1, −2, 0, −1, 1, −3 ],
[ −1, −1, −1, −2, −1, −1, 0, −4 ],
[ −1, −1, −1, −2, 0, −1, 1, −3 ],
[ −1, −1, −1, −1, −1, −1, 0, −3 ],
[ −1, −1, −1, −1, 0, −1, 1, −2 ],
[ −1, −1, −1, −1, 0, 0, 1, −1 ],
[ −1, −1, 0, −1, 0, −1, 0, −2 ],
[ −1, −1, 0, −1, 0, 0, 1, −1 ],
[ −1, −1, 0, −1, 1, 0, 1, 0 ],
[ −1, 0, −1, −2, −1, −1, 0, −3 ],
[ −1, 0, −1, −1, −1, −1, 0, −2 ],
[ −1, 0, −1, −1, 0, 0, 0, −2 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, −1, 0, −1, 0, −1 ],
[ −1, 0, 0, −1, 0, 0, 1, −1 ],
[ −1, 0, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, −1, −1, 0, −3 ],
[ 0, −1, −1, −1, 0, −1, 0, −2 ],
[ 0, −1, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, −1, 0, −2 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 1, 0 ],
[ 0, −1, 1, 0, 1, 0, 1, 1 ],
[ 0, 0, −1, −1, −1, −1,−1, −2 ],
[ 0, 0, −1, −1, −1, 0, 0, −2 ],
[ 0, 0, −1, 0, −1, −1,−1, −2 ],
[ 0, 0, −1, 0, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, −1, 0, −2 ],
[ 0, 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[ 1, 1, 1, 2, 1, 1,−1, 3 ],
[ −1,−1,−2,−2,−1,−1, 0,−4 ],
[ −1,−1,−1,−2,−1,−1, 0,−3 ],
[ −1,−1,−1,−2, 0,−1, 1,−2 ],
[ −1,−1,−1,−1, 0,−1, 0,−3 ],
[ −1,−1,−1,−1, 0, 0, 0,−2 ],
[ −1,−1,−1,−1, 1, 0, 1,−1 ],
[ −1,−1, 0,−1, 0,−1, 1,−2 ],
[ −1,−1, 0,−1, 1,−1, 1,−1 ],
[ −1,−1, 0,−1, 1, 0, 2, 0 ],
[ −1, 0,−1,−1,−1,−1, −1,−3 ],
[ −1, 0,−1,−1,−1, 0, 0,−2 ],
[ −1, 0,−1,−1, 0, 0, 0,−1 ],
[ −1, 0, 0,−1,−1,−1, 0,−2 ],
[ −1, 0, 0,−1, 0,−1, 1,−1 ],
[ −1, 0, 0,−1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ 0,−1,−1,−2,−1,−1, 0,−3 ],
[ 0,−1,−1,−1,−1,−1, 0,−2 ],
[ 0,−1,−1,−1, 0, 0, 0,−2 ],
[ 0,−1,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 0,−1, 0,−1 ],
[ 0,−1, 0,−1, 0, 0, 1,−1 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 1, 0, 1, 1 ],
[ 0, 0,−1,−1,−2,−1, −1,−3 ],
[ 0, 0,−1,−1,−1,−1, 0,−2 ],
[ 0, 0,−1,−1,−1, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 0, −1,−2 ],
[ 0, 0,−1, 0, 0, 0, −1,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0,−1,−1,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0, 0,−1,−1, −1,−2 ],
[ 0, 0, 0, 0,−1, 0, −1,−1 ],
[ 0, 0, 0, 0, 0,−1, −1,−1 ],
[ 0, 0, 0, 0, 0, 0, −1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
222
[ −2,−1,−1,−2, 0,−1, 1,−3 ],
[ −1,−1,−1,−2,−1,−2, 0,−4 ],
[ −1,−1,−1,−2, 0,−1, 0,−3 ],
[ −1,−1,−1,−2, 0, 0, 1,−2 ],
[ −1,−1,−1,−1, 0,−1, 0,−2 ],
[ −1,−1,−1,−1, 0, 0, 1,−2 ],
[ −1,−1, 0,−2, 0,−1, 1,−2 ],
[ −1,−1, 0,−1, 0,−1, 1,−1 ],
[ −1,−1, 0,−1, 1, 0, 1,−1 ],
[ −1,−1, 0, 0, 1, 0, 1, 0 ],
[ −1, 0,−1,−1,−1,−1, 0,−3 ],
[ −1, 0,−1,−1, 0,−1, 0,−2 ],
[ −1, 0,−1,−1, 0, 0, 1,−1 ],
[ −1, 0, 0,−1, 0,−1, 0,−2 ],
[ −1, 0, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0,−1, 1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 1, 0 ],
[ −1, 0, 1, 0, 1, 0, 1, 1 ],
[ 0,−1,−1,−1,−1,−1,−1,−3 ],
[ 0,−1,−1,−1,−1, 0, 0,−2 ],
[ 0,−1,−1,−1, 0, 0, 0,−1 ],
[ 0,−1, 0,−1,−1,−1, 0,−2 ],
[ 0,−1, 0,−1, 0,−1, 1,−1 ],
[ 0,−1, 0,−1, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 1, 1 ],
[ 0, 0,−1,−1,−1,−1,−1,−3 ],
[ 0, 0,−1,−1,−1, 0,−1,−2 ],
[ 0, 0,−1,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0, 0,−1,−1,−1,−1,−2 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1,−1,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 1, 1, 1 ],
2
1
1
1
0
1
0
−2











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
1,
1,
1,
0,
0,
0,
1,
1,
1,
1,
1,
2,
0, 1, 1, 1, 2 ],
1, 0, 0, 0, 1 ],
1, 1, 1, 0, 1 ],
0, 0, −1, 0, 0 ],
0, 0, 0, 1, 1 ],
0, 1, 0, 1, 2 ],
1, 1, 0, 0, 1 ],
1, 1, 1, 0, 2 ],
1, 2, 1, 1, 3 ],
0, −1, 0,−1, −1 ],
0, 0, 0,−1, 0 ],
0, 0, 1, 0, 1 ],
1, 0, 0,−1, 1 ],
1, 0, 1, 0, 1 ],
0, 0, 0, 0, 1 ],
1, 0, 0, 0, 2 ],
1, 1, 1, 0, 2 ],
2, 1, 1, 0, 3 ],
0, −1, −1,−1, −1 ],
0, −1, 0, 0, 0 ],
0, 0, 0, 0, 1 ],
1, 0, 0,−1, 0 ],
1, 0, 1,−1, 1 ],
1, 1, 1, 0, 2 ],
1, 0, 0, 0, 1 ],
1, 1, 0, 0, 2 ],
1, 1, 1, 1, 3 ],
1, −1, 0,−2, 0 ],
1, −1, 1,−1, 1 ],
1, 0, 1,−1, 2 ],
1, −1, 0,−1, 1 ],
1, 0, 0, 0, 2 ],
1, 0, 1, 0, 3 ],
2, 0, 1,−1, 2 ],
2, 1, 1, 0, 3 ],
2, 1, 1, 0, 4 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 0 ],
1, 0, 1 ],
1, 0, 2 ],
0, 0, 0 ],
0, 0, 1 ],
1, 1, 2 ],
0, 0, 2 ],
1, 1, 2 ],
0, −1,−1 ],
0, −1, 0 ],
0, 0, 0 ],
0, −1, 0 ],
0, 0, 1 ],
1, 0, 2 ],
0, −1, 1 ],
1, 0, 2 ],
1, 0, 3 ],
0, 0, 0 ],
0, −1,−1 ],
0, −1, 0 ],
1, 0, 1 ],
0, −1, 1 ],
1, 0, 1 ],
0, 0, 1 ],
0, 0, 2 ],
1, 0, 2 ],
1, 0, 3 ],
0, −1, 0 ],
0, −1, 1 ],
1, 0, 2 ],
0, −1, 1 ],
1, −1, 2 ],
1, 0, 3 ],
1, −1, 3 ],
1, 0, 4 ],
1, −1, 3 ],
0, 0, 0,
0, 0, 0,
0, 0, 0,
0, 0, 1,
0, 0, 1,
0, 0, 1,
0, 0, 1,
0, 0, 1,
0, 1,−1,
0, 1, 0,
0, 1, 0,
0, 1, 0,
0, 1, 0,
0, 1, 0,
0, 1, 1,
0, 1, 1,
0, 1, 1,
1,−1, 0,
1, 0, 0,
1, 0, 0,
1, 0, 0,
1, 0, 0,
1, 0, 0,
1, 0, 1,
1, 0, 1,
1, 0, 1,
1, 0, 1,
1, 1, 0,
1, 1, 0,
1, 1, 0,
1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 2, 1,
1, 0,
1, 0,
1, 1,
0, 0,
0, 1,
0, 1,
1, 1,
1, 1,
0,−1,
0,−1,
0, 0,
1,−1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
0, 0,
0,−1,
0, 0,
0, 0,
1, 0,
1, 0,
0, 0,
1, 0,
1, 1,
2, 1,
1,−1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
2, 0,
2, 1,
2, 0,
1
1
1
1
0
1
0
0
















bI =
C




[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0, 0,
0, 0,
0, 0,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
1, 1,
0,−1,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 1,
0, 1,
0, 1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
1, 0, 0, 0, 0 ],
1, 1, 0, 0, 1 ],
1, 1, 1, 1, 2 ],
0, 0, 0, 0, 1 ],
0, 1, 0, 1, 1 ],
1, 0, 0, 0, 1 ],
1, 1, 0, 1, 2 ],
1, 1, 1, 1, 3 ],
0,−1,−1,−1,−1 ],
0,−1, 0, 0, 0 ],
0, 0, 0, 0, 1 ],
1, 0, 0,−1, 0 ],
1, 0, 1,−1, 1 ],
1, 1, 1, 0, 2 ],
1, 0, 0, 0, 1 ],
1, 1, 0, 0, 2 ],
1, 1, 1, 1, 3 ],
0,−1, 0,−1,−1 ],
0,−1, 0,−1, 0 ],
0, 0, 0, 0, 0 ],
1,−1, 0,−1, 0 ],
1, 0, 0, 0, 1 ],
1, 0, 1, 0, 2 ],
1, 0, 0,−1, 1 ],
1, 0, 1, 0, 2 ],
1, 1, 1, 0, 3 ],
0,−1, 0,−1, 0 ],
1,−1, 0,−1, 1 ],
1, 0, 1,−1, 1 ],
2, 0, 1,−1, 2 ],
1, 0, 0,−1, 2 ],
1, 0, 1, 0, 2 ],
2, 0, 0,−1, 2 ],
2, 0, 1, 0, 3 ],
2, 1, 2, 0, 4 ],
2, 0, 1,−1, 3 ]
∗
7
• I ≡ P119 :
6
5
4
3
2
1





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
223
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
0
0
0
0
0
−1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
−1
−1
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
1
1
1
1
1
1
1
−1
















BI =



0
0
0
0
1
0
1
0
0
0
0
0
0
0
−1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
−1
1
1
0
0
0
0
0
0
0
0
−1
0
0
−1
0
0
0
−1
0
0
0
0
0
0
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 1, 1, 2, 1,−1,−1, 1 ],
[ −1,−1, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, −1, 1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, −1, 1 ],
[ −1, 0, 1, 2, 1, 0, −1, 1 ],
[ −1, 1, 0, 1, 0, 0, −1, 0 ],
[ −1, 1, 0, 1, 1, 0, −1, 0 ],
[ −1, 1, 0, 1, 1, 1, −1, 1 ],
[ −1, 1, 1, 1, 0, −1, −1, 0 ],
[ −1, 1, 1, 1, 0, 0, −1, 0 ],
[ −1, 1, 1, 1, 1, 0, −1, 1 ],
[ −1, 1, 1, 2, 0, −1, 0, 1 ],
[ −1, 1, 1, 2, 1, 0, −1, 1 ],
[ −1, 2, 1, 2, 0, −1, −1, 1 ],
[ 0,−1,−1,−1, 0, 1, 0,−1 ],
[ 0,−1,−1,−1, 1, 1, 0,−1 ],
[ 0,−1,−1,−1, 1, 2, 0, 0 ],
[ 0,−1, 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 0, 1, 0,−1 ],
[ 0,−1, 0,−1, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 1, 1, −1, 0 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1,−1, 0, 0, 1,−1 ],
[ 0, 0,−1,−1, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 1, 1, 0, 0 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, −1, 1, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, −1, 1 ],
[ 0, 0, 1, 0,−1, −1, 0,−1 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, −1, −1, 0 ],
[ 0, 0, 1, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, 1, 1, 0, −1, 1 ],
[ 0, 1, 0, 0,−1, −1, 0, 0 ],
[ 0, 1, 0, 0, 0, −1, 0, 0 ],
[ 1,−1,−1,−2,−1, 1, 1,−1 ],
[ −1, 0, −1, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 1, 1,−1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 1, 1, 0,−1, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 1, 0,−1, 1 ],
[ −1, 1, 0, 2, 1, 0,−1, 1 ],
[ −1, 1, 1, 1, 0,−1, 0, 0 ],
[ −1, 1, 1, 1, 0, 0,−1, 1 ],
[ −1, 1, 1, 2, 0,−1,−1, 0 ],
[ −1, 1, 1, 2, 0, 0,−1, 1 ],
[ −1, 1, 1, 2, 1, 0,−1, 2 ],
[ 0, −1, −1, −2, 0, 1, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 1, −1 ],
[ 0, −1, −1, −1, 1, 1, 0, 0 ],
[ 0, −1, −1, 0, 1, 1, 0, 0 ],
[ 0, −1, 0, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 0, 0 ],
[ 0, 0, −1, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, −1, 0, 0, 1, 0 ],
[ 0, 0, −1, −1, 0, 1, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, −1, −1, 0, 1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1,−1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, 0,−1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0,−1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1,−1, 0 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, −1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0,−1, 0, 0 ],
[ 0, 0, 1, 1, 0, 0,−1, 1 ],
[ 0, 1, −1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, −1,−1, 1, 0 ],
[ 0, 1, 0, 0, 0, 0,−1, 0 ],
224
[ −2, 1, 1, 2, 1, 0,−1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0,−1, 0 ],
[ −1, 0, 0, 1, 1, 1,−1, 0 ],
[ −1, 0, 0, 1, 2, 1,−1, 1 ],
[ −1, 0, 1, 1, 0, 0,−1, 0 ],
[ −1, 0, 1, 1, 1, 0,−1, 0 ],
[ −1, 0, 1, 1, 1, 1,−1, 1 ],
[ −1, 1, 0, 1, 0,−1, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 0, 1 ],
[ −1, 1, 0, 1, 1, 0, 0, 1 ],
[ −1, 1, 1, 1,−1,−1, 0, 0 ],
[ −1, 1, 1, 1, 0,−1, 0, 1 ],
[ −1, 1, 1, 1, 0, 0, 0, 1 ],
[ −1, 1, 1, 2, 0,−1,−1, 1 ],
[ −1, 1, 1, 2, 1, 0,−2, 1 ],
[ −1, 1, 2, 2, 0,−1,−1, 1 ],
[ 0,−1,−1,−1, 0, 0, 1,−1 ],
[ 0,−1,−1,−1, 0, 1, 1, 0 ],
[ 0,−1,−1,−1, 1, 1, 1, 0 ],
[ 0,−1, 0,−1,−1, 0, 1,−1 ],
[ 0,−1, 0,−1, 0, 0, 1, 0 ],
[ 0,−1, 0,−1, 0, 1, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 0, 1 ],
[ 0, 0,−1,−1, 0, 0, 0,−1 ],
[ 0, 0,−1,−1, 0, 1, 0,−1 ],
[ 0, 0,−1,−1, 1, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 1, 1,−1, 0 ],
[ 0, 0, 0,−1,−1,−1, 1,−1 ],
[ 0, 0, 0,−1,−1, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0,−1,−1, 1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1,−1, 1 ],
[ 0, 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 0, 1, 1, 0,−1, 0 ],
[ 0, 0, 0, 1, 1, 1,−1, 1 ],
[ 0, 0, 1, 0,−1,−1, 1, 0 ],
[ 0, 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 0, 1, 1,−1,−1, 0, 0 ],
[ 0, 0, 1, 1, 0,−1, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0,−1,−1, 0,−1 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
1
1
1
0
1
0
0
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 1, 0, −1, 0, 0 ],
0, 1, 0, 1, 0, 0, −1, 1 ],
0, 1, 1, 0,−1, −1, 0, 0 ],
0, 1, 1, 1,−1, −1, 0, 0 ],
0, 1, 1, 1, 0, −1, −1, 1 ],
0, 1, 1, 2, 0, −1, −1, 1 ],
1,−1,−1,−2,−1, 0, 1,−2 ],
1,−1,−1,−2, 0, 0, 1,−1 ],
1,−1,−1,−2, 0, 1, 1, 0 ],
1,−1,−1,−1, 0, 0, 1,−1 ],
1,−1,−1,−1, 0, 1, 0, 0 ],
1,−1, 0,−2,−1, 0, 1,−1 ],
1,−1, 0,−1,−1, 0, 1,−1 ],
1,−1, 0,−1, 0, 0, 0, 0 ],
1,−1, 0, 0, 0, 0, 0, 0 ],
1, 0,−1,−1,−1, 0, 0,−1 ],
1, 0,−1,−1, 0, 0, 0,−1 ],
1, 0,−1,−1, 0, 1, 0, 0 ],
1, 0, 0,−1,−1, −1, 0,−1 ],
1, 0, 0,−1,−1, 0, 0,−1 ],
1, 0, 0,−1, 0, 0, 0, 0 ],
1, 0, 0, 0,−1, −1, 1, 0 ],
1, 0, 0, 0, 0, 0, −1, 0 ],
1, 0, 1, 0,−1, −1, 0, 0 ],
0, 1, 0, 1, −1,−1,
0, 1, 0, 1, 0,−1,
0, 1, 0, 1, 0, 0,
0, 1, 1, 1, −1,−2,
0, 1, 1, 1, −1,−1,
0, 1, 1, 1, 0,−1,
1, −2, −1, −2, 0, 1,
1, −1, −1, −2, −1, 0,
1, −1, −1, −2, 0, 1,
1, −1, −1, −1, −1, 0,
1, −1, −1, −1, 0, 0,
1, −1, −1, −1, 0, 1,
1, −1, 0, −1, −1,−1,
1, −1, 0, −1, −1, 0,
1, −1, 0, −1, 0, 0,
1, 0, −1, −2, −1, 0,
1, 0, −1, −1, −1, 0,
1, 0, −1, −1, 0, 0,
1, 0, −1, 0, 0, 0,
1, 0, 0, −1, −1,−1,
1, 0, 0, −1, −1, 0,
1, 0, 0, 0, −1,−1,
1, 0, 0, 0, −1, 0,
1, 0, 0, 0, 0, 0,
1, 1, 0, 0, −1,−1,
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0 ],
0, 1 ],
0, 1 ],
0, 0 ],
0, 1 ],
0, 1 ],
1, −1 ],
1, −1 ],
0, −1 ],
1, −1 ],
1, 0 ],
1, 0 ],
1, −1 ],
1, 0 ],
1, 0 ],
1, −1 ],
1, −1 ],
0, 0 ],
0, 0 ],
1, −1 ],
0, 0 ],
0, −1 ],
0, 0 ],
0, 0 ],
0, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 1, 0, 1, 0,−1,−1, 0 ],
0, 1, 0, 1, 0, 0,−1, 0 ],
0, 1, 0, 1, 1, 0,−1, 1 ],
0, 1, 1, 1,−1,−1,−1, 0 ],
0, 1, 1, 1, 0,−1,−1, 0 ],
0, 1, 1, 1, 0, 0,−1, 1 ],
1,−1,−2,−2, 0, 1, 1,−1 ],
1,−1,−1,−2,−1, 0, 2,−1 ],
1,−1,−1,−2, 0, 1, 1,−1 ],
1,−1,−1,−1, 0, 0, 0,−1 ],
1,−1,−1,−1, 0, 1, 0,−1 ],
1,−1,−1,−1, 1, 1, 0, 0 ],
1,−1, 0,−1,−1, 0, 0,−1 ],
1,−1, 0,−1, 0, 0, 0,−1 ],
1,−1, 0,−1, 0, 1, 0, 0 ],
1, 0,−1,−1,−1,−1, 1,−1 ],
1, 0,−1,−1,−1, 0, 1, 0 ],
1, 0,−1,−1, 0, 0, 1, 0 ],
1, 0, 0,−1,−2,−1, 1,−1 ],
1, 0, 0,−1,−1,−1, 1, 0 ],
1, 0, 0,−1,−1, 0, 1, 0 ],
1, 0, 0, 0,−1,−1, 0, 0 ],
1, 0, 0, 0, 0,−1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
2,−1,−1,−2,−1, 0, 1,−1 ]
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
∗
• I ≡ P120 :
7
6
4
3
5
2
1





CI =








b I =
Cox




0
0
0
0
1
0
0
−1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
−1
0
0
1
0
0
0
1
0
−1
−1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
















b
CI =



1
1
1
1
1
1
1
−1
















BI =



1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
−1
0
0
0
0
0
−1
0
0
0
0
0
1
0
0
1
0
0
0
−1
0
0
0
−1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
−1
0
0
−1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
−1
−1
−1
−1
−1
−1
−1
−1
1
0
−1
0
0
0
0
0
0











0
0
0
0
0
0
1
0
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 1, 1, 2, 1, 1,−1, 2 ],
[ −1,−1, 0, 0, 0, 1, 1, 0 ],
[ 1,−1,−1,−2,−1,−1, 1,−2 ],
[ −1, 0, −1, 0, 0, 1, 1, 0 ],
225
[ −2, 1, 1, 2, 1, 1, 0, 2 ],
[ −1, 0, 0, 0,−1, 0, 0,−1 ],
0
0
0
0
0
0
0
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, 0, 0, 0, 0, 0,−1 ],
−1, 0, 0, 0, 0, 1, 0, 0 ],
−1, 0, 0, 0, 1, 1, 1, 1 ],
−1, 0, 0, 1, 0, 1, 0, 1 ],
−1, 0, 0, 1, 1, 1, 1, 1 ],
−1, 0, 1, 0, 0, 0, 0, 0 ],
−1, 0, 1, 1, 0, 0, 0, 1 ],
−1, 0, 1, 1, 1, 1, 0, 1 ],
−1, 0, 1, 2, 1, 1, 0, 2 ],
−1, 1, 0, 1, 0, 0, 0, 0 ],
−1, 1, 0, 1, 1, 0, 0, 1 ],
−1, 1, 0, 1, 1, 1, 1, 2 ],
−1, 1, 1, 1, 0, 0, −1, 0 ],
−1, 1, 1, 1, 1, 0, −1, 1 ],
−1, 1, 1, 1, 1, 1, 0, 2 ],
−1, 1, 1, 2, 1, 0, −1, 2 ],
−1, 1, 1, 2, 1, 1, 0, 3 ],
−1, 2, 1, 2, 1, 0, −1, 2 ],
0,−1,−1,−1,−1, 0, 1,−2 ],
0,−1,−1,−1, 0, 0, 1,−1 ],
0,−1,−1,−1, 0, 1, 2, 0 ],
0,−1, 0,−1,−1, 0, 0,−2 ],
0,−1, 0,−1, 0, 0, 0,−1 ],
0,−1, 0,−1, 0, 1, 1, 0 ],
0,−1, 0, 0, 0, 0, 0, 0 ],
0,−1, 0, 0, 0, 1, 1, 0 ],
0,−1, 1, 0, 0, 0, 0, 0 ],
0, 0,−1,−1,−1, 0, 0,−1 ],
0, 0,−1,−1, 0, 0, 1,−1 ],
0, 0,−1, 0,−1, 0, 0,−1 ],
0, 0,−1, 0, 0, 0, 1, 0 ],
0, 0,−1, 0, 0, 1, 1, 1 ],
0, 0, 0,−1,−1,−1, 0,−2 ],
0, 0, 0,−1, 0,−1, 0,−1 ],
0, 0, 0,−1, 0, 0, 1, 0 ],
0, 0, 0, 0,−1,−1, 0,−1 ],
0, 0, 0, 0,−1, 0, 0, 0 ],
0, 0, 0, 0, 0,−1, 0, 0 ],
0, 0, 0, 0, 0, 0, 0,−1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 1, 1 ],
0, 0, 0, 0, 1, 0, 1, 1 ],
0, 0, 0, 0, 1, 1, 1, 2 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 1, 1, 0, 1 ],
0, 0, 1, 0,−1,−1, −1,−1 ],
0, 0, 1, 0, 0,−1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 1, 0, 0, −1, 0 ],
0, 0, 1, 1, 1, 0, −1, 1 ],
0, 0, 1, 1, 1, 1, 0, 2 ],
0, 1, 0, 0, 0,−1, −1,−1 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
0, 1, 0, 1, 0, 0, −1, 1 ],
0, 1, 0, 1, 1, 0, 0, 1 ],
0, 1, 1, 0, 0,−1, −1, 0 ],
0, 1, 1, 1, 0,−1, −1, 1 ],
0, 1, 1, 1, 1, 0, −1, 1 ],
0, 1, 1, 2, 1, 0, −1, 2 ],
1,−1,−1,−2,−2,−1, 0,−3 ],
1,−1,−1,−2,−1, 0, 0,−2 ],
1,−1,−1,−2, 0, 0, 1,−1 ],
1,−1,−1,−1,−1, 0, 0,−1 ],
1,−1,−1,−1, 0, 0, 1,−1 ],
1,−1, 0,−2,−1,−1, 0,−2 ],
1,−1, 0,−1,−1,−1, 0,−1 ],
1,−1, 0,−1, 0, 0, 0,−1 ],
1,−1, 0, 0, 0, 0, 0, 0 ],
1, 0,−1,−1,−1,−1, 0,−2 ],
1, 0,−1,−1, 0,−1, 0,−1 ],
1, 0,−1,−1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 2 ],
[ −1, 0, 1, 1, 0, 0,−1, 0 ],
[ −1, 0, 1, 1, 0, 1, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 0, 2 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 0, 1 ],
[ −1, 1, 0, 1, 1, 1, 0, 1 ],
[ −1, 1, 0, 2, 1, 1, 0, 2 ],
[ −1, 1, 1, 1, 0, 0,−1, 1 ],
[ −1, 1, 1, 1, 1, 0, 0, 1 ],
[ −1, 1, 1, 2, 0, 0,−1, 1 ],
[ −1, 1, 1, 2, 1, 0, 0, 2 ],
[ −1, 1, 1, 2, 2, 1, 0, 3 ],
[ 0, −1, −1, −2, −1, 0, 1, −2 ],
[ 0, −1, −1, −1, −1, 0, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 1, −1 ],
[ 0, −1, −1, 0, 0, 1, 1, 0 ],
[ 0, −1, 0, −1, −1, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, −1, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, −1, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, 1, 1, 1, 1 ],
[ 0, 0, 0, −1, −1, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, −1,−1, −2 ],
[ 0, 0, 0, 0, −1, 0,−1, −1 ],
[ 0, 0, 0, 0, 0, −1,−1, −1 ],
[ 0, 0, 0, 0, 0, 0,−1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 0, 1, 0, 0, −1,−1, −1 ],
[ 0, 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 0,−1, 1 ],
[ 0, 0, 1, 1, 1, 0, 0, 1 ],
[ 0, 1, −1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, −1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, −1,−1, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 1, 0, 0, 2 ],
[ 0, 1, 1, 1, 0, −1,−2, 0 ],
[ 0, 1, 1, 1, 0, 0,−1, 1 ],
[ 0, 1, 1, 1, 1, 0,−1, 2 ],
[ 1, −2, −1, −2, −1, 0, 1, −2 ],
[ 1, −1, −1, −2, −1, −1, 0, −3 ],
[ 1, −1, −1, −2, −1, 0, 1, −2 ],
[ 1, −1, −1, −1, −1, −1, 0, −2 ],
[ 1, −1, −1, −1, −1, 0, 1, −1 ],
[ 1, −1, −1, −1, 0, 0, 1, 0 ],
[ 1, −1, 0, −1, −1, −1,−1, −2 ],
[ 1, −1, 0, −1, −1, 0, 0, −1 ],
[ 1, −1, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, −1, −2, −1, −1, 0, −2 ],
[ 1, 0, −1, −1, −1, −1, 0, −1 ],
[ 1, 0, −1, −1, 0, 0, 0, −1 ],
[ 1, 0, −1, 0, 0, 0, 0, 0 ],
226
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 2, 1, 2 ],
[ −1, 0, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 1, 1, 2 ],
[ −1, 1, 0, 1, 0, 0,−1, 0 ],
[ −1, 1, 0, 1, 0, 1, 0, 1 ],
[ −1, 1, 0, 1, 1, 1, 0, 2 ],
[ −1, 1, 1, 1, 0,−1,−1, 0 ],
[ −1, 1, 1, 1, 0, 0, 0, 1 ],
[ −1, 1, 1, 1, 1, 0, 0, 2 ],
[ −1, 1, 1, 2, 1, 0,−1, 1 ],
[ −1, 1, 1, 2, 1, 1, 0, 2 ],
[ −1, 1, 2, 2, 1, 0,−1, 2 ],
[ 0,−1,−1,−1,−1, 0, 0,−2 ],
[ 0,−1,−1,−1,−1, 1, 1,−1 ],
[ 0,−1,−1,−1, 0, 1, 1, 0 ],
[ 0,−1, 0,−1,−1,−1, 0,−2 ],
[ 0,−1, 0,−1,−1, 0, 1,−1 ],
[ 0,−1, 0,−1, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 1, 1 ],
[ 0, 0,−1,−1,−1, 0, 0,−2 ],
[ 0, 0,−1,−1, 0, 0, 0,−1 ],
[ 0, 0,−1,−1, 0, 1, 1, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 1, 1, 0 ],
[ 0, 0, 0,−1,−1,−1,−1,−2 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1,−1,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 0, 1, 0, 0,−1,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0,−1,−1, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 0, 2 ],
[ 0, 1, 0, 0,−1,−1,−1,−1 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0, 1, 1, 0,−1, 1 ],
[ 0, 1, 0, 1, 1, 1, 0, 2 ],
[ 0, 1, 1, 1, 0,−1,−1, 0 ],
[ 0, 1, 1, 1, 1,−1,−1, 1 ],
[ 0, 1, 1, 1, 1, 0, 0, 2 ],
[ 1,−1,−2,−2,−1, 0, 1,−2 ],
[ 1,−1,−1,−2,−1,−1, 0,−2 ],
[ 1,−1,−1,−2,−1, 0, 1,−1 ],
[ 1,−1,−1,−1,−1, 0, 0,−2 ],
[ 1,−1,−1,−1, 0, 0, 0,−1 ],
[ 1,−1,−1,−1, 0, 1, 1, 0 ],
[ 1,−1, 0,−1,−1,−1, 0,−2 ],
[ 1,−1, 0,−1, 0,−1, 0,−1 ],
[ 1,−1, 0,−1, 0, 0, 1, 0 ],
[ 1, 0,−1,−1,−1,−1,−1,−2 ],
[ 1, 0,−1,−1,−1, 0, 0,−1 ],
[ 1, 0,−1,−1, 0, 0, 0, 0 ],
[ 1, 0, 0,−1,−1,−2,−1,−2 ],
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,−1,−1,−1, −1,−2 ],
0,−1, 0,−1, −1,−1 ],
0,−1, 0, 0, 0, 0 ],
0, 0, 0,−1, −1, 0 ],
0, 0, 0, 0, 0, 0 ],
1, 0, 0,−1, −1, 0 ],
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
0, −1, −1, −1,−1, −1 ],
0, −1, 0, −1, 0, −1 ],
0, 0, −1, −1,−1, −1 ],
0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 1 ],
0, 0, 0, −1,−1, 0 ],
0,
0,
0,
0,
0,
1,
[
[
[
[
[
[
1, 0, 0,−1,−1,−1, 0,−1 ],
1, 0, 0,−1, 0,−1, 0, 0 ],
1, 0, 0, 0, 0,−1,−1,−1 ],
1, 0, 0, 0, 0, 0,−1, 0 ],
1, 0, 0, 0, 1, 0, 0, 1 ],
2,−1,−1,−2,−1,−1, 0,−2 ]
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
∗
7
6
• I ≡ P121 :
3
5
2
4
1





CI =








b
CoxI =



0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
−1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
−1
0
0
−1
0
0
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
1
1
1
1
1
1
1
0
















BI =



0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
−1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
−1
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0











0
0
0
−1
0
0
0
0
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,
[ −1, −1,
[ −1, −1,
[ −1, −1,
[ −1, −1,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 1,
[ −1, 1,
[ −1, 1,
2, 1,
1,−1,
1, 0,
2, 0,
2, 0,
0, 0,
0, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
1, 1,
1, 1,
2, 1,
2, 1,
0, 1,
0, 1,
1, 1,
1, 1,−1,
1, 1, 0,
1, 1, −1,
1, 1, −1,
1, 2, −1,
0, 0, 0,
1, 0, 0,
0, 1, −1,
1, 0, −1,
1, 1, −1,
0, 0, −1,
0, 1, −1,
1, 0, −1,
1, 1, −1,
1, 0, −1,
1, 1, −1,
0,−1, 0,
0, 0, 0,
0, 0, 0,
1 ],
0 ],
0 ],
0 ],
1 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
0 ],
1 ],
1 ],
2 ],
0 ],
1 ],
1 ],
[ 1, 1,−2,−1,−1,−1, 1,−1 ],
[ −1,−1, 1, 0, 0, 1, 0, 0 ],
[ −1,−1, 1, 0, 1, 1, 0, 0 ],
[ −1,−1, 2, 0, 1, 1,−1, 1 ],
[ −1,−1, 2, 0, 2, 1,−1, 1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 1,−1, 1 ],
[ −1, 0, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 1,−1, 1 ],
[ −1, 0, 1, 1, 1, 0,−1, 1 ],
[ −1, 0, 2, 0, 1, 1,−1, 1 ],
[ −1, 0, 2, 1, 1, 1,−2, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0,−1, 0 ],
[ −1, 1, 1, 1, 0, 0,−1, 0 ],
[ −1, 1, 1, 1, 0, 1,−1, 1 ],
227
[ −2, 0,
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 1,
[ −1, 1,
[ −1, 1,
[ −1, 1,
2,
1,
1,
2,
0,
0,
1,
1,
1,
1,
1,
1,
1,
2,
2,
0,
0,
1,
1,
1, 1,
0, 1,
0, 1,
0, 1,
0, 0,
0, 0,
0, 0,
0, 0,
0, 1,
0, 1,
1, 0,
1, 0,
1, 1,
1, 0,
1, 1,
1,−1,
1, 0,
1, 0,
1, 1,
1,−1, 1 ],
0, 0, 0 ],
1, 0, 1 ],
1, 0, 1 ],
0, 0,−1 ],
1, 0, 0 ],
0, 0, 0 ],
1, 0, 1 ],
0, 0, 1 ],
1, 0, 1 ],
0, 0, 1 ],
1, 0, 1 ],
0, 0, 1 ],
1,−1, 1 ],
1,−1, 1 ],
0, 0, 0 ],
0, 0, 0 ],
0,−1, 1 ],
0,−1, 1 ],
1
1
0
1
1
1
0
−1











[ −1, 1, 1, 2, 0, 0, −1, 1 ],
[ 0, −1, 0,−1, 0, 0, 0,−1 ],
[ 0, −1, 0,−1, 0, 1, 0,−1 ],
[ 0, −1, 0,−1, 1, 0, 0,−1 ],
[ 0, −1, 0,−1, 1, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 1,−1, 0, 1, 0, 0 ],
[ 0, −1, 1,−1, 1, 1, 0, 0 ],
[ 0, −1, 1, 0, 0, 1, −1, 0 ],
[ 0, −1, 1, 0, 1, 0, −1, 0 ],
[ 0, −1, 1, 0, 1, 1, −1, 0 ],
[ 0, −1, 2, 0, 1, 1, −1, 1 ],
[ 0, 0,−1,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1,−1, 1,−1 ],
[ 0, 0,−1, 0,−1, 0, 1, 0 ],
[ 0, 0,−1, 0, 0,−1, 1, 0 ],
[ 0, 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, −1, 1 ],
[ 0, 0, 1, 1, 1, 0, −1, 1 ],
[ 0, 1,−1, 0,−1,−1, 1,−1 ],
[ 0, 1,−1, 0,−1, 0, 0, 0 ],
[ 0, 1,−1, 0, 0,−1, 0, 0 ],
[ 0, 1,−1, 1,−1,−1, 0,−1 ],
[ 0, 1,−1, 1,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1,−1, 0, 0, 0 ],
[ 0, 1, 0, 1, 0,−1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, −1, 1 ],
[ 0, 2,−1, 1,−1,−1, 0, 0 ],
[ 1, −1,−1,−1, 0,−1, 1,−1 ],
[ 1, −1,−1,−1, 0, 0, 1, 0 ],
[ 1, −1, 0,−1, 0, 0, 1, 0 ],
[ 1, −1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0,−2,−1,−1,−1, 2,−1 ],
[ 1, 0,−2, 0,−1,−1, 1,−1 ],
[ 1, 0,−1,−1,−1, 0, 1,−1 ],
[ 1, 0,−1,−1, 0,−1, 1,−1 ],
[ 1, 0,−1,−1, 0, 0, 0, 0 ],
[ 1, 0,−1, 0,−1,−1, 1,−1 ],
[ 1, 0,−1, 0,−1, 0, 0, 0 ],
[ 1, 0,−1, 0, 0,−1, 0, 0 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, −1, 0 ],
[ 1, 1,−2, 0,−2,−1, 1,−1 ],
[ 1, 1,−2, 0,−1,−1, 1,−1 ],
[ 1, 1,−1, 0,−1,−1, 0, 0 ],
[ 1, 1,−1, 0, 0,−1, 0, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,−2, 1, −1, 1, 1, 0, 0 ],
0,−1, 0, −1, 0, 0, 1, −1 ],
0,−1, 0, −1, 0, 1, 0, 0 ],
0,−1, 0, −1, 1, 0, 0, 0 ],
0,−1, 0, 0, 0, 0, 0, −1 ],
0,−1, 0, 0, 0, 1, 0, 0 ],
0,−1, 1, −1, 1, 0, 0, 0 ],
0,−1, 1, −1, 1, 1, 0, 1 ],
0,−1, 1, 0, 0, 1, 0, 0 ],
0,−1, 1, 0, 1, 0, 0, 0 ],
0,−1, 1, 0, 1, 1,−1, 1 ],
0, 0, −1, −1, −1, 0, 1, −1 ],
0, 0, −1, −1, 0, 0, 1, −1 ],
0, 0, −1, 0, −1, 0, 0, −1 ],
0, 0, −1, 0, 0, −1, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 1, 0, 0 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0,−1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1,−1, 0 ],
0, 0, 0, 0, 1, −1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0,−1, 0 ],
0, 0, 1, 0, 0, 0,−1, 0 ],
0, 0, 1, 0, 0, 1,−1, 0 ],
0, 0, 1, 0, 1, 0,−1, 0 ],
0, 0, 1, 0, 1, 1,−1, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 1, −2, 0, −1, −1, 1, −1 ],
0, 1, −1, 0, −1, −1, 1, 0 ],
0, 1, −1, 0, −1, 0, 1, 0 ],
0, 1, −1, 0, 0, −1, 1, 0 ],
0, 1, −1, 1, −1, −1, 0, 0 ],
0, 1, −1, 1, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0,−1, 0 ],
0, 1, 0, 1, −1, −1, 0, 0 ],
0, 1, 0, 1, −1, 0, 0, 1 ],
0, 1, 0, 1, 0, −1, 0, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
1,−1, −1, −2, 0, 0, 1, −1 ],
1,−1, −1, −1, 0, 0, 0, −1 ],
1,−1, 0, −1, 0, 0, 0, −1 ],
1,−1, 0, −1, 0, 1, 0, 0 ],
1, 0, −2, −1, −1, −1, 1, −2 ],
1, 0, −2, −1, −1, 0, 1, −1 ],
1, 0, −1, −1, −1, −1, 1, −1 ],
1, 0, −1, −1, −1, 0, 1, 0 ],
1, 0, −1, −1, 0, −1, 1, 0 ],
1, 0, −1, −1, 0, 0, 1, 0 ],
1, 0, −1, 0, −1, −1, 1, 0 ],
1, 0, −1, 0, −1, 0, 1, 0 ],
1, 0, −1, 0, 0, −1, 1, 0 ],
1, 0, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 1, −2, 0, −1, −2, 1, −1 ],
1, 1, −2, 0, −1, −1, 1, 0 ],
1, 1, −1, 0, −1, −1, 1, 0 ],
1, 1, −1, 1, −1, −1, 0, 0 ],
228
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,−1,−1,−1, 0, 0, 1,−1 ],
0,−1, 0,−1, 0, 0, 1, 0 ],
0,−1, 0,−1, 0, 1, 1, 0 ],
0,−1, 0,−1, 1, 0, 1, 0 ],
0,−1, 0, 0, 0, 0, 0, 0 ],
0,−1, 0, 0, 1, 0, 0, 0 ],
0,−1, 1,−1, 1, 1,−1, 0 ],
0,−1, 1, 0, 0, 0, 0, 0 ],
0,−1, 1, 0, 0, 1, 0, 1 ],
0,−1, 1, 0, 1, 0, 0, 1 ],
0,−1, 1, 0, 1, 1, 0, 1 ],
0, 0,−1,−1, 0,−1, 1,−1 ],
0, 0,−1,−1, 0, 0, 1, 0 ],
0, 0,−1, 0,−1, 0, 1,−1 ],
0, 0,−1, 0, 0,−1, 1,−1 ],
0, 0,−1, 0, 0, 0, 0, 0 ],
0, 0, 0,−1, 0, 0, 0, 0 ],
0, 0, 0,−1, 1, 0, 0, 0 ],
0, 0, 0, 0,−1, 0, 1, 0 ],
0, 0, 0, 0, 0,−1, 0, 0 ],
0, 0, 0, 0, 0, 0,−1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0,−1, 0 ],
0, 0, 0, 1,−1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 1,−1, 1 ],
0, 0, 1, 0, 1, 0,−1, 1 ],
0, 0, 1, 1, 0, 0,−1, 0 ],
0, 0, 1, 1, 0, 1,−1, 1 ],
0, 1,−1, 0,−1,−1, 0,−1 ],
0, 1,−1, 0,−1, 0, 0,−1 ],
0, 1,−1, 0, 0,−1, 0,−1 ],
0, 1,−1, 0, 0, 0, 0, 0 ],
0, 1,−1, 1,−1,−1, 1, 0 ],
0, 1, 0, 0,−1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 1,−1, 0,−1, 0 ],
0, 1, 0, 1, 0,−1,−1, 0 ],
0, 1, 0, 1, 0, 0,−1, 0 ],
0, 1, 1, 1, 0, 0,−1, 1 ],
1,−1,−1,−1,−1, 0, 1,−1 ],
1,−1,−1,−1, 0, 0, 1,−1 ],
1,−1, 0,−1, 0, 0, 0, 0 ],
1,−1, 0,−1, 1, 0, 0, 0 ],
1, 0,−2,−1,−1,−1, 1,−1 ],
1, 0,−2,−1, 0,−1, 1,−1 ],
1, 0,−1,−1,−1, 0, 0,−1 ],
1, 0,−1,−1, 0,−1, 0,−1 ],
1, 0,−1,−1, 0, 0, 0,−1 ],
1, 0,−1, 0,−1,−1, 0,−1 ],
1, 0,−1, 0,−1, 0, 0,−1 ],
1, 0,−1, 0, 0,−1, 0,−1 ],
1, 0,−1, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0,−1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 1,−2, 0,−1,−1, 0,−1 ],
1, 1,−1, 0,−1,−1, 0,−1 ],
1, 1,−1, 0,−1, 0, 0, 0 ],
2, 0,−2,−1,−1,−1, 1,−1 ]
∗
7
• I ≡ P122 :
4
6
3
5
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
−1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
−1
0
0
0
0
0
0





CI =








b I =
Cox




0
1
1
1
1
1
1
−1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
















b
CI =



1
1
1
1
1
1
1
−1
















BI =



1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
−1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
−1
0
0
1
0
0
0
0
0
0
0
−1
−1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
−1
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
−1
0
0
−1
0
0











0
0
0
0
−1
0
0
0
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 1, 1,−2,−1,−1,−1,−2 ],
[ −1,−1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0,−1, 0, −1, 0, 0, −1 ],
[ −1, 0,−1, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, −1, −1, 0, 0, −2 ],
[ −1, 0, 0, −1, 0, −1, 0, −2 ],
[ −1, 0, 0, −1, 0, 0, −1, −1 ],
[ −1, 0, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, −1, 0, −1, −1, −1 ],
[ −1, 0, 1, −1, 1, −1, −1, −1 ],
[ −1, 1,−1, −1, −1, 0, −1, −2 ],
[ −1, 1,−1, 0, −1, 0, 0, −1 ],
[ −1, 1, 0, −2, −1, −1, 0, −2 ],
[ −1, 1, 0, −1, −1, −1, −1, −2 ],
[ −1, 1, 0, −1, −1, 0, −1, −2 ],
[ −1, 1, 0, −1, 0, −1, −1, −2 ],
[ −1, 1, 0, −1, 0, 0, −1, −1 ],
[ −1, 1, 1, −2, 0, −1, −1, −2 ],
[ −1, 2, 0, −2, −1, −1, −1, −2 ],
[ 0,−1,−1, 1, 0, 1, 0, 0 ],
[ 0,−1,−1, 2, 0, 1, 1, 1 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 0, 1, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 1, 0, 1 ],
[ 0,−1, 1, 0, 1, 0, −1, 0 ],
[ 0,−1, 1, 1, 1, 0, 0, 1 ],
[ 0, 0,−1, 0, −1, 0, 1, −1 ],
[ 1,−1,−1, 2, 1, 1, 1, 2 ],
[ −1, 0, −1,−1,−1, 0, 0,−2 ],
[ −1, 0, −1, 0,−1, 0, 1,−1 ],
[ −1, 0, 0,−1,−1,−1, 0,−2 ],
[ −1, 0, 0,−1,−1, 0, 0,−1 ],
[ −1, 0, 0,−1, 0,−1, 0,−1 ],
[ −1, 0, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 1,−2, 0,−1,−1,−2 ],
[ −1, 0, 1,−1, 0,−1, 0,−1 ],
[ −1, 1, −1,−1,−2, 0, 0,−2 ],
[ −1, 1, −1,−1,−1, 0, 0,−2 ],
[ −1, 1, 0,−2,−1,−1,−1,−3 ],
[ −1, 1, 0,−2,−1, 0,−1,−2 ],
[ −1, 1, 0,−1,−1,−1, 0,−2 ],
[ −1, 1, 0,−1,−1, 0,−1,−1 ],
[ −1, 1, 0,−1, 0,−1,−1,−1 ],
[ −1, 1, 1,−2, 0,−2,−1,−2 ],
[ −1, 1, 1,−2, 0,−1,−1,−1 ],
[ 0, −1, −1, 1,−1, 1, 1, 0 ],
[ 0, −1, −1, 1, 0, 1, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0,−1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 1, 0, 0, 1, 0 ],
[ 0, −1, 0, 1, 0, 1, 0, 1 ],
[ 0, −1, 0, 1, 1, 0, 0, 1 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, 0, 1, 0, 0, 0 ],
[ 0, 0, −2, 1,−1, 1, 1, 0 ],
[ 0, 0, −1, 0,−1, 0, 1, 0 ],
229
[ −2, 1, 0,−2,−1,−1,−1,−3 ],
[ −1, 0,−1, 0,−1, 0, 0,−2 ],
[ −1, 0,−1, 0,−1, 1, 0,−1 ],
[ −1, 0, 0,−1,−1, 0,−1,−2 ],
[ −1, 0, 0,−1, 0,−1,−1,−2 ],
[ −1, 0, 0,−1, 0, 0,−1,−2 ],
[ −1, 0, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 1,−1, 0,−1,−1,−2 ],
[ −1, 0, 1,−1, 0, 0,−1,−1 ],
[ −1, 1,−1,−1,−1,−1, 0,−2 ],
[ −1, 1,−1,−1,−1, 0, 0,−1 ],
[ −1, 1, 0,−2,−1,−1,−1,−2 ],
[ −1, 1, 0,−2, 0,−1,−1,−2 ],
[ −1, 1, 0,−1,−1,−1, 0,−1 ],
[ −1, 1, 0,−1,−1, 0, 0,−1 ],
[ −1, 1, 0,−1, 0,−1, 0,−1 ],
[ −1, 1, 1,−2, 0,−1,−2,−2 ],
[ −1, 1, 1,−1, 0,−1,−1,−1 ],
[ 0,−1,−1, 1, 0, 0, 1, 0 ],
[ 0,−1,−1, 1, 0, 1, 1, 1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 1, 0, 0, 1, 1 ],
[ 0,−1, 0, 1, 0, 1, 1, 1 ],
[ 0,−1, 0, 1, 1, 0, 1, 1 ],
[ 0,−1, 1, 0, 1,−1, 0, 0 ],
[ 0,−1, 1, 0, 1, 0, 0, 1 ],
[ 0, 0,−1, 0,−1, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 1, 0,−1 ],
0
0
0
0
0
0
0
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0,−1, 0, −1, 1, 0, 0 ],
0, 0,−1, 0, 0, 0, 0, 0 ],
0, 0,−1, 1, −1, 0, 1, 0 ],
0, 0,−1, 1, −1, 1, 1, 1 ],
0, 0,−1, 1, 0, 0, 1, 1 ],
0, 0,−1, 1, 0, 1, 1, 1 ],
0, 0, 0, −1, 0, 0, −1, −1 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, −1, 1, 0, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 1, 0, 0, 1 ],
0, 0, 1, −1, 0, −1, 0, 0 ],
0, 0, 1, −1, 0, 0, 0, 0 ],
0, 0, 1, −1, 1, −1, 0, 0 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 0, 1, 0, 1, −1, −1, 0 ],
0, 0, 1, 0, 1, 0, −1, 0 ],
0, 0, 2, −1, 1, −1, −1, 0 ],
0, 1,−1, 0, −1, 0, 0, 0 ],
0, 1,−1, 0, 0, 0, 0, 0 ],
0, 1, 0, −1, −1, 0, 0, −1 ],
0, 1, 0, −1, 0, −1, 0, −1 ],
0, 1, 0, −1, 0, 0, −1, 0 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 1, −1, 0, −1, −1, 0 ],
0, 1, 1, −1, 1, −1, −1, 0 ],
1,−1,−1, 2, 0, 1, 1, 1 ],
1,−1,−1, 2, 0, 2, 1, 2 ],
1,−1, 0, 1, 0, 1, 1, 1 ],
1,−1, 0, 1, 1, 0, 1, 1 ],
1,−1, 0, 1, 1, 1, 0, 2 ],
1,−1, 0, 2, 1, 0, 1, 2 ],
1,−1, 0, 2, 1, 1, 1, 3 ],
1,−1, 1, 1, 1, 0, 0, 2 ],
1,−1, 1, 1, 2, 0, 0, 2 ],
1, 0,−1, 1, 0, 1, 0, 1 ],
1, 0,−1, 2, 0, 1, 1, 2 ],
1, 0, 0, 0, 0, 0, 1, 1 ],
1, 0, 0, 1, 0, 0, 0, 1 ],
1, 0, 0, 1, 0, 1, 0, 1 ],
1, 0, 0, 1, 1, 0, 0, 1 ],
1, 0, 0, 1, 1, 1, 0, 2 ],
1, 0, 1, 0, 1, 0, −1, 1 ],
1, 0, 1, 1, 1, 0, 0, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, −1, 0,−1, 1, 1, 0 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, −1, 1,−1, 1, 0, 0 ],
0, 0, −1, 1, 0, 0, 0, 0 ],
0, 0, −1, 1, 0, 1, 0, 0 ],
0, 0, 0,−1,−1, 0, 0,−1 ],
0, 0, 0,−1, 0, 0, 0,−1 ],
0, 0, 0, 0,−1, 0, 0, 0 ],
0, 0, 0, 0, 0,−1, 0,−1 ],
0, 0, 0, 0, 0, 0,−1,−1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1,−1, 0 ],
0, 0, 0, 0, 1,−1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, 1, 1 ],
0, 0, 1,−1, 0,−1,−1,−1 ],
0, 0, 1,−1, 0, 0,−1,−1 ],
0, 0, 1,−1, 1,−1,−1,−1 ],
0, 0, 1,−1, 1, 0,−1, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 1,−1, 0, 0 ],
0, 0, 1, 0, 1, 0,−1, 1 ],
0, 1, −1,−1,−1, 0, 0,−1 ],
0, 1, −1, 0,−1, 0, 1, 0 ],
0, 1, 0,−1,−1,−1, 0,−1 ],
0, 1, 0,−1,−1, 0, 0, 0 ],
0, 1, 0,−1, 0,−1, 0, 0 ],
0, 1, 0,−1, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0,−1, 0 ],
0, 1, 1,−2, 0,−1,−1,−1 ],
0, 1, 1,−1, 0,−1, 0, 0 ],
1, −2, 0, 2, 1, 1, 1, 2 ],
1, −1, −1, 2, 0, 1, 1, 2 ],
1, −1, 0, 1, 0, 0, 1, 1 ],
1, −1, 0, 1, 0, 1, 1, 2 ],
1, −1, 0, 1, 1, 0, 1, 2 ],
1, −1, 0, 1, 1, 1, 1, 2 ],
1, −1, 0, 2, 1, 1, 0, 2 ],
1, −1, 1, 0, 1, 0, 0, 1 ],
1, −1, 1, 1, 1, 0, 1, 2 ],
1, 0, −1, 1,−1, 1, 1, 1 ],
1, 0, −1, 1, 0, 1, 1, 1 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
1, 0, 0, 1, 0, 0, 1, 1 ],
1, 0, 0, 1, 0, 1, 0, 2 ],
1, 0, 0, 1, 1, 0, 0, 2 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 0, 1, 0, 1, 0, 0, 1 ],
1, 1, 0, 0, 0, 0, 0, 1 ],
∗
• I ≡ P123 :
7
6
5
4
3
2
1
230
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0,−1, 0, 0, 0, 0,−1 ],
0, 0,−1, 0, 0, 1, 0, 0 ],
0, 0,−1, 1,−1, 1, 1, 0 ],
0, 0,−1, 1, 0, 0, 1, 0 ],
0, 0,−1, 1, 0, 1, 0, 1 ],
0, 0, 0,−1, 0,−1, 0,−1 ],
0, 0, 0,−1, 0, 0, 0, 0 ],
0, 0, 0, 0,−1, 0, 1, 0 ],
0, 0, 0, 0, 0,−1, 0, 0 ],
0, 0, 0, 0, 0, 0,−1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0,−1, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 0, 1, 0, 1, 0, 1 ],
0, 0, 1,−1, 0,−1, 0,−1 ],
0, 0, 1,−1, 0, 0,−1, 0 ],
0, 0, 1,−1, 1,−1,−1, 0 ],
0, 0, 1, 0, 0,−1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 1,−1, 0, 1 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 1,−1, 0,−1, 0, 0,−1 ],
0, 1,−1, 0,−1, 1, 0, 0 ],
0, 1, 0,−1,−1, 0,−1,−1 ],
0, 1, 0,−1, 0,−1,−1,−1 ],
0, 1, 0,−1, 0, 0,−1,−1 ],
0, 1, 0, 0,−1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 1,−1, 0,−1,−1,−1 ],
0, 1, 1,−1, 0, 0,−1, 0 ],
1,−1,−1, 1, 0, 1, 1, 1 ],
1,−1,−1, 2, 0, 1, 2, 2 ],
1,−1, 0, 1, 0, 1, 0, 1 ],
1,−1, 0, 1, 1, 0, 0, 1 ],
1,−1, 0, 1, 1, 1, 0, 1 ],
1,−1, 0, 2, 0, 1, 1, 2 ],
1,−1, 0, 2, 1, 1, 1, 2 ],
1,−1, 1, 1, 1, 0, 0, 1 ],
1,−1, 1, 1, 1, 1, 0, 2 ],
1, 0,−1, 1, 0, 0, 1, 1 ],
1, 0,−1, 1, 0, 1, 1, 2 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 0, 1, 0, 0, 1 ],
1, 0, 0, 1, 0, 0, 1, 2 ],
1, 0, 0, 1, 0, 1, 1, 2 ],
1, 0, 0, 1, 1, 0, 1, 2 ],
1, 0, 1, 0, 1,−1, 0, 1 ],
1, 0, 1, 0, 1, 0, 0, 2 ],
2,−1, 0, 2, 1, 1, 1, 3 ]





CI =








b I =
Cox




0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
−1
−1
0
0
0
0
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
1
1
1
1
1
1
1
0
















BI =



0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
−1
−1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
−1
−1
−1
−1
−1
−1
−1
−1
1
1
0
0
0
0
0
0
0











1
1
1
1
1
0
1
−1
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1, 1, 1, 2, 1,−1, 1 ],
[ −1, −2, 1, 1, 2, 1, 0, 1 ],
[ −1, −1, 0, 0, 1, 1, 1, 0 ],
[ −1, −1, 0, 1, 1, 0, 0, 0 ],
[ −1, −1, 0, 1, 1, 1, 1, 1 ],
[ −1, −1, 1, 0, 1, 1, 0, 0 ],
[ −1, −1, 1, 0, 2, 1, 0, 1 ],
[ −1, −1, 1, 1, 1, 0, 0, 1 ],
[ −1, −1, 1, 1, 2, 0, −1, 1 ],
[ −1, −1, 1, 1, 2, 1, 0, 2 ],
[ −1, 0,−1, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 0, 1, 0, −1, 0 ],
[ −1, 0, 1, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 1, 1, 0, −1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0,−1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 1, 1 ],
[ 0, −1, 0, 1, 1, 0, 0, 0 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, 0, 1, 0, 0, 1 ],
[ 0, −1, 1, 1, 1, 0, −1, 0 ],
[ 0, −1, 1, 1, 2, 0, −1, 1 ],
[ 0, 0,−1,−1,−1, 1, 1, 0 ],
[ 0, 0,−1, 0,−1, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 1, 1, 0 ],
[ 0, 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 1, 1, 1 ],
[ 0, 0, 0,−1,−1, 0, 1,−1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 1, 1,−1,−1,−2,−1, 1,−1 ],
[ −1,−1, 0, 0, 0, 1, 1, 0 ],
[ −1,−1, 0, 0, 1, 1, 1, 1 ],
[ −1,−1, 0, 1, 1, 1, 0, 0 ],
[ −1,−1, 0, 1, 2, 1, 0, 1 ],
[ −1,−1, 1, 0, 1, 1, 0, 1 ],
[ −1,−1, 1, 1, 1, 0,−1, 0 ],
[ −1,−1, 1, 1, 1, 1, 0, 1 ],
[ −1,−1, 1, 1, 2, 0, 0, 1 ],
[ −1,−1, 1, 2, 2, 0,−1, 1 ],
[ −1, 0, 0, −1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 0,−1, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 1, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, −1,−1, 0 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ 0,−1, −1, 0, 0, 1, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 1, 1, 0 ],
[ 0,−1, 0, 0, 1, 1, 0, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 0, 1 ],
[ 0,−1, 1, 0, 1, 0,−1, 0 ],
[ 0,−1, 1, 0, 1, 1, 0, 1 ],
[ 0,−1, 1, 1, 1, 0,−1, 1 ],
[ 0, 0, −1, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, −1, −1, 1, 2, 0 ],
[ 0, 0, −1, 0, −1, 0, 1, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, −1, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 0, 1, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, −1,−1, −1 ],
[ 0, 0, 0, 0, 0, 0,−1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
231
[ −2,−1, 1, 1, 2, 1, 0, 1 ],
[ −1,−1, 0, 0, 1, 1, 0, 0 ],
[ −1,−1, 0, 0, 1, 2, 1, 1 ],
[ −1,−1, 0, 1, 1, 1, 0, 1 ],
[ −1,−1, 1, 0, 1, 0, 0, 0 ],
[ −1,−1, 1, 0, 1, 1, 1, 1 ],
[ −1,−1, 1, 1, 1, 0, 0, 0 ],
[ −1,−1, 1, 1, 2, 0,−1, 0 ],
[ −1,−1, 1, 1, 2, 1, 0, 1 ],
[ −1,−1, 2, 1, 2, 0,−1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 0,−1, 0 ],
[ −1, 0, 1, 1, 2, 0,−1, 1 ],
[ 0,−1, 0,−1, 0, 1, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 1, 1, 1 ],
[ 0,−1, 0, 0, 1, 1, 0, 1 ],
[ 0,−1, 0, 1, 1, 0,−1, 0 ],
[ 0,−1, 0, 1, 1, 1, 0, 1 ],
[ 0,−1, 1, 0, 1, 0, 0, 0 ],
[ 0,−1, 1, 1, 1,−1,−1, 0 ],
[ 0,−1, 1, 1, 1, 0, 0, 1 ],
[ 0, 0,−1,−1,−1, 1, 1,−1 ],
[ 0, 0,−1,−1, 0, 1, 1, 0 ],
[ 0, 0,−1, 0,−1, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 1, 1, 0 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1,−1, 1, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 1, 1, 1 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0,−1,−1,−1 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, 0, 1, 0,−1, −1, 0 ],
0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 1, 0, −1, 0 ],
0, 1,−1, 0, 0, 0, 0 ],
0, 1, 0, 0,−1, 0, 0 ],
0, 1, 0, 0, 0, 0, 1 ],
0, 1, 0, 1, 0, −1, 1 ],
0, 1, 1, 1,−1, −2, 0 ],
0, 1, 1, 1, 0, −1, 1 ],
1,−1,−1,−1, 0, 1,−1 ],
1,−1, 0,−1,−1, 0,−1 ],
1,−1, 0,−1, 0, 1, 0 ],
1, 0,−1,−1, 0, 0,−1 ],
1, 0,−1, 0, 0, 0, 0 ],
1, 0, 0,−1,−1, 0, 0 ],
1, 0, 0, 0,−1, −1, 0 ],
1, 0, 0, 0, 0, 0, 0 ],
1, 1, 0, 0,−1, −1, 0 ],
0,−1,−1,−1, 0, 0,−1 ],
0,−1,−1,−1, 1, 1, 0 ],
0,−1, 0,−1, 0, 0, 0 ],
0, 0,−1,−1,−1, 0,−1 ],
0, 0,−1,−1, 0, 1, 0 ],
0, 0, 0,−1,−1, 0,−1 ],
0, 0, 0, 0,−1, −1,−1 ],
0, 0, 0, 0, 0, −1, 0 ],
0, 0, 1, 0,−1, −1, 0 ],
1,−1,−2,−2, 0, 1,−1 ],
1,−1,−1,−2, 0, 0,−1 ],
1,−1,−1,−1,−1, 0,−1 ],
1,−1,−1,−1, 0, 1, 0 ],
1,−1, 0,−1,−1, 0,−1 ],
1, 0,−1,−2,−1, 0,−1 ],
1, 0,−1,−1,−1, 0, 0 ],
1, 0, 0,−1,−1, −1,−1 ],
1, 0, 0, 0,−1, −1, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 1, 0,−1, 1 ],
0, 0, 1, 0, 0, −1,−1, −1 ],
0, 0, 1, 0, 0, 0,−1, 0 ],
0, 0, 1, 0, 1, −1,−1, 0 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 0, 1, 1, 1, −1,−1, 0 ],
0, 1, −1, −1, −2, 0, 1, −1 ],
0, 1, −1, −1, −1, 0, 1, 0 ],
0, 1, −1, 0, −1, 0, 0, −1 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, 0, −1, −1, 0, 0, 0 ],
0, 1, 0, 0, −1, −1,−1, −1 ],
0, 1, 0, 0, −1, 0, 0, 0 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
1,−1, 0, 0, 0, 0, 0, 0 ],
1, 0, −1, −1, −1, 0, 1, −1 ],
1, 0, −1, 0, −1, −1, 0, −1 ],
1, 0, −1, 0, −1, 0, 1, 0 ],
1, 0, 0, −1, −1, 0, 0, −1 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, −1, −1, 0, 0 ],
1, 0, 0, 0, 0, −1,−1, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 1, 0, 0, −1,−1, 0 ],
1, 1, −1, −1, −2, −1, 0, −2 ],
1, 1, −1, −1, −2, 0, 1, −1 ],
1, 1, −1, −1, −1, 0, 0, −1 ],
1, 1, −1, 0, −2, −1, 0, −1 ],
1, 1, −1, 0, −1, −1, 0, 0 ],
1, 1, 0, −1, −1, −1,−1, −1 ],
1, 1, 0, −1, −1, 0, 0, 0 ],
1, 1, 0, 0, −1, −1,−1, 0 ],
1, 2, −1, −1, −2, −1, 0, −1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0, 0, 1, 0, 0,−1, 0 ],
0, 0, 1, 1,−1,−1, 0 ],
0, 0, 1, 1, 0, 0, 1 ],
0, 1, 0, 0,−1,−1, 0 ],
0, 1, 0, 0, 0, 0, 0 ],
0, 1, 0, 1, 0,−1, 0 ],
0, 1, 1, 0,−1,−1, 0 ],
0, 1, 1, 1,−1,−1, 1 ],
1,−1,−1,−1, 0, 0,−1 ],
1,−1,−1,−1, 1, 1, 0 ],
1,−1, 0,−1, 0, 0, 0 ],
1, 0,−1,−1,−1, 0,−1 ],
1, 0,−1,−1, 0, 1, 0 ],
1, 0, 0,−1,−1, 0,−1 ],
1, 0, 0, 0,−1,−1,−1 ],
1, 0, 0, 0, 0,−1, 0 ],
1, 0, 1, 0,−1,−1, 0 ],
0,−1,−1,−2, 0, 1,−1 ],
0,−1,−1,−1, 0, 1, 0 ],
0,−1, 0,−1, 0, 0,−1 ],
0,−1, 0, 0, 0, 0, 0 ],
0, 0,−1,−1, 0, 0, 0 ],
0, 0, 0,−1,−1,−1,−1 ],
0, 0, 0,−1, 0, 0, 0 ],
0, 0, 0, 0,−1, 0, 0 ],
0, 0, 0, 0, 0, 0, 1 ],
1,−2,−1,−2, 0, 1,−1 ],
1,−1,−1,−2,−1, 0,−1 ],
1,−1,−1,−2, 0, 1, 0 ],
1,−1,−1,−1, 0, 0, 0 ],
1,−1, 0,−1,−1,−1,−1 ],
1,−1, 0,−1, 0, 0, 0 ],
1, 0,−1,−1,−1, 0,−1 ],
1, 0, 0,−1,−2,−1,−1 ],
1, 0, 0,−1,−1, 0, 0 ],
1,−1,−1,−2,−1, 0,−1 ]
∗
7
• I ≡ P124 :
4
6
3
5
2
1





CI =



1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
















bI =
C




232
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
















b I =
Cox




0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1











0
 0

 −1

BI = 00

 0
 0
0
0
−1
0
0
−1
0
0
0

−1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
−1
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−1, 2, 1, 1, 1, 1 ],
[ −1, −2, 0, 2, 1, 1, 1, 1 ],
[ −1, −1, −1, 2, 0, 1, 1, 1 ],
[ −1, −1, 0, 1, 0, 0, 1, 0 ],
[ −1, −1, 0, 1, 0, 1, 1, 1 ],
[ −1, −1, 0, 1, 1, 0, 1, 1 ],
[ −1, −1, 0, 1, 1, 1, 1, 1 ],
[ −1, −1, 0, 2, 1, 1, 0, 1 ],
[ −1, −1, 1, 0, 1, 0, 0, 0 ],
[ −1, −1, 1, 1, 1, 0, 1, 1 ],
[ −1, 0, −1, 1,−1, 1, 1, 0 ],
[ −1, 0, −1, 1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, 1, 0, 1, 0, 0 ],
[ 0, −1, −1, 2, 0, 1, 1, 1 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 1, 0, 0, 0, 0 ],
[ 0, −1, 0, 1, 0, 1, 0, 0 ],
[ 0, −1, 0, 1, 1, 0, 0, 0 ],
[ 0, −1, 0, 1, 1, 1, 0, 1 ],
[ 0, −1, 1, 0, 1, 0,−1, 0 ],
[ 0, −1, 1, 1, 1, 0, 0, 1 ],
[ 0, 0, −1, 0,−1, 0, 1,−1 ],
[ 0, 0, −1, 0,−1, 1, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 1,−1, 0, 1, 0 ],
[ 0, 0, −1, 1,−1, 1, 1, 1 ],
[ 0, 0, −1, 1, 0, 0, 1, 1 ],
[ 0, 0, −1, 1, 0, 1, 1, 1 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 1,−1, 0,−1, 0, 0 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1,−1, 1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 0, 1, 0, 1,−1,−1, 0 ],
[ 0, 0, 1, 0, 1, 0,−1, 0 ],
[ 0, 0, 2,−1, 1,−1,−1, 0 ],
[ 0, 1, −1, 0,−1, 0, 0, 0 ],
[ 0, 1, −1, 0, 0, 0, 0, 0 ],
[ 1, 1, 1,−2,−1,−1,−1,−1 ],
[ −1,−1,−1, 1, 0, 1, 1, 0 ],
[ −1,−1,−1, 2, 0, 1, 2, 1 ],
[ −1,−1, 0, 1, 0, 1, 0, 0 ],
[ −1,−1, 0, 1, 1, 0, 0, 0 ],
[ −1,−1, 0, 1, 1, 1, 0, 0 ],
[ −1,−1, 0, 2, 0, 1, 1, 1 ],
[ −1,−1, 0, 2, 1, 1, 1, 1 ],
[ −1,−1, 1, 1, 1, 0, 0, 0 ],
[ −1,−1, 1, 1, 1, 1, 0, 1 ],
[ −1, 0,−1, 1, 0, 0, 1, 0 ],
[ −1, 0,−1, 1, 0, 1, 1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 1, 1 ],
[ −1, 0, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 0, 1, 1 ],
[ −1, 0, 1, 0, 1, −1, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 0, 1 ],
[ 0,−1,−1, 1, −1, 1, 1, 0 ],
[ 0,−1,−1, 1, 0, 1, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, −1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 1, 0, 0, 1, 0 ],
[ 0,−1, 0, 1, 0, 1, 0, 1 ],
[ 0,−1, 0, 1, 1, 0, 0, 1 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 1, 0, 0, 0 ],
[ 0, 0,−2, 1, −1, 1, 1, 0 ],
[ 0, 0,−1, 0, −1, 0, 1, 0 ],
[ 0, 0,−1, 0, −1, 1, 1, 0 ],
[ 0, 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 1, −1, 1, 0, 0 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0,−1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, −1, 0, −1, −1, −1 ],
[ 0, 0, 1, −1, 0, 0, −1, −1 ],
[ 0, 0, 1, −1, 1, −1, −1, −1 ],
[ 0, 0, 1, −1, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, −1, 1 ],
[ 0, 1,−1, −1, −1, 0, 0, −1 ],
[ 0, 1,−1, 0, −1, 0, 1, 0 ],
[ 0, 1, 0, −1, −1, −1, 0, −1 ],
233
[ −2,−1, 0, 2, 1, 1, 1, 1 ],
[ −1,−1,−1, 2, 0, 1, 1, 0 ],
[ −1,−1,−1, 2, 0, 2, 1, 1 ],
[ −1,−1, 0, 1, 0, 1, 1, 0 ],
[ −1,−1, 0, 1, 1, 0, 1, 0 ],
[ −1,−1, 0, 1, 1, 1, 0, 1 ],
[ −1,−1, 0, 2, 1, 0, 1, 1 ],
[ −1,−1, 0, 2, 1, 1, 1, 2 ],
[ −1,−1, 1, 1, 1, 0, 0, 1 ],
[ −1,−1, 1, 1, 2, 0, 0, 1 ],
[ −1, 0,−1, 1, 0, 1, 0, 0 ],
[ −1, 0,−1, 2, 0, 1, 1, 1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 1, 0, 1, 0,−1, 0 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ 0,−1,−1, 1, 0, 0, 1, 0 ],
[ 0,−1,−1, 1, 0, 1, 1, 1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 1, 0, 0, 1, 1 ],
[ 0,−1, 0, 1, 0, 1, 1, 1 ],
[ 0,−1, 0, 1, 1, 0, 1, 1 ],
[ 0,−1, 1, 0, 1,−1, 0, 0 ],
[ 0,−1, 1, 0, 1, 0, 0, 1 ],
[ 0, 0,−1, 0,−1, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 1,−1, 1, 1, 0 ],
[ 0, 0,−1, 1, 0, 0, 1, 0 ],
[ 0, 0,−1, 1, 0, 1, 0, 1 ],
[ 0, 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1,−1, 0,−1, 0,−1 ],
[ 0, 0, 1,−1, 0, 0,−1, 0 ],
[ 0, 0, 1,−1, 1,−1,−1, 0 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1,−1, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1,−1, 0,−1, 0, 0,−1 ],
[ 0, 1,−1, 0,−1, 1, 0, 0 ],
[ 0, 1, 0,−1,−1, 0,−1,−1 ],
1
1
1
1
1
1
0
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1, 0,−1,−1, 0, 0,−1 ],
1, 0,−1, 0,−1, 0,−1 ],
1, 0,−1, 0, 0,−1, 0 ],
1, 0, 0, 0,−1, 0, 0 ],
1, 0, 0, 0, 0, 0, 1 ],
1, 1,−1, 0,−1,−1, 0 ],
1, 1,−1, 1,−1,−1, 0 ],
0, −1, 0,−1, 0, 0,−1 ],
0, −1, 0,−1, 1, 0, 0 ],
0, 0,−1,−1, 0,−1,−1 ],
0, 0,−1, 0,−1,−1,−1 ],
0, 0,−1, 0, 0,−1,−1 ],
0, 0, 0,−1, 0, 0, 0 ],
0, 0, 0, 0, 0, 0, 0 ],
0, 1,−1, 0,−1,−1,−1 ],
0, 1,−1, 0, 0,−1, 0 ],
1, −1,−1,−1,−1, 0,−1 ],
1, −1,−1,−1, 0, 0, 0 ],
1, 0,−2,−1,−1,−1,−1 ],
1, 0,−2, 0,−1,−1,−1 ],
1, 0,−1,−1,−1, 0, 0 ],
1, 0,−1,−1, 0, 0, 0 ],
1, 0,−1, 0,−1, 0, 0 ],
1, 1,−2, 0,−1,−2,−1 ],
1, 1,−1, 0,−1,−1, 0 ],
0, 1, 0, −1, −1, 0, 0, 0 ],
0, 1, 0, −1, 0, −1, 0, 0 ],
0, 1, 0, −1, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 1, −2, 0, −1, −1, −1 ],
0, 1, 1, −1, 0, −1, 0, 0 ],
1,−1, 0, 0, 0, 0, 0, 0 ],
1, 0,−1, 0, −1, 0, 0, 0 ],
1, 0,−1, 0, 0, 0, 0, 0 ],
1, 0, 0, −1, −1, 0, 0, −1 ],
1, 0, 0, −1, 0, −1, 0, −1 ],
1, 0, 0, −1, 0, 0, −1, 0 ],
1, 0, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 1, −1, 0, −1, −1, 0 ],
1, 0, 1, −1, 1, −1, −1, 0 ],
1, 1,−1, −1, −1, 0, −1, −1 ],
1, 1,−1, 0, −1, 0, 0, 0 ],
1, 1, 0, −2, −1, −1, 0, −1 ],
1, 1, 0, −1, −1, −1, −1, −1 ],
1, 1, 0, −1, −1, 0, −1, −1 ],
1, 1, 0, −1, 0, −1, −1, −1 ],
1, 1, 0, −1, 0, 0, −1, 0 ],
1, 1, 1, −2, 0, −1, −1, −1 ],
1, 2, 0, −2, −1, −1, −1, −1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1, 0,−1, 0,−1,−1,−1 ],
1, 0,−1, 0, 0,−1,−1 ],
1, 0, 0,−1, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0 ],
1, 1,−1, 0,−1,−1,−1 ],
1, 1,−1, 0, 0,−1, 0 ],
0,−1,−1,−1, 0, 0,−1 ],
0,−1, 0,−1, 0, 1, 0 ],
0, 0,−1,−1,−1, 0,−1 ],
0, 0,−1,−1, 0, 0, 0 ],
0, 0,−1, 0,−1, 0, 0 ],
0, 0,−1, 0, 0, 0, 0 ],
0, 0, 0, 0, 0,−1, 0 ],
0, 1,−2, 0,−1,−1,−1 ],
0, 1,−1, 0,−1, 0, 0 ],
1,−1,−1,−2, 0, 0,−1 ],
1,−1,−1,−1, 0, 0,−1 ],
1, 0,−2,−1,−1,−1,−2 ],
1, 0,−2,−1, 0,−1,−1 ],
1, 0,−1,−1,−1, 0,−1 ],
1, 0,−1,−1, 0,−1, 0 ],
1, 0,−1, 0,−1,−1, 0 ],
1, 1,−2, 0,−2,−1,−1 ],
1, 1,−2, 0,−1,−1, 0 ],
1, 0,−2,−1,−1,−1,−1 ]
∗
5
• I ≡ P125 :
7
6
4
3
2
1





CI =








b I =
Cox




0
0
1
0
0
1
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
−1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
−1
−1
0
0
−1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
















b
CI =



1
1
1
1
1
1
1
−1
















BI =



1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
−1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
−1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
−1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
1
0
0
1
0
−1











0
−1
0
0
0
0
0
0
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 1, 1, 1, 2, 1, 1, 3 ],
[ −1,−1,−1, 0, 0, 0, 1,−1 ],
[ 1,−1,−1,−1,−2,−1,−1,−3 ],
[ −1, 0, −1, −1, 0, 0, 1, −1 ],
234
[ −2, 1, 0, 1, 2, 1, 1, 2 ],
[ −1, 0,−1, 0, 0, 0, 0,−1 ],
1
1
1
0
0
0
0
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0,−1, 0, 0, 0, 1,−1 ],
−1, 0,−1, 0, 1, 0, 1, 0 ],
−1, 0,−1, 0, 1, 1, 2, 1 ],
−1, 0, 0, 0, 0, 0, 0,−1 ],
−1, 0, 0, 0, 1, 0, 0, 0 ],
−1, 0, 0, 0, 1, 1, 1, 1 ],
−1, 0, 0, 1, 1, 0, 0, 1 ],
−1, 0, 0, 1, 1, 1, 1, 1 ],
−1, 0, 1, 1, 1, 0, 0, 1 ],
−1, 1, 0, 0, 1, 0, 0, 0 ],
−1, 1, 0, 0, 1, 1, 0, 1 ],
−1, 1, 0, 0, 2, 1, 1, 2 ],
−1, 1, 0, 1, 1, 1, 0, 2 ],
−1, 1, 0, 1, 2, 1, 1, 2 ],
−1, 1, 1, 0, 1, 0, 0, 1 ],
−1, 1, 1, 1, 1, 0, 0, 2 ],
−1, 1, 1, 1, 2, 1, 0, 2 ],
−1, 2, 1, 1, 2, 1, 0, 3 ],
0,−1,−1,−1,−1,−1, 0,−3 ],
0,−1,−1,−1,−1, 0, 0,−2 ],
0,−1,−1,−1, 0, 0, 1,−1 ],
0,−1,−1, 0,−1, 0, 0,−1 ],
0,−1,−1, 0, 0, 0, 1,−1 ],
0,−1, 0,−1,−1,−1, 0,−2 ],
0,−1, 0, 0,−1,−1, 0,−1 ],
0,−1, 0, 0, 0, 0, 0,−1 ],
0,−1, 0, 1, 0, 0, 0, 0 ],
0, 0,−1,−1,−1, 0, 0,−1 ],
0, 0,−1,−1, 0, 0, 1,−1 ],
0, 0,−1, 0,−1, 0, 0,−1 ],
0, 0,−1, 0, 0, 0, 1, 0 ],
0, 0,−1, 0, 0, 1, 1, 1 ],
0, 0, 0,−1,−1,−1, 0,−2 ],
0, 0, 0,−1, 0,−1, 0,−1 ],
0, 0, 0,−1, 0, 0, 1, 0 ],
0, 0, 0, 0,−1,−1, 0,−1 ],
0, 0, 0, 0,−1, 0, 0, 0 ],
0, 0, 0, 0, 0,−1, 0, 0 ],
0, 0, 0, 0, 0, 0, 0,−1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 1, 1 ],
0, 0, 0, 0, 1, 0, 1, 1 ],
0, 0, 0, 0, 1, 1, 1, 2 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 1, 1, 0, 1 ],
0, 0, 1, 0,−1,−1,−1,−1 ],
0, 0, 1, 0, 0,−1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 1, 0, 0,−1, 0 ],
0, 0, 1, 1, 1, 0,−1, 1 ],
0, 0, 1, 1, 1, 1, 0, 2 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
0, 1, 0, 0, 1, 1, 1, 2 ],
0, 1, 1, 0, 0, 0,−1, 0 ],
0, 1, 1, 0, 1, 0,−1, 1 ],
0, 1, 1, 0, 1, 1, 0, 2 ],
0, 1, 1, 1, 1, 0,−1, 2 ],
0, 1, 1, 1, 1, 1, 0, 2 ],
0, 1, 2, 1, 1, 0,−1, 2 ],
1,−1,−1,−1,−2,−1, 0,−3 ],
1,−1,−1,−1,−1,−1, 0,−2 ],
1,−1,−1,−1,−1, 0, 1,−1 ],
1,−1, 0,−1,−2,−1,−1,−3 ],
1,−1, 0,−1,−1,−1,−1,−2 ],
1,−1, 0,−1,−1, 0, 0,−1 ],
1,−1, 0, 0,−1,−1,−1,−1 ],
1,−1, 0, 0,−1, 0, 0,−1 ],
1,−1, 1, 0,−1,−1,−1,−1 ],
1, 0, 0,−1,−1,−1,−1,−2 ],
1, 0, 0,−1,−1, 0,−1,−1 ],
1, 0, 0,−1, 0, 0, 0, 0 ],
[ −1, 0, −1, 0, 0, 0, 1, 0 ],
[ −1, 0, −1, 0, 1, 1, 1, 0 ],
[ −1, 0, −1, 1, 1, 1, 1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 2 ],
[ −1, 1, −1, 0, 1, 1, 1, 1 ],
[ −1, 1, 0, 0, 1, 0, 0, 1 ],
[ −1, 1, 0, 0, 1, 1, 1, 1 ],
[ −1, 1, 0, 1, 1, 0, 0, 1 ],
[ −1, 1, 0, 1, 1, 1, 1, 2 ],
[ −1, 1, 0, 1, 2, 1, 1, 3 ],
[ −1, 1, 1, 1, 1, 0, −1, 1 ],
[ −1, 1, 1, 1, 1, 1, 0, 2 ],
[ −1, 1, 1, 1, 2, 1, 0, 3 ],
[ 0, −1, −2, −1, −1, 0, 1, −2 ],
[ 0, −1, −1, −1, −1, −1, 0, −2 ],
[ 0, −1, −1, −1, −1, 0, 1, −2 ],
[ 0, −1, −1, 0, −1, −1, 0, −2 ],
[ 0, −1, −1, 0, −1, 0, 1, −1 ],
[ 0, −1, −1, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, −1, −1, −1, −2 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, −1, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, 1, 1, 1, 1 ],
[ 0, 0, 0, −1, −1, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1, −2 ],
[ 0, 0, 0, 0, −1, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 0, 1, 0, 0, −1, −1, −1 ],
[ 0, 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, −1, 1 ],
[ 0, 0, 1, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, −1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1, 1, 0, 1 ],
[ 0, 1, 0, 1, 1, 1, 0, 2 ],
[ 0, 1, 1, 0, 0, 0, −1, 1 ],
[ 0, 1, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 1, 0, 0, −1, 1 ],
[ 0, 1, 1, 1, 1, 0, 0, 2 ],
[ 0, 1, 1, 1, 1, 1, 0, 3 ],
[ 1, −2, −1, −1, −2, −1, 0, −3 ],
[ 1, −1, −1, −1, −2, −1, 0, −2 ],
[ 1, −1, −1, −1, −1, 0, 0, −2 ],
[ 1, −1, −1, 0, −1, 0, 0, −1 ],
[ 1, −1, 0, −1, −2, −1, −1, −2 ],
[ 1, −1, 0, −1, −1, −1, 0, −2 ],
[ 1, −1, 0, 0, −2, −1, −1, −2 ],
[ 1, −1, 0, 0, −1, −1, 0, −1 ],
[ 1, −1, 0, 0, −1, 0, 0, 0 ],
[ 1, 0, −1, −1, −1, 0, 0, −1 ],
[ 1, 0, 0, −1, −1, −1, −1, −1 ],
[ 1, 0, 0, −1, −1, 0, 0, −1 ],
[ 1, 0, 0, 0, −1, −1, −1, −1 ],
235
[ −1, 0,−1, 0, 0, 1, 1, 0 ],
[ −1, 0,−1, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 1, 0, 1, 1 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 2, 1, 1, 2 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 1, 1 ],
[ −1, 1, 0, 0, 1, 1, 1, 2 ],
[ −1, 1, 0, 1, 1, 1, 0, 1 ],
[ −1, 1, 0, 1, 2, 1, 0, 2 ],
[ −1, 1, 0, 1, 2, 2, 1, 3 ],
[ −1, 1, 1, 1, 1, 0, 0, 1 ],
[ −1, 1, 1, 1, 2, 0, 0, 2 ],
[ −1, 1, 1, 2, 2, 1, 0, 3 ],
[ 0,−1,−1,−1,−2,−1, 0,−3 ],
[ 0,−1,−1,−1,−1,−1, 1,−2 ],
[ 0,−1,−1,−1,−1, 0, 1,−1 ],
[ 0,−1,−1, 0,−1, 0, 0,−2 ],
[ 0,−1,−1, 0, 0, 0, 0,−1 ],
[ 0,−1,−1, 0, 0, 1, 1, 0 ],
[ 0,−1, 0, 0,−1,−1, 0,−2 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0, 0,−1,−1,−1, 0, 0,−2 ],
[ 0, 0,−1,−1, 0, 0, 0,−1 ],
[ 0, 0,−1,−1, 0, 1, 1, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 1, 1, 0 ],
[ 0, 0, 0,−1,−1,−1,−1,−2 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1,−1,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 0, 1, 0, 0,−1,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0,−1,−1, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 0, 2 ],
[ 0, 1, 0, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 1, 1, 0, 2 ],
[ 0, 1, 1, 0, 0,−1,−1, 0 ],
[ 0, 1, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 1, 0, 0, 2 ],
[ 0, 1, 1, 1, 1, 0,−1, 1 ],
[ 0, 1, 1, 1, 1, 1,−1, 2 ],
[ 0, 1, 1, 1, 2, 1, 0, 3 ],
[ 1,−1,−1,−2,−2,−1, 0,−3 ],
[ 1,−1,−1,−1,−2, 0, 0,−2 ],
[ 1,−1,−1,−1,−1, 0, 0,−1 ],
[ 1,−1, 0,−1,−2,−2,−1,−3 ],
[ 1,−1, 0,−1,−2,−1, 0,−2 ],
[ 1,−1, 0,−1,−1,−1, 0,−1 ],
[ 1,−1, 0, 0,−1,−1,−1,−2 ],
[ 1,−1, 0, 0,−1, 0,−1,−1 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1,−2,−1,−1,−2 ],
[ 1, 0, 0,−1,−1,−1, 0,−1 ],
[ 1, 0, 0,−1,−1, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0,−1,−1 ],
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0, 0,−1, 0,−1, 0 ],
0, 0, 0, 0, 0, 0 ],
1,−1,−1,−1,−1,−1 ],
1, 0,−1,−1,−1, 0 ],
1, 0, 0, 0,−1, 0 ],
1, 1, 0, 0,−1, 1 ],
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
1,
0, −1, 0, 0, 0 ],
0, 0, 0, 0, 1 ],
0, −1, −1, −2, −1 ],
0, −1, 0, −1, 0 ],
0, 0, 0, −1, 1 ],
0, 0, 0, −1, 1 ],
0,
0,
1,
1,
1,
1,
[
[
[
[
[
[
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
2,−1,
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0, 0, 0, 0,−1, 0 ],
0, 0, 0, 1, 0, 1 ],
1, 0,−1,−1,−1,−1 ],
1, 0, 0,−1,−1, 0 ],
1, 0, 0, 0, 0, 1 ],
0,−1,−2,−1,−1,−2 ]
∗
5
• I ≡ P126 :
4
7
3
6
2





CI =








b I =
Cox




0
1
1
1
0
1
1
−1
1
0
0
0
0
1
0
−1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
−1
−1
0
0
−1
−1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
−1
0
0
0
0
0
1
0
0
−1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
















b
CI =



1
1
1
1
1
1
1
−1
















BI =



1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
−1
0
0
0
0
−1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
−1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
1
0
0
−1
0
0
0
0
0
0
−1
−1
−1
−1
−1
−1
−1
1











0
1
1
1
0
0
0
−1
0
0
0
−1
0
0
0
0
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −2,−1,−1,−1,
[ −2, −1, −1, −1,
[ −2, −1, −1, 0,
[ −2, 0, −1, −2,
[ −2, 0, −1, −1,
[ −1, −2, 0, 0,
[ −1, −1, −1, 0,
[ −1, −1, −1, 0,
[ −1, −1, 0, −1,
[ −1, −1, 0, 0,
[ −1, −1, 0, 0,
[ −1, −1, 0, 0,
[ −1, −1, 0, 0,
[ −1, 0, −1, −1,
[ −1, 0, −1, −1,
[ −1, 0, −1, −1,
[ −1, 0, −1, 0,
[ −1, 0, −1, 0,
[ −1, 0, −1, 0,
[ −1, 0, 0, −1,
[ −1, 0, 0, −1,
1,−1,−1,−3 ],
1, −1, 0, −3 ],
1, −1, 0, −2 ],
1, −1, −1, −3 ],
1, −1, −1, −2 ],
1, −1, 1, −1 ],
1, −1, 0, −2 ],
1, 0, 0, −1 ],
1, −1, 0, −1 ],
0, −1, 0, −2 ],
0, 0, 0, −1 ],
1, −1, 1, 0 ],
1, 0, 1, 0 ],
0, −1, 0, −2 ],
1, −1, 0, −2 ],
1, 0, −1, −1 ],
0, −1, 0, −2 ],
0, 0, −1, −1 ],
1, 0, −1, −1 ],
0, −1, −1, −2 ],
0, 0, −1, −2 ],
[ 2, 1, 1, 1,−1, 1, 1, 3 ],
[ −2,−1,−1,−1, 1,−1, 0,−2 ],
[ −2,−1, 0,−1, 1,−1, 0,−2 ],
[ −2, 0,−1,−1, 0,−1,−1,−3 ],
[ −2, 0,−1,−1, 1,−1, 0,−2 ],
[ −1,−1,−1,−1, 1,−1, 0,−2 ],
[ −1,−1,−1, 0, 1,−1, 0,−1 ],
[ −1,−1, 0,−1, 0,−1, 0,−2 ],
[ −1,−1, 0,−1, 1,−1, 1,−1 ],
[ −1,−1, 0, 0, 0,−1, 0,−1 ],
[ −1,−1, 0, 0, 1,−1, 0,−1 ],
[ −1,−1, 0, 0, 1, 0, 0,−1 ],
[ −1, 0,−1,−1, 0,−1,−1,−3 ],
[ −1, 0,−1,−1, 0, 0,−1,−2 ],
[ −1, 0,−1,−1, 1,−1, 0,−1 ],
[ −1, 0,−1,−1, 1, 0, 0,−1 ],
[ −1, 0,−1, 0, 0,−1, 0,−1 ],
[ −1, 0,−1, 0, 0, 0, 0,−1 ],
[ −1, 0,−1, 0, 1, 0, 0,−1 ],
[ −1, 0, 0,−1, 0,−1, 0,−2 ],
[ −1, 0, 0,−1, 0, 0,−1,−1 ],
236
[ −2,−1,−1,−1,
[ −2,−1,−1,−1,
[ −2, 0,−2,−1,
[ −2, 0,−1,−1,
[ −2, 0,−1,−1,
[ −1,−1,−1, 0,
[ −1,−1,−1, 0,
[ −1,−1, 0,−1,
[ −1,−1, 0,−1,
[ −1,−1, 0, 0,
[ −1,−1, 0, 0,
[ −1,−1, 0, 0,
[ −1, 0,−1,−1,
[ −1, 0,−1,−1,
[ −1, 0,−1,−1,
[ −1, 0,−1, 0,
[ −1, 0,−1, 0,
[ −1, 0,−1, 0,
[ −1, 0,−1, 0,
[ −1, 0, 0,−1,
[ −1, 0, 0,−1,
1,−2, 0,−3 ],
2,−1, 0,−2 ],
1,−1,−1,−3 ],
1,−1,−1,−3 ],
1, 0,−1,−2 ],
0,−1, 0,−2 ],
1,−1, 1,−1 ],
1,−1, 0,−2 ],
1, 0, 0,−1 ],
0,−1, 1,−1 ],
1,−1, 1,−1 ],
1, 0, 0, 0 ],
0,−1,−1,−2 ],
1,−1,−1,−2 ],
1, 0,−1,−2 ],
0,−1,−1,−2 ],
0, 0,−1,−2 ],
1,−1, 0,−1 ],
1, 0, 0, 0 ],
0,−1, 0,−1 ],
0, 0, 0,−1 ],
0
1
0
0
−1
0
0
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, 0, −1, 1, −1, 0, −1 ],
−1, 0, 0, −1, 1, 0, 0, 0 ],
−1, 0, 0, 0, 0, 0, 0, −1 ],
−1, 1, −1, −1, 0, −1, −1, −2 ],
−1, 1, −1, −1, 0, 0, −1, −1 ],
−1, 1, 0, −1, 0, 0, −1, −1 ],
0, −1, 0, 0, 0, −1, 1, 0 ],
0, −1, 0, 0, 0, 0, 1, 0 ],
0, −1, 0, 0, 1, 0, 1, 0 ],
0, −1, 0, 1, 0, 0, 0, 0 ],
0, −1, 0, 1, 1, 0, 1, 1 ],
0, −1, 1, 0, 0, 0, 1, 0 ],
0, −1, 1, 1, 0, 0, 1, 1 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, −1, 1, 0, 0, 0, 0 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, 0,−1, −1, 0, −1 ],
0, 0, 0, 0,−1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 1, 1 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 0, 1, 0, 1, 0, 1 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 1, 0, 1 ],
0, 1, −1, 0, 0, 0, −1, −1 ],
0, 1, −1, 0, 0, 1, −1, 0 ],
0, 1, 0, −1, 0, 0, −1, 0 ],
0, 1, 0, 0,−1, 0, −1, −1 ],
0, 1, 0, 0,−1, 1, −1, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 0, 1, 0, 1 ],
1, −1, 1, 1,−1, 0, 1, 1 ],
1, −1, 1, 1, 0, 0, 2, 2 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
1, 0, 0, 1,−1, 0, 1, 1 ],
1, 0, 0, 1, 0, 0, 1, 1 ],
1, 0, 0, 1, 0, 1, 0, 2 ],
1, 0, 1, 0,−1, 0, 0, 1 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 0, 1, 0, 0, 1, 0, 1 ],
1, 0, 1, 1,−1, 0, 0, 1 ],
1, 0, 1, 1,−1, 1, 0, 1 ],
1, 0, 1, 1, 0, 0, 1, 2 ],
1, 0, 1, 1, 0, 1, 1, 3 ],
1, 1, 0, 0,−1, 0, 0, 1 ],
1, 1, 0, 0,−1, 1, 0, 1 ],
1, 1, 0, 0, 0, 1, 0, 1 ],
1, 1, 0, 1,−1, 1, −1, 1 ],
1, 1, 0, 1, 0, 1, 0, 2 ],
1, 1, 1, 0,−1, 1, 0, 1 ],
1, 1, 1, 1,−1, 1, 0, 2 ],
2, 0, 1, 1,−1, 1, 0, 2 ],
2, 0, 1, 1, 0, 1, 1, 3 ],
2, 1, 0, 1,−1, 1, 0, 2 ],
2, 1, 1, 1,−1, 1, 0, 2 ],
[ −1, 0, 0,−1, 1, 0,−1,−1 ],
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 1,−1,−1, 0, 0,−2,−2 ],
[ −1, 1,−1,−1, 1, 0,−1,−1 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 1,−1, 1, 0 ],
[ 0,−1, 0, 0, 1, 0, 1, 1 ],
[ 0,−1, 0, 1, 0, 0, 1, 0 ],
[ 0,−1, 1, 0, 0,−1, 1, 0 ],
[ 0,−1, 1, 0, 0, 0, 1, 1 ],
[ 0, 0,−1, 0, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0,−1,−1 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1,−1,−1, 0, 0,−1,−1 ],
[ 0, 1,−1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0,−1, −1, 0,−1,−1 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, −1, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 1,−1, 0 ],
[ 1,−1, 0, 1, 0, 0, 1, 1 ],
[ 1,−1, 1, 1, 0, 0, 1, 1 ],
[ 1,−1, 1, 1, 0, 1, 1, 2 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 1, −1, 0, 0, 0 ],
[ 1, 0, 0, 1, −1, 1, 0, 1 ],
[ 1, 0, 0, 1, 0, 0, 1, 2 ],
[ 1, 0, 0, 1, 0, 1, 1, 2 ],
[ 1, 0, 1, 0, −1, 0, 1, 1 ],
[ 1, 0, 1, 0, 0, 0, 1, 1 ],
[ 1, 0, 1, 0, 0, 1, 0, 2 ],
[ 1, 0, 1, 1, −1, 0, 1, 1 ],
[ 1, 0, 1, 1, −1, 1, 0, 2 ],
[ 1, 0, 1, 1, 0, 1, 0, 2 ],
[ 1, 1, 0, 0, −1, 0,−1, 0 ],
[ 1, 1, 0, 0, −1, 1,−1, 0 ],
[ 1, 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, 1, 0, 2 ],
[ 1, 1, 0, 1, −1, 1, 0, 1 ],
[ 1, 1, 1, 0, −1, 0, 0, 1 ],
[ 1, 1, 1, 0, −1, 1, 0, 2 ],
[ 1, 2, 0, 0, −1, 1,−1, 1 ],
[ 2, 0, 1, 1, −1, 1, 1, 2 ],
[ 2, 0, 1, 2, −1, 1, 1, 3 ],
[ 2, 1, 1, 0, −1, 1, 0, 2 ],
[ 2, 1, 1, 1, −1, 1, 0, 3 ],
∗
• I ≡ P127 :
7
5
2
6
4
1
3
237
[ −1, 0, 0,−1, 1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 1,−1,−1, 0, 0,−1,−2 ],
[ −1, 1,−1, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 0, 0,−1, 1,−1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 1, 0,−1, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 1, 1 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0,−1, 1, 0, 1, 0, 1, 1 ],
[ 0, 0,−1, 0, 0, 0,−1,−1 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 1,−1, 0,−1, 0,−1,−1 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0,−1, 0, 0,−1,−1 ],
[ 0, 1, 0,−1, 0, 1,−1, 0 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1,−1, 1 ],
[ 1,−1, 1, 0, 0, 0, 1, 1 ],
[ 1,−1, 1, 1, 0, 0, 1, 2 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 1, 1 ],
[ 1, 0, 0, 1,−1, 0, 0, 1 ],
[ 1, 0, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 0, 1, 0, 1, 0, 1 ],
[ 1, 0, 1, 0,−1, 0, 0, 0 ],
[ 1, 0, 1, 0,−1, 1, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 1, 2 ],
[ 1, 0, 1, 0, 0, 1, 1, 2 ],
[ 1, 0, 1, 1,−1, 0, 1, 2 ],
[ 1, 0, 1, 1,−1, 1, 1, 2 ],
[ 1, 0, 1, 1, 0, 1, 1, 2 ],
[ 1, 1, 0, 0,−1, 0, 0, 0 ],
[ 1, 1, 0, 0,−1, 1,−1, 1 ],
[ 1, 1, 0, 0, 0, 1,−1, 1 ],
[ 1, 1, 0, 1,−1, 0, 0, 1 ],
[ 1, 1, 0, 1,−1, 1, 0, 2 ],
[ 1, 1, 1, 0,−1, 1,−1, 1 ],
[ 1, 1, 1, 0, 0, 1, 0, 2 ],
[ 2, 0, 1, 1,−1, 0, 1, 2 ],
[ 2, 0, 1, 1,−1, 1, 1, 3 ],
[ 2, 0, 2, 1,−1, 1, 1, 3 ],
[ 2, 1, 1, 1,−2, 1, 0, 2 ],
[ 2, 1, 1, 1,−1, 2, 0, 3 ]





CI =








b I =
Cox




0
0
1
1
0
1
1
−1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
−1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
−1
0
0
−1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
−1
0
0
0
0
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
1
1
0
0
1
0
0
0
















BI =



0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
−1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
−1
−1
0
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
1
1
0
1
1
−1











0
0
0
−1
0
0
−1
0
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1, 1,−1,−1, 2, 1, 1, 1 ],
[ −1,−1, 0, −1, 0,−1, 0,−2 ],
[ −1, 0, −1, −1, 1, 0, 1,−1 ],
[ −1, 0, −1, 0, 0, 0, 0,−1 ],
[ −1, 0, −1, 0, 1, 0, 1, 0 ],
[ −1, 0, 0, −1, 0,−1, 0,−2 ],
[ −1, 0, 0, −1, 0, 0, 0,−1 ],
[ −1, 0, 0, −1, 1,−1, 1, 0 ],
[ −1, 0, 0, −1, 1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 1, −1, 0,−1, 0,−1 ],
[ −1, 1, −1, −1, 2, 0, 1, 0 ],
[ −1, 1, −1, 0, 1, 0, 0, 0 ],
[ −1, 1, −1, 0, 1, 1, 0, 0 ],
[ −1, 1, −1, 0, 2, 0, 1, 1 ],
[ −1, 1, −1, 0, 2, 1, 1, 2 ],
[ −1, 1, 0, −1, 1, 0, 0, 0 ],
[ −1, 1, 0, −1, 2, 0, 1, 1 ],
[ −1, 1, 0, 0, 1, 0, 0, 1 ],
[ −1, 2, −1, 0, 2, 1, 1, 2 ],
[ 0,−1, 0, −1, 0,−1, 0,−2 ],
[ 0,−1, 0, −1, 0, 0, 0,−1 ],
[ 0,−1, 0, 0,−1,−1, 0,−1 ],
[ 0,−1, 0, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 1, −1,−1,−2, 0,−2 ],
[ 0,−1, 1, −1,−1,−1, 0,−1 ],
[ 0,−1, 1, 0,−1,−1,−1,−2 ],
[ 0,−1, 1, 0,−1, 0,−1,−1 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 1, 0, 0 ],
[ 0, 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, 1, 0, 1, 0, 1 ],
[ 0, 0, 0, −1, 0,−1, 1,−1 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, −1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[ 1,−1, 1, 1,−2,−1,−1,−1 ],
[ −1, 0,−1,−1, 1, −1, 1, −1 ],
[ −1, 0,−1,−1, 1, 0, 1, 0 ],
[ −1, 0,−1, 0, 1, 0, 0, −1 ],
[ −1, 0,−1, 0, 1, 1, 0, 0 ],
[ −1, 0, 0,−1, 0, −1, 0, −1 ],
[ −1, 0, 0,−1, 1, −1, 0, −1 ],
[ −1, 0, 0,−1, 1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 1,−2, 0, 2, 1, 1, 1 ],
[ −1, 1,−1,−1, 2, 0, 1, 1 ],
[ −1, 1,−1, 0, 1, 0, 1, 0 ],
[ −1, 1,−1, 0, 1, 1, 0, 1 ],
[ −1, 1,−1, 0, 2, 1, 0, 1 ],
[ −1, 1,−1, 1, 1, 1, 0, 1 ],
[ −1, 1, 0,−1, 1, 0, 1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 1, 1 ],
[ 0, −1,−1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0,−1, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, −1, −1, −1, −2 ],
[ 0, −1, 0, 0, −1, 0, −1, −2 ],
[ 0, −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 1,−1, −1, −1, −1, −2 ],
[ 0, −1, 1,−1, 0, −1, 0, −1 ],
[ 0, −1, 1, 0, −1, −1, −1, −1 ],
[ 0, 0,−1,−1, 1, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 1, 0, 1, 0 ],
[ 0, 0,−1, 0, 1, 1, 0, 1 ],
[ 0, 0,−1, 1, 0, 1, −1, 0 ],
[ 0, 0,−1, 1, 1, 1, 0, 1 ],
[ 0, 0, 0,−1, 0, −1, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0,−1, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
238
[ −2, 1,−1,−1, 2, 0, 1, 0 ],
[ −1, 0,−1,−1, 1, 0, 0,−1 ],
[ −1, 0,−1,−1, 2, 0, 1, 0 ],
[ −1, 0,−1, 0, 1, 0, 0, 0 ],
[ −1, 0, 0,−2, 1,−1, 1,−1 ],
[ −1, 0, 0,−1, 0,−1, 1,−1 ],
[ −1, 0, 0,−1, 1,−1, 1,−1 ],
[ −1, 0, 0,−1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0,−1,−1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 1,−1,−1, 1, 0, 1, 0 ],
[ −1, 1,−1,−1, 2, 0, 2, 1 ],
[ −1, 1,−1, 0, 1, 0, 1, 1 ],
[ −1, 1,−1, 0, 1, 1, 1, 1 ],
[ −1, 1,−1, 0, 2, 1, 1, 1 ],
[ −1, 1, 0,−1, 1,−1, 1, 0 ],
[ −1, 1, 0,−1, 1, 0, 1, 1 ],
[ −1, 1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 1, 1, 0, 1 ],
[ 0,−1, 0,−1,−1,−1, 0,−2 ],
[ 0,−1, 0,−1, 0,−1, 1,−1 ],
[ 0,−1, 0, 0,−1,−1, 0,−2 ],
[ 0,−1, 0, 0,−1, 0,−1,−1 ],
[ 0,−1, 0, 0, 0, 0,−1,−1 ],
[ 0,−1, 0, 1,−1, 0,−1,−1 ],
[ 0,−1, 1,−1,−1,−1, 0,−2 ],
[ 0,−1, 1, 0,−2,−1,−1,−2 ],
[ 0,−1, 1, 0,−1,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 1, 1 ],
[ 0, 0,−1, 0, 1, 1, 1, 1 ],
[ 0, 0,−1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 1,−1, 1, 0 ],
[ 0, 0, 0,−1, 1, 0, 1, 1 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1,−1, 0,−1,−1 ],
1
0
1
1
1
0
0
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 0, 1,−1, 0,−1, 0 ],
0, 0, 0, 1, 0, 0,−1, 0 ],
0, 0, 0, 1, 0, 1,−1, 0 ],
0, 0, 1, −1,−1,−1, 0,−1 ],
0, 0, 1, −1, 0,−1, 1, 0 ],
0, 0, 1, 0,−1,−1, 0,−1 ],
0, 0, 1, 0,−1, 0,−1, 0 ],
0, 0, 1, 0, 0, 0,−1, 0 ],
0, 0, 1, 1,−1, 0,−1, 0 ],
0, 1, −1, 0, 1, 1, 1, 1 ],
0, 1, −1, 1, 0, 1, 0, 1 ],
0, 1, −1, 1, 1, 1, 1, 2 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 1, 0, 1 ],
0, 1, 0, 0, 1, 0, 1, 2 ],
0, 1, 0, 0, 1, 1, 1, 2 ],
0, 1, 0, 1, 0, 1, 0, 1 ],
0, 1, 1, 0, 0, 0, 0, 1 ],
1,−1, 0, 0,−1, 0,−1,−1 ],
1,−1, 0, 0, 0, 0, 0, 0 ],
1,−1, 0, 1,−1, 0,−1, 0 ],
1,−1, 1, −1,−1,−1, 0,−1 ],
1,−1, 1, 0,−2,−1, 0,−1 ],
1,−1, 1, 0,−1,−1, 0,−1 ],
1,−1, 1, 0,−1, 0,−1, 0 ],
1,−1, 1, 1,−2, 0,−1,−1 ],
1,−1, 2, 0,−2,−1,−1,−1 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
1, 0, 0, 1,−1, 0, 0, 1 ],
1, 0, 0, 1,−1, 1, 0, 1 ],
1, 0, 0, 1, 0, 1, 0, 1 ],
1, 0, 1, 0,−1,−1, 0, 0 ],
1, 0, 1, 0,−1, 0, 0, 1 ],
1, 0, 1, 1,−1, 0,−1, 0 ],
1, 0, 1, 1,−1, 1,−1, 1 ],
0, 0, 0, 1, −1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 0, 1, 0, 1, −1, 1 ],
0, 0, 1,−1, 0, −1, 0, −1 ],
0, 0, 1,−1, 0, 0, 0, 0 ],
0, 0, 1, 0, −1, −1, 0, 0 ],
0, 0, 1, 0, −1, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 1,−1, 0, 1, 0, 1, 1 ],
0, 1,−1, 0, 1, 1, 1, 2 ],
0, 1,−1, 1, 1, 1, 0, 1 ],
0, 1,−1, 1, 1, 2, 0, 2 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
0, 1, 0, 0, 1, 1, 0, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
0, 1, 0, 1, 0, 1, 0, 2 ],
1, −2, 1, 0, −2, −1, −1, −2 ],
1, −1, 0, 0, −1, 0, 0, −1 ],
1, −1, 0, 1, −2, 0, −1, −1 ],
1, −1, 0, 1, −1, 0, 0, 0 ],
1, −1, 1, 0, −2, −1, −1, −2 ],
1, −1, 1, 0, −2, 0, −1, −1 ],
1, −1, 1, 0, −1, −1, 0, 0 ],
1, −1, 1, 0, −1, 0, 0, 0 ],
1, −1, 1, 1, −2, 0, −1, 0 ],
1, 0,−1, 1, 0, 1, 0, 1 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 1, −1, 0, −1, 0 ],
1, 0, 0, 1, −1, 1, −1, 0 ],
1, 0, 0, 1, 0, 0, 0, 1 ],
1, 0, 0, 1, 0, 1, 0, 2 ],
1, 0, 1, 0, −1, 0, −1, 0 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 0, 1, 1, −1, 0, −1, 1 ],
1, 1, 0, 1, 0, 1, 0, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 0, 1,−1, 1,−1, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 0, 1, 0, 1 ],
0, 0, 1,−1, 0,−1, 0, 0 ],
0, 0, 1, 0,−1,−1,−1,−1 ],
0, 0, 1, 0,−1, 0,−1,−1 ],
0, 0, 1, 0, 0,−1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 1,−1, 0, 1, 1, 0, 1 ],
0, 1,−1, 0, 2, 1, 1, 2 ],
0, 1,−1, 1, 1, 1, 0, 2 ],
0, 1, 0,−1, 1, 0, 1, 1 ],
0, 1, 0, 0, 0, 0, 1, 1 ],
0, 1, 0, 0, 1, 0, 1, 1 ],
0, 1, 0, 0, 1, 1, 0, 2 ],
0, 1, 0, 1, 0, 1,−1, 1 ],
0, 1, 0, 1, 1, 1, 0, 2 ],
1,−1, 0, 0,−1,−1, 0,−1 ],
1,−1, 0, 0,−1, 0, 0, 0 ],
1,−1, 0, 1,−1, 0,−1,−1 ],
1,−1, 0, 1,−1, 1,−1, 0 ],
1,−1, 1, 0,−2,−1,−1,−1 ],
1,−1, 1, 0,−1,−1,−1,−1 ],
1,−1, 1, 0,−1, 0,−1,−1 ],
1,−1, 1, 1,−2, 0,−2,−1 ],
1,−1, 1, 1,−1, 0,−1, 0 ],
1, 0, 0, 0,−1, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 1, 1 ],
1, 0, 0, 1,−1, 0, 0, 0 ],
1, 0, 0, 1,−1, 1,−1, 1 ],
1, 0, 0, 1, 0, 1,−1, 1 ],
1, 0, 0, 2,−1, 1,−1, 1 ],
1, 0, 1, 0,−1, 0, 0, 0 ],
1, 0, 1, 1,−2, 0,−1, 0 ],
1, 0, 1, 1,−1, 0, 0, 1 ],
2,−1, 1, 1,−2, 0,−1, 0 ]
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
















BI =



1
1
0
1
1
0
1
−1
∗
7
• I ≡ P128 :
4
5
6
1
2
3





CI =








b
CoxI =



0
1
1
0
0
1
0
−1
1
0
1
1
0
0
0
−1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
1
−1
1
0
0
0
1
0
0
0
0
0
−1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
−1
0
0
−1
0
0
0
1
1
1
0
1
1
0
1
0
−1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
Number of sincere Tits roots of poset I sI = 2.
239
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
−1
0
0
0
0
0
1
0
0
0
0
0
−1
0
0
−1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
−1
0
0
−1
0
−1
0











0
−1
0
0
0
−1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
−1











Table of roots of qbI
[ −1,−2,−1,−1, 1, 1, 1,−1 ],
[ −1, −2, −2, −1, 0, 1, 1, −2 ],
[ −1, −2, −1, −1, 0, 1, 1, −1 ],
[ −1, −2, −1, 0, 1, 1, 0, −1 ],
[ −1, −2, −1, 0, 1, 2, 1, 0 ],
[ −1, −1, −1, −1, 0, 0, 0, −2 ],
[ −1, −1, −1, −1, 0, 1, 1, −1 ],
[ −1, −1, −1, 0, 0, 0, 1, −1 ],
[ −1, −1, −1, 0, 0, 1, 1, 0 ],
[ −1, −1, −1, 0, 1, 1, 0, 0 ],
[ −1, −1, 0, −1, 0, 0, 1, −1 ],
[ −1, −1, 0, 0, 0, 0, 1, 0 ],
[ −1, −1, 0, 0, 1, 0, 0, 0 ],
[ −1, −1, 0, 0, 1, 1, 1, 0 ],
[ −1, −1, 0, 1, 1, 1, 0, 0 ],
[ −1, −1, 0, 1, 2, 1, 0, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ 0, −1, −1, −1,−1, 0, 0, −2 ],
[ 0, −1, −1, −1,−1, 1, 1, −1 ],
[ 0, −1, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 1, 0 ],
[ 0, −1, −1, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, −1,−1, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 1, 1, 0 ],
[ 0, −1, 0, 0, 1, 1, 0, 0 ],
[ 0, −1, 0, 1, 1, 1, 0, 1 ],
[ 0, 0, −1, −1,−1, 0, 0, −1 ],
[ 0, 0, −1, 0,−1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, −1,−1,−1, 0, −1 ],
[ 0, 0, 0, −1,−1, 0, 1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0,−1,−1, 0, −1 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 0,−1, 0 ],
[ 0, 0, 0, 1, 1, 1,−1, 1 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 1, 1, 0,−1, 1 ],
[ 0, 0, 1, 1, 1, 1, 0, 2 ],
[ 0, 1, 0, 0,−1,−1, 0, −1 ],
[ 0, 1, 0, 0, 0,−1,−1, −1 ],
[ 0, 1, 0, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 1, 0,−1,−1, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0,−1,−1, 0 ],
[ 0, 1, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 0,−1, 0, 1 ],
[ 0, 1, 1, 1, 0, 0, 0, 2 ],
[ 0, 1, 1, 1, 1, 0,−1, 2 ],
[ 0, 2, 1, 1, 0,−1,−1, 1 ],
[ 1, 0, 0, −1,−1, 0, 0, −1 ],
[ 1, 0, 0, −1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 1, 0, −1,−1,−1, 0, −1 ],
[ 1, 2, 1, 1,−1,−1,−1, 1 ],
[ −1,−2,−1,−1, 0, 0, 1,−2 ],
[ −1,−2,−1,−1, 0, 1, 2,−1 ],
[ −1,−2,−1, 0, 1, 1, 1,−1 ],
[ −1,−2, 0, 0, 1, 1, 1, 0 ],
[ −1,−1,−1,−1, 0, 0, 1,−2 ],
[ −1,−1,−1, 0, 0, 0, 0,−2 ],
[ −1,−1,−1, 0, 0, 1, 0,−1 ],
[ −1,−1,−1, 0, 1, 0, 0,−1 ],
[ −1,−1,−1, 0, 1, 1, 1, 0 ],
[ −1,−1, 0, 0, 0, 0, 0,−1 ],
[ −1,−1, 0, 0, 0, 1, 1, 0 ],
[ −1,−1, 0, 0, 1, 0, 1, 0 ],
[ −1,−1, 0, 0, 1, 1, 1, 1 ],
[ −1,−1, 0, 1, 1, 1, 0, 1 ],
[ −1, 0,−1, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ 0,−2,−1,−1, 0, 1, 1,−1 ],
[ 0,−1,−1,−1, −1, 0, 1,−2 ],
[ 0,−1,−1,−1, 0, 0, 0,−2 ],
[ 0,−1,−1,−1, 0, 1, 0,−1 ],
[ 0,−1,−1, 0, 0, 0, 0,−1 ],
[ 0,−1,−1, 0, 0, 1, 1, 0 ],
[ 0,−1, 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 0, 1, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 1, 1, 1 ],
[ 0,−1, 0, 0, 1, 1, 0, 1 ],
[ 0, 0,−1,−1, −1, −1, 0,−2 ],
[ 0, 0,−1,−1, −1, 0, 1,−1 ],
[ 0, 0,−1, 0, 0, 0, −1,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, −1, −1, 1,−1 ],
[ 0, 0, 0,−1, −1, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, −1, −1,−1 ],
[ 0, 0, 0, 0, 0, 0, −1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, −1, 1 ],
[ 0, 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 0, 1 ],
[ 0, 1, 0,−1, −1, −1, 0,−1 ],
[ 0, 1, 0, 0, −1, −1, 0, 0 ],
[ 0, 1, 0, 0, 0, −1, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, −1, 0 ],
[ 0, 1, 0, 1, 1, 0, −1, 1 ],
[ 0, 1, 1, 0, 0, −1, 0, 0 ],
[ 0, 1, 1, 1, 0, −1, −1, 0 ],
[ 0, 1, 1, 1, 0, 0, −1, 1 ],
[ 0, 1, 1, 1, 1, −1, −1, 1 ],
[ 0, 1, 1, 1, 1, 0, 0, 2 ],
[ 1, 0,−1,−1, −1, 0, 0,−1 ],
[ 1, 0, 0,−1, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, −1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 1, 0,−1, −2, −1, 0,−1 ],
[ 1, 1, 0,−1, −1, −1, 0, 0 ],
240
[ −2,−2,−1, 0, 1, 1, 1,−1 ],
[ −1,−2,−1,−1, 0, 1, 1,−2 ],
[ −1,−2,−1, 0, 0, 1, 1,−1 ],
[ −1,−2,−1, 0, 1, 1, 1, 0 ],
[ −1,−1,−1,−1,−1, 0, 1,−2 ],
[ −1,−1,−1,−1, 0, 0, 1,−1 ],
[ −1,−1,−1, 0, 0, 0, 0,−1 ],
[ −1,−1,−1, 0, 0, 1, 1,−1 ],
[ −1,−1,−1, 0, 1, 1, 0,−1 ],
[ −1,−1,−1, 1, 1, 1, 0, 0 ],
[ −1,−1, 0, 0, 0, 0, 1,−1 ],
[ −1,−1, 0, 0, 1, 0, 0,−1 ],
[ −1,−1, 0, 0, 1, 1, 0, 0 ],
[ −1,−1, 0, 1, 1, 0, 0, 0 ],
[ −1,−1, 0, 1, 1, 1, 1, 1 ],
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 0,−1, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ 0,−1,−1,−2,−1, 0, 1,−2 ],
[ 0,−1,−1,−1,−1, 0, 1,−1 ],
[ 0,−1,−1,−1, 0, 0, 0,−1 ],
[ 0,−1,−1,−1, 0, 1, 1,−1 ],
[ 0,−1,−1, 0, 0, 1, 0,−1 ],
[ 0,−1,−1, 0, 1, 1, 0, 0 ],
[ 0,−1, 0,−1, 0, 0, 1,−1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 1, 1 ],
[ 0, 0,−1,−1,−1, 0, 0,−2 ],
[ 0, 0,−1,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0, 0,−1,−1,−1, 0,−2 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 0, 2 ],
[ 0, 1, 0, 0,−1,−1,−1,−1 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 0,−1, 1 ],
[ 0, 1, 1, 0,−1,−1, 0, 0 ],
[ 0, 1, 1, 0, 0,−1, 0, 1 ],
[ 0, 1, 1, 1, 0,−1,−1, 1 ],
[ 0, 1, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 1, 0,−1, 1 ],
[ 0, 1, 1, 2, 1, 0,−1, 2 ],
[ 1, 0, 0,−1,−1,−1, 0,−1 ],
[ 1, 0, 0,−1,−1, 0, 1, 0 ],
[ 1, 0, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 0, 0, 1, 0, 1 ],
[ 1, 1, 0,−1,−1,−1,−1,−1 ],
[ 1, 1, 0,−1,−1, 0, 0, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
2,
2,
2,
0,
0,
0,
0,
1,
1,
1,
1,
1,
0,
1,
1,
1,
0,−1,−1,−1, −1 ],
0,−1, 0,−1, 0 ],
0, 0,−1,−1, 0 ],
0, 0, 0, 0, 1 ],
0,−1,−1,−1, 0 ],
0,−1, 0, 0, 1 ],
0, 0,−1, 0, 1 ],
0, 0, 0, 0, 2 ],
1, 0, 0,−1, 2 ],
0,−1,−1,−1, 0 ],
0,−1,−1,−1, 1 ],
1, 0,−1,−2, 1 ],
1, 0, 0,−1, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
2,
2,
2,
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
0
−1
0
0
0
0
1
0
0
0
0
1
0
0
0
−1
0
0
0
−1
0
0
0
0, −1, −1, −1,
0, −1, 0, 0,
0, 0, 0, −1,
1, 0, 0, −1,
0, −1, −1, 0,
0, 0, −1, −1,
0, 0, 0, −1,
1, 0, −1, −1,
1, 0, 0, 0,
0, −1, −2, −1,
0, −1, −1, 0,
1, 0, −1, −1,
1, 0, −1, −1,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
2,
0 ],
0 ],
0 ],
1 ],
0 ],
0 ],
1 ],
1 ],
2 ],
0 ],
1 ],
1 ],
2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
2,
2,
2,
0, 0,−1,−1, 0,
0, 0,−1, 0, 0,
0, 0, 0, 0,−1,
1,−1,−1,−1, 0,
1, 0,−1,−1, 0,
1, 0, 0,−1,−1,
1, 0, 0, 0, 0,
1, 1, 0, 0,−1,
1, 1, 1, 0,−1,
1, 0,−1,−1,−1,
1, 0, 0,−1,−1,
1, 1, 0,−1,−1,
1, 0,−1,−1,−1,
0 ],
1 ],
1 ],
0 ],
1 ],
1 ],
1 ],
1 ],
2 ],
0 ],
1 ],
2 ],
1]
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1

1
1
1
1
1
1
1
−1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
−1
−1
−1
−1
−1
0
0,
1,
1,
2,
0,
0,
0,
0,
1,
1,
0,
0,
1,
1,
1,
1,
0,
1,
0,
1,
0,
1,
0,
1,
∗
7
6
• I ≡ P129 :
2
5
1
4
3





CI =








b I =
Cox




0
0
1
1
0
0
0
−1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
−1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
0
 0

 −1

BI = −10

 0
 0
1






















Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −2, 0,−2,−1,
[ −2, 0,−1,−1,
[ −2, 0,−1,−1,
[ −2, 1,−1,−1,
[ −2, 1,−1, 0,
[ −1,−1,−1,−1,
[ −1,−1,−1,−1,
[ −1, 0,−1,−1,
[ −1, 0,−1,−1,
[ −1, 0,−1,−1,
[ −1, 0,−1,−1,
[ −1, 0,−1, 0,
1,
1,
1,
1,
1,
0,
1,
0,
0,
1,
1,
0,
1,
0,
1,
1,
1,
0,
0,
0,
1,
0,
1,
0,
1,−1 ],
1,−1 ],
1, 0 ],
1, 0 ],
0, 0 ],
1,−1 ],
1,−1 ],
1,−1 ],
1, 0 ],
1, 0 ],
1, 0 ],
1, 0 ],
[ −2, 0,−1,−2,
[ −2, 0,−1,−1,
[ −2, 1,−1,−1,
[ −2, 1,−1,−1,
[ −2, 1, 0,−1,
[ −1,−1,−1,−1,
[ −1,−1,−1, 0,
[ −1, 0,−1,−1,
[ −1, 0,−1,−1,
[ −1, 0,−1,−1,
[ −1, 0,−1, 0,
[ −1, 0,−1, 0,
1,
1,
1,
1,
1,
0,
0,
0,
1,
1,
0,
0,
241
1,
1,
1,
2,
1,
0,
0,
1,
0,
1,
0,
1,
1,−1 ],
0,−1 ],
0,−1 ],
0, 0 ],
0, 0 ],
2,−1 ],
1,−1 ],
0,−1 ],
0,−1 ],
0,−1 ],
0,−1 ],
0,−1 ],
[ −2, 0,−1,−1,
[ −2, 0,−1,−1,
[ −2, 1,−1,−1,
[ −2, 1,−1,−1,
[ −1,−1,−1,−1,
[ −1,−1,−1,−1,
[ −1,−1, 0,−1,
[ −1, 0,−1,−1,
[ −1, 0,−1,−1,
[ −1, 0,−1,−1,
[ −1, 0,−1, 0,
[ −1, 0,−1, 0,
1,−1 ],
1,−1 ],
0, 0 ],
0, 0 ],
1,−2 ],
1,−1 ],
1,−1 ],
1,−1 ],
1,−1 ],
0, 0 ],
1,−1 ],
0, 0 ],
1
0
0
0
1
1
0
0











[ −1, 0,−1, 0, 0, 1, 1, 0 ],
[ −1, 0,−1, 0, 1, 0, 1, 0 ],
[ −1, 0, 0,−1, 0, 0, 1,−1 ],
[ −1, 0, 0,−1, 0, 1, 0, 0 ],
[ −1, 0, 0,−1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 1,−1, 0, 0, 1, 0, 0 ],
[ −1, 1,−1, 0, 1, 1, 0, 0 ],
[ −1, 1, 0,−1, 1, 0, 0, 0 ],
[ −1, 1, 0,−1, 1, 1, 0, 1 ],
[ −1, 1, 0, 0, 0, 1, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 0, 1, 1,−1, 1 ],
[ 0,−1,−1,−1, 0, 0, 1,−1 ],
[ 0,−1,−1, 0, 0, 0, 0,−1 ],
[ 0,−1, 0,−1,−1, 0, 1,−1 ],
[ 0,−1, 0,−1, 0, 0, 1,−1 ],
[ 0,−1, 0, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0,−1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1,−1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0,−1, 0 ],
[ 0, 0, 1,−1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 0, 1,−1, 0 ],
[ 0, 1, 0, 0, 1, 0,−1, 0 ],
[ 0, 1, 0, 0, 1, 1,−1, 1 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, 0,−1, 0 ],
[ 0, 1, 1, 0, 0, 1,−1, 1 ],
[ 1,−2, 0, 0,−1,−1, 1,−1 ],
[ 1,−1, 0, 0,−1,−1, 1, 0 ],
[ 1,−1, 0, 0,−1, 0, 1, 0 ],
[ 1,−1, 0, 0, 0,−1, 1, 0 ],
[ 1,−1, 0, 1,−1,−1, 0, 0 ],
[ 1,−1, 0, 1, 0,−1, 0, 0 ],
[ 1,−1, 1, 0,−1,−1, 1, 0 ],
[ 1,−1, 1, 1,−1,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 0, 1,−1,−1, 0, 0 ],
[ 1, 0, 0, 1,−1, 0, 0, 1 ],
[ 1, 0, 0, 1, 0,−1, 0, 1 ],
[ 1, 0, 0, 1, 0, 0, 0, 1 ],
[ 1, 0, 1, 0,−1, 0, 0, 0 ],
[ 1, 0, 1, 0, 0,−1, 0, 0 ],
[ 1, 0, 1, 0, 0, 0,−1, 1 ],
[ 1, 0, 1, 1,−1,−1, 0, 0 ],
[ 1, 0, 1, 1,−1, 0,−1, 1 ],
[ 1, 0, 1, 1, 0,−1,−1, 1 ],
[ 1, 1, 0, 1, 0, 0,−1, 1 ],
[ 1, 1, 1, 1, 0,−1,−1, 1 ],
[ 1, 1, 1, 1, 0, 0,−1, 2 ],
[ 2,−1, 1, 1,−2,−1, 0, 0 ],
[ 2,−1, 1, 1,−1,−1, 0, 0 ],
[ 2, 0, 1, 1,−1,−1,−1, 1 ],
[ 2, 0, 1, 1, 0,−1,−1, 1 ],
[ −1, 0,−1, 0, 1, 0, 0,−1 ],
[ −1, 0,−1, 0, 1, 1, 0, 0 ],
[ −1, 0, 0,−1, 0, 0, 1, 0 ],
[ −1, 0, 0,−1, 0, 1, 1, 0 ],
[ −1, 0, 0,−1, 1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 1,−1, 0, 1, 0, 0, 0 ],
[ −1, 1,−1, 0, 1, 1, 0, 1 ],
[ −1, 1, 0,−1, 1, 1,−1, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 0, 1, 0, 1 ],
[ −1, 1, 0, 0, 1, 0, 0, 1 ],
[ −1, 1, 0, 0, 1, 1, 0, 1 ],
[ 0,−1,−1, 0,−1, 0, 1,−1 ],
[ 0,−1,−1, 0, 0, 0, 1,−1 ],
[ 0,−1, 0,−1, 0,−1, 1,−1 ],
[ 0,−1, 0,−1, 0, 0, 1, 0 ],
[ 0,−1, 0, 0,−1, 0, 1,−1 ],
[ 0,−1, 0, 0, 0,−1, 1,−1 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 1,−1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1,−1, 1 ],
[ 0, 1, 0, 0, 1, 0,−1, 1 ],
[ 0, 1, 0, 1, 0, 0,−1, 0 ],
[ 0, 1, 0, 1, 0, 1,−1, 1 ],
[ 0, 1, 1, 0, 0, 0,−1, 1 ],
[ 0, 1, 1, 0, 1, 0,−1, 1 ],
[ 1,−1, 0, 0,−1,−1, 0,−1 ],
[ 1,−1, 0, 0,−1, 0, 0,−1 ],
[ 1,−1, 0, 0, 0,−1, 0,−1 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1,−1, 0, 1,−1,−1, 1, 0 ],
[ 1,−1, 1, 0,−1,−1, 0,−1 ],
[ 1,−1, 1, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1,−1, 0,−1, 0 ],
[ 1, 0, 0, 1, 0,−1,−1, 0 ],
[ 1, 0, 0, 1, 0, 0,−1, 0 ],
[ 1, 0, 1, 0,−1,−1, 0, 0 ],
[ 1, 0, 1, 0,−1, 0, 0, 1 ],
[ 1, 0, 1, 0, 0,−1, 0, 1 ],
[ 1, 0, 1, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 1,−1,−1, 0, 1 ],
[ 1, 0, 1, 1,−1, 0, 0, 1 ],
[ 1, 0, 1, 1, 0,−1, 0, 1 ],
[ 1, 1, 1, 0, 0, 0,−1, 1 ],
[ 1, 1, 1, 1, 0, 0,−2, 1 ],
[ 2,−1, 0, 1,−1,−1, 0, 0 ],
[ 2,−1, 1, 1,−1,−2, 0, 0 ],
[ 2,−1, 1, 1,−1,−1, 0, 1 ],
[ 2, 0, 1, 1,−1,−1, 0, 1 ],
[ 2, 0, 1, 2,−1,−1,−1, 1 ],
242
[ −1, 0,−1, 0, 1, 0, 0, 0 ],
[ −1, 0, 0,−1, 0, 0, 0,−1 ],
[ −1, 0, 0,−1, 0, 1, 0,−1 ],
[ −1, 0, 0,−1, 1, 0, 0,−1 ],
[ −1, 0, 0,−1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 1,−1,−1, 1, 1, 0, 0 ],
[ −1, 1,−1, 0, 1, 1,−1, 0 ],
[ −1, 1, 0,−1, 0, 1, 0, 0 ],
[ −1, 1, 0,−1, 1, 1, 0, 0 ],
[ −1, 1, 0, 0, 0, 1,−1, 0 ],
[ −1, 1, 0, 0, 1, 0,−1, 0 ],
[ −1, 1, 0, 0, 1, 1,−1, 0 ],
[ −1, 2, 0, 0, 1, 1,−1, 1 ],
[ 0,−1,−1, 0, 0,−1, 1,−1 ],
[ 0,−1,−1, 0, 0, 0, 1, 0 ],
[ 0,−1, 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 0, 0,−1,−1, 1,−1 ],
[ 0,−1, 0, 0,−1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0,−1, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0,−1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 0,−1, 1 ],
[ 0, 1, 0, 1, 1, 0,−1, 1 ],
[ 0, 1, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 1, 0, 0,−1, 1 ],
[ 1,−1, 0, 0,−1,−1, 1,−1 ],
[ 1,−1, 0, 0,−1, 0, 0, 0 ],
[ 1,−1, 0, 0, 0,−1, 0, 0 ],
[ 1,−1, 0, 1,−1,−1, 0,−1 ],
[ 1,−1, 0, 1,−1, 0, 0, 0 ],
[ 1,−1, 1, 0,−1,−1, 0, 0 ],
[ 1,−1, 1, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 1,−1, 0, 0, 0 ],
[ 1, 0, 0, 1, 0,−1, 0, 0 ],
[ 1, 0, 0, 1, 0, 0,−1, 1 ],
[ 1, 0, 1, 0,−1, 0,−1, 0 ],
[ 1, 0, 1, 0, 0,−1,−1, 0 ],
[ 1, 0, 1, 0, 0, 0,−1, 0 ],
[ 1, 0, 1, 1,−1,−1,−1, 0 ],
[ 1, 0, 1, 1,−1, 0,−1, 0 ],
[ 1, 0, 1, 1, 0,−1,−1, 0 ],
[ 1, 0, 1, 1, 0, 0,−1, 1 ],
[ 1, 1, 1, 1,−1, 0,−1, 1 ],
[ 1, 1, 1, 1, 0, 0,−1, 1 ],
[ 2,−1, 1, 0,−1,−1, 0, 0 ],
[ 2,−1, 1, 1,−1,−1,−1, 0 ],
[ 2, 0, 1, 1,−1,−1,−1, 0 ],
[ 2, 0, 1, 1,−1, 0,−1, 1 ],
[ 2, 0, 2, 1,−1,−1,−1, 1 ]
∗
7
• I ≡ P130 :
3
6
2
5
1
4





CI =








b I =
Cox




0
1
1
1
1
1
1
−1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
−1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
−1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
−1
0
0
−1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
















b
CI =



1
1
1
1
1
1
1
−1
















BI =



1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
−1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
−1
0
0
0
1
1
1
1
0
0
0
0
0
−1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
−1
0
0
0
0
0
0
1
0
0
0
−1
0
0
0
0
0
−1
−1
−1
−1
−1
−1
−1
1











0
−1
0
−1
−1
−1
−1
1
0
0
0
0
0
0
1
0
Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−2, 1,−1,−1, 1, 1,−1 ],
[ −1, −2, 0, −2, −1, 1, 1, −2 ],
[ −1, −2, 0, −1, −1, 1, 0, −2 ],
[ −1, −1,−1, −1, −1, 0, 0, −3 ],
[ −1, −1,−1, −1, −1, 1, 0, −2 ],
[ −1, −1, 0, −1, −1, 0, 0, −2 ],
[ −1, −1, 0, −1, −1, 1, 0, −2 ],
[ −1, −1, 0, −1, 0, 0, 0, −2 ],
[ −1, −1, 0, −1, 0, 1, 0, −1 ],
[ −1, −1, 0, 0, −1, 0, 1, −1 ],
[ −1, 0,−1, −1, −1, 0, 0, −2 ],
[ −1, 0,−1, −1, 0, 0, 0, −2 ],
[ −1, 0,−1, 0, −1, 0,−1, −2 ],
[ −1, 0,−1, 0, 0,−1,−1, −2 ],
[ −1, 0,−1, 0, 0, 0,−1, −2 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0,−1, −1 ],
[ −1, 1,−2, 0, 0,−1,−1, −2 ],
[ −1, 1,−1, 0, 0,−1, 0, −1 ],
[ −1, 1,−1, 1, 0,−1,−1, −1 ],
[ 0, −2, 1, −1, −1, 1, 1, 0 ],
[ 0, −2, 1, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, −1, −1, 1, 0, −1 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 1, 0, −1 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, −1, 1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 1, −1, 0, 1, 0, 0 ],
[ 1, 2,−1, 1, 1,−1,−1, 1 ],
[ −1,−2, 0,−1,−2, 1, 1,−2 ],
[ −1,−2, 0,−1,−1, 1, 1,−2 ],
[ −1,−1, −1,−1,−1, 0, 0,−2 ],
[ −1,−1, −1,−1, 0, 0, 0,−2 ],
[ −1,−1, 0,−1,−1, 0, 1,−2 ],
[ −1,−1, 0,−1,−1, 1, 0,−1 ],
[ −1,−1, 0,−1, 0, 0, 0,−1 ],
[ −1,−1, 0, 0,−1, 0, 0,−2 ],
[ −1,−1, 0, 0,−1, 1, 0,−1 ],
[ −1, 0, −1,−1, 0, −1, 0,−2 ],
[ −1, 0, −1,−1, 0, 0, 0,−1 ],
[ −1, 0, −1, 0,−1, 0, 0,−2 ],
[ −1, 0, −1, 0, 0, −1, 0,−2 ],
[ −1, 0, −1, 0, 0, 0, −1,−1 ],
[ −1, 0, 0, 0,−1, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 1, −1, 0, 0, −1, −1,−2 ],
[ −1, 1, −1, 0, 0, 0, −1,−1 ],
[ 0,−2, 0,−1,−1, 1, 1,−1 ],
[ 0,−2, 1,−1,−1, 1, 2, 0 ],
[ 0,−2, 1, 0,−1, 1, 1, 0 ],
[ 0,−1, 0,−1,−1, 1, 1,−1 ],
[ 0,−1, 0,−1, 0, 0, 1,−1 ],
[ 0,−1, 0,−1, 0, 1, 0, 0 ],
[ 0,−1, 0, 0,−1, 0, 1,−1 ],
[ 0,−1, 0, 0,−1, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 1,−1,−1, 1, 1, 0 ],
[ 0,−1, 1,−1, 0, 1, 1, 0 ],
243
[ −2,−1,−1,−1,−1, 0, 0,−3 ],
[ −1,−2, 0,−1,−1, 0, 1,−2 ],
[ −1,−2, 0,−1,−1, 1, 1,−1 ],
[ −1,−1,−1,−1,−1, 0, 1,−2 ],
[ −1,−1,−1, 0,−1, 0, 0,−2 ],
[ −1,−1, 0,−1,−1, 0, 1,−1 ],
[ −1,−1, 0,−1,−1, 1, 1,−1 ],
[ −1,−1, 0,−1, 0, 0, 1,−1 ],
[ −1,−1, 0, 0,−1, 0, 0,−1 ],
[ −1,−1, 0, 0, 0, 0, 0,−1 ],
[ −1, 0,−1,−1, 0, 0,−1,−2 ],
[ −1, 0,−1, 0,−1,−1, 0,−2 ],
[ −1, 0,−1, 0,−1, 0, 0,−1 ],
[ −1, 0,−1, 0, 0,−1, 0,−1 ],
[ −1, 0,−1, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0,−1, 0,−1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 1,−1, 0, 0,−1,−1,−1 ],
[ −1, 1,−1, 0, 1,−1,−1,−1 ],
[ 0,−2, 1,−1,−1, 1, 1,−1 ],
[ 0,−2, 1,−1,−1, 2, 1, 0 ],
[ 0,−1, 0,−1,−1, 0, 1,−1 ],
[ 0,−1, 0,−1,−1, 1, 1, 0 ],
[ 0,−1, 0,−1, 0, 0, 1, 0 ],
[ 0,−1, 0,−1, 0, 1, 1, 0 ],
[ 0,−1, 0, 0,−1, 0, 1, 0 ],
[ 0,−1, 0, 0,−1, 1, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 1,−1, 0, 0, 1, 0 ],
[ 0,−1, 1,−1, 0, 1, 1, 1 ],
0
0
0
0
0
0
0
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 1, 0, −1, 0, 1, 0 ],
0, −1, 1, 0, −1, 1, 1, 1 ],
0, −1, 1, 0, 0, 0, 1, 1 ],
0, −1, 1, 0, 0, 1, 1, 1 ],
0, 0,−1, 0, 0,−1, 0, −1 ],
0, 0,−1, 0, 0, 0, 0, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, −1, 1, 0, 0 ],
0, 0, 0, 0, 0,−1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0,−1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, 0, 1, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 1,−1, 0, 0,−1, 0, 0 ],
0, 1,−1, 0, 0, 0, 0, 0 ],
0, 1,−1, 0, 1,−1, 0, 0 ],
0, 1,−1, 1, 0,−1,−1, 0 ],
0, 1,−1, 1, 1,−1,−1, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 1,−1, 0, 0 ],
0, 1, 0, 0, 1, 0,−1, 1 ],
0, 1, 0, 1, 0,−1, 0, 0 ],
0, 1, 0, 1, 0, 0,−1, 1 ],
0, 1, 0, 1, 1,−1,−1, 1 ],
0, 2,−1, 0, 1,−1,−1, 0 ],
0, 2,−1, 1, 1,−1,−2, 0 ],
0, 2, 0, 1, 1,−1,−1, 1 ],
1, −1, 1, 0, 0, 0, 1, 1 ],
1, −1, 1, 0, 0, 1, 1, 2 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 0, 1, 0, 0, 1 ],
1, 0, 1, 0, 0, 0, 1, 1 ],
1, 0, 1, 0, 0, 1, 0, 2 ],
1, 0, 1, 0, 1, 0, 0, 2 ],
1, 0, 1, 1, 0, 0, 0, 1 ],
1, 0, 1, 1, 0, 1, 0, 2 ],
1, 1, 0, 0, 1,−1, 0, 1 ],
1, 1, 0, 0, 1, 0, 0, 2 ],
1, 1, 0, 1, 0, 0, 0, 1 ],
1, 1, 0, 1, 1,−1, 0, 1 ],
1, 1, 0, 1, 1, 0,−1, 2 ],
1, 1, 1, 1, 0, 0, 0, 2 ],
1, 1, 1, 1, 1, 0, 0, 2 ],
1, 2, 0, 1, 1,−1,−1, 2 ],
1, 2, 0, 1, 2,−1,−1, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,−1, 1, 0,−1, 1, 0, 0 ],
0,−1, 1, 0, 0, 0, 0, 0 ],
0,−1, 1, 0, 0, 1, 0, 0 ],
0, 0, −1,−1, 0, 0, 0,−1 ],
0, 0, −1, 0, 0, 0, −1,−1 ],
0, 0, 0,−1, 0, 0, 0,−1 ],
0, 0, 0,−1, 0, 1, 0, 0 ],
0, 0, 0, 0,−1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0,−1 ],
0, 0, 0, 0, 0, 0, −1,−1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1, −1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 1, 0, 1 ],
0, 1, −1, 0, 0, −1, −1,−1 ],
0, 1, −1, 0, 0, 0, −1,−1 ],
0, 1, −1, 0, 1, −1, −1,−1 ],
0, 1, −1, 0, 1, 0, −1, 0 ],
0, 1, −1, 1, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 1, −1, 0, 1 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
0, 1, 0, 1, 0, −1, 0, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
0, 1, 0, 1, 1, −1, 0, 1 ],
0, 2, −1, 1, 0, −1, −1, 0 ],
0, 2, −1, 1, 1, −1, −1, 0 ],
1,−1, 1,−1, 0, 1, 1, 1 ],
1,−1, 1, 0, 0, 1, 0, 1 ],
1,−1, 2, 0, 0, 1, 1, 2 ],
1, 0, 0, 0, 0, 0, 1, 1 ],
1, 0, 0, 1, 0, 0, 0, 1 ],
1, 0, 1, 0, 0, 0, 1, 2 ],
1, 0, 1, 0, 0, 1, 1, 2 ],
1, 0, 1, 0, 1, 0, 1, 2 ],
1, 0, 1, 1, 0, 0, 0, 2 ],
1, 0, 1, 1, 1, 0, 0, 2 ],
1, 1, 0, 0, 1, 0, −1, 1 ],
1, 1, 0, 1, 0, −1, 0, 1 ],
1, 1, 0, 1, 0, 0, 0, 2 ],
1, 1, 0, 1, 1, −1, 0, 2 ],
1, 1, 0, 1, 1, 0, 0, 2 ],
1, 1, 1, 1, 1, −1, 0, 2 ],
1, 1, 1, 1, 1, 0, 0, 3 ],
1, 2, 0, 1, 1, −1, 0, 2 ],
1, 2, 0, 2, 1, −1, −1, 2 ],
∗
7
6
• I ≡ P131 :
5
4
3
2
1
244
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,−1, 1, 0,−1, 1, 1, 0 ],
0,−1, 1, 0, 0, 0, 1, 0 ],
0,−1, 1, 0, 0, 1, 0, 1 ],
0, 0,−1, 0,−1, 0, 0,−1 ],
0, 0,−1, 0, 0, 0, 0,−1 ],
0, 0, 0,−1, 0, 0, 0, 0 ],
0, 0, 0,−1, 1, 0, 0, 0 ],
0, 0, 0, 0,−1, 0, 1, 0 ],
0, 0, 0, 0, 0,−1, 0, 0 ],
0, 0, 0, 0, 0, 0,−1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0,−1, 0 ],
0, 0, 0, 1,−1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 1,−1, 0, 0,−1, 0,−1 ],
0, 1,−1, 0, 0, 0,−1, 0 ],
0, 1,−1, 0, 1,−1,−1, 0 ],
0, 1,−1, 1, 0,−1,−1,−1 ],
0, 1,−1, 1, 0, 0,−1, 0 ],
0, 1, 0, 0, 0, 0,−1, 0 ],
0, 1, 0, 0, 1,−1,−1, 0 ],
0, 1, 0, 0, 1, 0,−1, 0 ],
0, 1, 0, 1, 0,−1,−1, 0 ],
0, 1, 0, 1, 0, 0,−1, 0 ],
0, 1, 0, 1, 1,−1,−1, 0 ],
0, 1, 0, 1, 1, 0,−1, 1 ],
0, 2,−1, 1, 1,−2,−1, 0 ],
0, 2,−1, 1, 1,−1,−1, 1 ],
1,−1, 1, 0,−1, 1, 1, 1 ],
1,−1, 1, 0, 0, 1, 1, 1 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 0, 1, 0, 0, 1, 0, 1 ],
1, 0, 1, 0, 1, 0, 0, 1 ],
1, 0, 1, 0, 1, 1, 0, 2 ],
1, 0, 1, 1, 0, 0, 1, 2 ],
1, 1, 0, 0, 0, 0, 0, 1 ],
1, 1, 0, 0, 1, 0, 0, 1 ],
1, 1, 0, 1, 0, 0,−1, 1 ],
1, 1, 0, 1, 1,−1,−1, 1 ],
1, 1, 0, 1, 1, 0,−1, 1 ],
1, 1, 1, 0, 1, 0, 0, 2 ],
1, 1, 1, 1, 1, 0,−1, 2 ],
1, 2, 0, 1, 1,−1,−1, 1 ],
1, 2, 0, 1, 1, 0,−1, 2 ],
2, 1, 1, 1, 1, 0, 0, 3 ]





CI =








b I =
Cox




0
0
1
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
−1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
−1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
−1
0
−1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
















BI =



0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
−1
















bI =
C




1
1
1
1
1
1
1
−1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
−1
0
−1
−1
0
−1
−1
−1
−1
−1
−1
−1
1
1
0
0
0
0
0
0
0











−1
−1
0
0
−1
0
0
0
Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −2,−1,−1, 1, 2, 1, 0, 0 ],
[ −1,−1,−1, 0, 0, 0, 1,−1 ],
[ −1,−1,−1, 0, 1, 0, 1, 0 ],
[ −1,−1,−1, 0, 1, 1, 1, 0 ],
[ −1,−1,−1, 1, 1, 0, 0, 0 ],
[ −1,−1,−1, 1, 2, 0, 0, 0 ],
[ −1,−1,−1, 1, 2, 1, 0, 1 ],
[ −1,−1, 0, 1, 1, 1,−1, 0 ],
[ −1,−1, 0, 1, 2, 1,−1, 0 ],
[ −1,−1, 0, 1, 2, 2,−1, 1 ],
[ −1, 0,−1, 0, 0,−1, 1,−1 ],
[ −1, 0,−1, 0, 0, 0, 1, 0 ],
[ −1, 0,−1, 0, 1, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 0,−1, 0 ],
[ −1, 0, 0, 1, 1, 1,−1, 0 ],
[ −1, 0, 0, 1, 2, 1,−1, 1 ],
[ 0,−1,−1,−1, 0, 0, 1,−1 ],
[ 0,−1,−1, 0, 0, 0, 1,−1 ],
[ 0,−1,−1, 0, 1, 0, 0, 0 ],
[ 0,−1,−1, 1, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 1, 1,−1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 0, 0, 1 ],
[ 0,−1, 0, 1, 1, 1, 0, 1 ],
[ 0, 0,−1,−1,−1,−1, 1,−2 ],
[ 0, 0,−1,−1,−1, 0, 1,−1 ],
[ 0, 0,−1,−1, 0, 0, 1,−1 ],
[ 0, 0,−1, 0, 0,−1, 0,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0, 0,−1,−1, 0, 1,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1,−1, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1,−1, 0 ],
[ −1,−2,−1, 1, 2, 1, 0, 0 ],
[ −1,−1,−1, 0, 1, 0, 0,−1 ],
[ −1,−1,−1, 0, 1, 1, 0,−1 ],
[ −1,−1,−1, 0, 2, 1, 0, 0 ],
[ −1,−1,−1, 1, 1, 0, 1, 0 ],
[ −1,−1,−1, 1, 2, 1,−1, 0 ],
[ −1,−1, 0, 0, 1, 1, 0, 0 ],
[ −1,−1, 0, 1, 1, 1, 0, 0 ],
[ −1,−1, 0, 1, 2, 1,−1, 1 ],
[ −1,−1, 0, 2, 2, 1,−1, 1 ],
[ −1, 0,−1, 0, 0, 0, 0,−1 ],
[ −1, 0,−1, 0, 1, 0, 0,−1 ],
[ −1, 0,−1, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 1,−1, 1 ],
[ −1, 0, 1, 1, 1, 1,−1, 1 ],
[ 0,−1,−1, 0, 0,−1, 1,−1 ],
[ 0,−1,−1, 0, 0, 0, 1, 0 ],
[ 0,−1,−1, 0, 1, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 0, 0 ],
[ 0,−1, 0, 1, 1, 0,−1, 0 ],
[ 0,−1, 0, 1, 1, 1,−1, 0 ],
[ 0,−1, 0, 1, 2, 1,−1, 1 ],
[ 0, 0,−1,−1,−1,−1, 1,−1 ],
[ 0, 0,−1,−1, 0,−1, 1,−1 ],
[ 0, 0,−1,−1, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0,−1, 1,−1 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0,−1,−1,−1, 1,−1 ],
[ 0, 0, 0,−1,−1, 0, 1, 0 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0,−1,−1, 1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1,−1, 1 ],
245
[ −1,−1,−2, 0, 1, 0, 1,−1 ],
[ −1,−1,−1, 0, 1, 0, 1,−1 ],
[ −1,−1,−1, 0, 1, 1, 0, 0 ],
[ −1,−1,−1, 1, 1, 0, 0,−1 ],
[ −1,−1,−1, 1, 1, 1, 0, 0 ],
[ −1,−1,−1, 1, 2, 1, 0, 0 ],
[ −1,−1, 0, 1, 1, 0, 0, 0 ],
[ −1,−1, 0, 1, 1, 1, 0, 1 ],
[ −1,−1, 0, 1, 2, 1, 0, 1 ],
[ −1, 0,−1,−1, 0, 0, 1,−1 ],
[ −1, 0,−1, 0, 0, 0, 1,−1 ],
[ −1, 0,−1, 0, 1, 0, 0, 0 ],
[ −1, 0,−1, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 1, 1,−1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1,−1, 0, 0, 0, 0,−1 ],
[ 0,−1,−1, 0, 1, 0, 0,−1 ],
[ 0,−1,−1, 0, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 0, 1 ],
[ 0,−1, 0, 1, 1, 0, 0, 0 ],
[ 0,−1, 0, 1, 1, 1,−1, 1 ],
[ 0,−1, 1, 1, 1, 1,−1, 1 ],
[ 0, 0,−1,−1,−1,−1, 2,−1 ],
[ 0, 0,−1,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1,−1, 1,−1 ],
[ 0, 0,−1, 0, 0,−1, 1, 0 ],
[ 0, 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1,−1, 1, 0 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
1
1
0
1
0
1
0
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 0, 1, 0,−1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 1, 0, 0, 1 ],
0, 0, 1, 0, 0, 0,−1, 0 ],
0, 0, 1, 0, 0, 1,−1, 0 ],
0, 0, 1, 0, 1, 1,−1, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 0, 1, 1, 1, 1,−2, 1 ],
0, 1,−1,−1,−1,−1, 1,−1 ],
0, 1, 0,−1,−1,−1, 1,−1 ],
0, 1, 0,−1,−1, 0, 0, 0 ],
0, 1, 0, 0,−1,−1, 0,−1 ],
0, 1, 0, 0,−1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 1, 0,−1,−1, 0, 0 ],
0, 1, 1, 0,−1, 0, 0, 1 ],
0, 1, 1, 0, 0, 0, 0, 1 ],
1,−1, 0, 0, 0, 0, 0, 0 ],
1, 0, 0,−1,−1,−1, 0,−1 ],
1, 0, 0,−1,−1, 0, 0,−1 ],
1, 0, 0,−1, 0, 0, 0, 0 ],
1, 0, 0, 0,−1,−1, 1, 0 ],
1, 0, 0, 0, 0, 0,−1, 0 ],
1, 0, 1,−1,−1, 0, 0, 0 ],
1, 0, 1, 0,−1, 0, 0, 0 ],
1, 0, 1, 0, 0, 0,−1, 1 ],
1, 0, 1, 1, 0, 0,−1, 1 ],
1, 1, 0,−1,−2,−1, 0,−1 ],
1, 1, 0,−1,−1,−1, 0,−1 ],
1, 1, 0,−1,−1, 0, 0, 0 ],
1, 1, 1,−1,−2,−1, 0, 0 ],
1, 1, 1,−1,−1,−1, 0, 0 ],
1, 1, 1,−1,−1, 0, 0, 1 ],
1, 1, 1, 0,−1,−1, 0, 0 ],
1, 1, 1, 0,−1, 0,−1, 1 ],
1, 1, 2, 0,−1, 0,−1, 1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, 0, 1, 0, 0,−1, 0 ],
0, 0, 1, 1, 0,−1, 0 ],
0, 0, 1, 1, 1,−1, 1 ],
0, 1, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 1,−1, 1 ],
0, 1, 1, 0, 0,−1, 0 ],
0, 1, 1, 0, 1,−1, 1 ],
0, 1, 1, 1, 1,−1, 1 ],
1, 0,−1,−2,−1, 1,−1 ],
1, 0,−1,−1,−1, 1, 0 ],
1, 0,−1,−1, 0, 1, 0 ],
1, 0, 0,−1,−1, 0, 0 ],
1, 0, 0, 0,−1, 0, 0 ],
1, 0, 0, 0, 0, 0, 1 ],
1, 1, 0,−1, 0,−1, 0 ],
1, 1, 0, 0, 0,−1, 0 ],
1, 1, 0, 0, 1,−1, 1 ],
0,−1,−1,−1,−1, 1,−1 ],
0, 0,−1,−1,−1, 1,−1 ],
0, 0,−1,−1, 0, 0, 0 ],
0, 0, 0,−1,−1, 0,−1 ],
0, 0, 0,−1, 0, 0, 0 ],
0, 0, 0, 0, 0, 0, 0 ],
0, 1, 0,−1,−1, 0, 0 ],
0, 1, 0,−1, 0, 0, 1 ],
0, 1, 0, 0, 0, 0, 1 ],
1, 0,−2,−2,−1, 1,−1 ],
1, 0,−1,−2,−1, 1,−1 ],
1, 0,−1,−1,−1, 0, 0 ],
1, 0, 0,−1,−1, 0, 0 ],
1, 1,−1,−2,−1, 1, 0 ],
1, 1,−1,−1, 0,−1, 0 ],
1, 1, 0,−2,−1, 0, 0 ],
1, 1, 0,−1,−1, 0, 1 ],
1, 1, 0,−1, 0, 0, 1 ],
2, 1,−1,−2,−1, 0, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, 1, 0, 0, 0, 0 ],
0, 1, 1, 0,−1, 1 ],
1, 0,−1, 0, 0, 0 ],
1, 0, 0, 0, 0, 1 ],
1, 0, 0, 1, 0, 1 ],
1, 1, 0, 0,−1, 1 ],
1, 1, 1, 0,−1, 1 ],
1, 1, 1, 1,−1, 2 ],
0,−1,−1,−1, 0,−1 ],
0,−1,−1, 0, 0,−1 ],
0,−1, 0, 0, 0, 0 ],
0, 0,−1,−1, 1, 0 ],
0, 0, 0, 0,−1, 0 ],
1,−1,−1, 0, 0, 0 ],
1, 0,−1, 0, 0, 0 ],
1, 0, 0, 0,−1, 1 ],
1, 1, 0, 0,−1, 1 ],
0,−1,−2,−1, 1,−1 ],
0,−1,−1,−1, 1, 0 ],
0,−1,−1, 0, 1, 0 ],
0, 0,−1,−1, 0, 0 ],
0, 0, 0,−1, 0, 0 ],
0, 0, 0, 0, 0, 1 ],
1, 0,−1, 0,−1, 0 ],
1, 0, 0, 0,−1, 0 ],
1, 0, 0, 1,−1, 1 ],
0,−1,−2,−2, 1,−1 ],
0,−1,−2,−1, 1, 0 ],
0,−1,−1,−1, 1, 0 ],
1,−1,−2,−1, 0,−1 ],
1,−1,−2, 0, 0, 0 ],
1,−1,−1, 0, 0, 0 ],
1, 0,−1,−1,−1, 0 ],
1, 0,−1, 0,−1, 0 ],
1, 0, 0, 0,−1, 1 ],
1,−1,−2,−1, 0, 0 ]
∗
• I ≡ P132 :
6
7
3
4
5
2
1





CI =








b I =
Cox




0
0
1
0
1
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
−1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
−1
0
0
0
0
1
0
0
0
−1
0
0
0
−1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
















b
CI =



1
1
1
1
1
1
1
−1
















BI =



246
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
−1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
−1
0
0
0
0
1
0
0
0
0
−1
0
−1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
0
0
1
0
0
−1
−1
−2
−1
−1
0
−1
−1
1











−1
−1
0
0
0
−1
0
0
0
0
0
0
0
0
0
−1











Number of sincere Tits roots of poset I sI = 2.
Table of roots of qbI
[ −1,−1,−1, 1, 1, 2, 1, 1 ],
[ −1, −2, −1, 1, 0, 2, 1, 0 ],
[ −1, −1, −1, 0,−1, 1, 0,−2 ],
[ −1, −1, −1, 0, 0, 1, 0,−1 ],
[ −1, −1, −1, 0, 0, 2, 1, 0 ],
[ −1, −1, −1, 1, 0, 1, 0, 0 ],
[ −1, −1, −1, 1, 0, 2, 1, 0 ],
[ −1, −1, 0, 1, 0, 1, 0, 0 ],
[ −1, −1, 0, 1, 0, 2, 1, 1 ],
[ −1, −1, 0, 1, 1, 2, 1, 2 ],
[ −1, 0, −1,−1,−1, 0, 0,−2 ],
[ −1, 0, −1, 0,−1, 0, 0,−1 ],
[ −1, 0, −1, 0, 0, 1, 0,−1 ],
[ −1, 0, −1, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 2 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, 0,−1, 0, 0,−2 ],
[ 0, −1, −1, 0, 0, 0, 0,−1 ],
[ 0, −1, −1, 0, 0, 1, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0,−1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 1, 1 ],
[ 0, −1, 0, 1, 0, 1, 0, 1 ],
[ 0, −1, 0, 1, 1, 1, 1, 1 ],
[ 0, −1, 1, 1, 1, 1, 1, 2 ],
[ 0, 0, −1,−1,−1,−1,−1,−2 ],
[ 0, 0, −1,−1,−1, 0, 0,−2 ],
[ 0, 0, −1, 0,−1,−1,−1,−2 ],
[ 0, 0, −1, 0,−1, 0, 0,−1 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0,−1,−1,−1, 0,−2 ],
[ 0, 0, 0,−1, 0,−1, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 0, 0, 1, 1, 1, 2 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 1 ],
[ 0, 0, 1, 0, 1, 0, 1, 2 ],
[ 0, 0, 1, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 1, 0, 2 ],
[ 0, 0, 1, 1, 2, 1, 1, 3 ],
[ 0, 1, 0,−1,−1,−1,−1,−2 ],
[ 0, 1, 0,−1, 0,−1,−1,−1 ],
[ 0, 1, 0,−1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 1,−1, 0,−1, 0, 0 ],
[ 0, 1, 1, 0, 0,−1, 0, 1 ],
[ 0, 1, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 1, 1, 0, 0, 2 ],
[ 1, 0, 0,−1,−1,−2,−1,−2 ],
[ 1, 0, 0,−1,−1,−1, 0,−1 ],
[ 1, 1, 1,−1,−1,−2,−1,−1 ],
[ −1,−1,−2, 0, −1, 1, 0, −2 ],
[ −1,−1,−1, 0, −1, 1, 0, −1 ],
[ −1,−1,−1, 0, 0, 1, 1, −1 ],
[ −1,−1,−1, 1, −1, 1, 0, −1 ],
[ −1,−1,−1, 1, 0, 1, 1, 0 ],
[ −1,−1,−1, 1, 0, 2, 1, 1 ],
[ −1,−1, 0, 1, 0, 1, 1, 0 ],
[ −1,−1, 0, 1, 1, 1, 1, 1 ],
[ −1,−1, 0, 1, 1, 2, 2, 2 ],
[ −1, 0,−1, 0, −1, 0, −1, −2 ],
[ −1, 0,−1, 0, −1, 1, 0, −1 ],
[ −1, 0,−1, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 2, 1, 2 ],
[ 0,−1,−1, −1, −1, 0, 0, −2 ],
[ 0,−1,−1, 0, −1, 0, 0, −1 ],
[ 0,−1,−1, 0, 0, 1, 0, −1 ],
[ 0,−1,−1, 1, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 1, 1, 0 ],
[ 0,−1, 0, 1, 0, 0, 0, 0 ],
[ 0,−1, 0, 1, 0, 1, 1, 1 ],
[ 0,−1, 0, 1, 1, 1, 1, 2 ],
[ 0, 0,−1, −1, −2, −1, −1, −3 ],
[ 0, 0,−1, −1, −1, −1, 0, −2 ],
[ 0, 0,−1, −1, −1, 0, 0, −1 ],
[ 0, 0,−1, 0, −1, 0, −1, −2 ],
[ 0, 0,−1, 0, 0, 0, −1, −1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, −1, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1, −2 ],
[ 0, 0, 0, 0, −1, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 1, 1, 2 ],
[ 0, 0, 1, 1, 1, 0, 0, 2 ],
[ 0, 0, 1, 1, 1, 1, 1, 2 ],
[ 0, 1,−1, −1, −1, −1, −1, −2 ],
[ 0, 1, 0, −1, −1, −1, −1, −1 ],
[ 0, 1, 0, −1, 0, −1, 0, −1 ],
[ 0, 1, 0, 0, −1, −1, −1, −1 ],
[ 0, 1, 0, 0, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, −1, −1, 0 ],
[ 0, 1, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 1, 0, 0, 2 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, −1, −1, −1, −1, −2 ],
[ 1, 0, 0, −1, 0, −1, −1, −1 ],
247
[ −2,−1,−1, 1, 0, 2, 1, 0 ],
[ −1,−1,−1, 0,−1, 0, 0,−2 ],
[ −1,−1,−1, 0,−1, 1, 1,−1 ],
[ −1,−1,−1, 0, 0, 1, 1, 0 ],
[ −1,−1,−1, 1, 0, 1, 0,−1 ],
[ −1,−1,−1, 1, 0, 2, 0, 0 ],
[ −1,−1, 0, 0, 0, 1, 1, 0 ],
[ −1,−1, 0, 1, 0, 1, 1, 1 ],
[ −1,−1, 0, 1, 1, 2, 1, 1 ],
[ −1,−1, 0, 2, 1, 2, 1, 2 ],
[ −1, 0,−1, 0,−1, 0, 0,−2 ],
[ −1, 0,−1, 0, 0, 0, 0,−1 ],
[ −1, 0,−1, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 1, 0, 1, 0, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 1 ],
[ −1, 0, 1, 1, 1, 1, 1, 2 ],
[ 0,−1,−1, 0,−1, 0,−1,−2 ],
[ 0,−1,−1, 0,−1, 1, 0,−1 ],
[ 0,−1,−1, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 1, 1, 1 ],
[ 0,−1, 0, 1, 0, 1, 0, 0 ],
[ 0,−1, 0, 1, 1, 1, 0, 1 ],
[ 0,−1, 0, 1, 1, 2, 1, 2 ],
[ 0, 0,−1,−1,−1,−1,−1,−3 ],
[ 0, 0,−1,−1,−1, 0,−1,−2 ],
[ 0, 0,−1,−1, 0, 0, 0,−1 ],
[ 0, 0,−1, 0,−1, 0,−1,−1 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0, 0,−1,−1,−1,−1,−2 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1,−1,−1,−1 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 1, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 1, 2 ],
[ 0, 0, 1, 1, 1, 1, 1, 3 ],
[ 0, 1, 0,−1,−1,−2,−1,−2 ],
[ 0, 1, 0,−1,−1,−1, 0,−1 ],
[ 0, 1, 0,−1, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0,−1,−1,−1 ],
[ 0, 1, 0, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0,−1, 0, 0 ],
[ 0, 1, 1, 0, 1,−1, 0, 1 ],
[ 0, 1, 1, 0, 1, 0, 1, 2 ],
[ 1, 0,−1,−1,−1,−1,−1,−2 ],
[ 1, 0, 0,−1,−1,−1,−1,−1 ],
[ 1, 0, 0,−1, 0,−1, 0,−1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,−1, 0,−1, 0, 0 ],
0, 0, 0,−1,−1,−1 ],
0, 0, 0, 0,−1, 0 ],
0, 0, 1, 0, 0, 1 ],
1, 0, 0,−1, 0, 0 ],
1, 0, 1,−1, 0, 1 ],
1, 0, 1, 0, 1, 2 ],
0,−1,−1,−2,−2,−2 ],
0,−1,−1,−1,−1,−1 ],
0,−1, 0,−1,−1, 0 ],
1,−1, 0,−2,−1,−1 ],
1,−1, 0,−1,−1, 0 ],
1,−1, 1,−1, 0, 1 ],
1, 0, 0,−1,−1, 1 ],
1, 0, 1,−1, 0, 1 ],
2, 0, 1,−1, 0, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, −1, 0, 0, 0, 0 ],
0, 0, 0, −1, −1, 0 ],
0, 0, 0, 0, 0, 0 ],
1, −1, 0, −1, 0, 0 ],
1, 0, 0, −1, 0, 1 ],
1, 0, 1, 0, 0, 1 ],
1, 1, 1, 0, 0, 2 ],
0, −1, −1, −2, −1, −2 ],
0, −1, 0, −2, −1, −1 ],
0, −1, 0, −1, 0, 0 ],
1, −1, 0, −2, −1, 0 ],
1, −1, 0, −1, 0, 0 ],
1, 0, 0, −2, −1, 0 ],
1, 0, 0, −1, 0, 1 ],
1, 0, 1, −1, 0, 2 ],
1, −1, 0, −2, −1, 0 ],
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
2,
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, 0,−1,−1,−1,−1 ],
0, 0, 0,−1, 0, 0 ],
0, 0, 0, 0, 0, 1 ],
1, 0, 0,−1,−1, 0 ],
1, 0, 0, 0, 0, 1 ],
1, 0, 1, 0, 0, 2 ],
0,−2,−1,−2,−1,−2 ],
0,−1,−1,−2,−1,−1 ],
0,−1, 0,−1,−1,−1 ],
0, 0, 0,−1,−1, 0 ],
1,−1, 0,−2, 0, 0 ],
1,−1, 0,−1, 0, 1 ],
1, 0, 0,−1,−1, 0 ],
1, 0, 1,−1,−1, 1 ],
1, 0, 1, 0, 0, 2 ],
1,−1, 0,−2,−1, 0 ]
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
−1
0
0
0
0
0
0
0
1
0
0
1
0
0
−1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
[ −1,−1,−1,
[ −1,−1,−1,
[ −1,−1, 0,
[ −1,−1, 0,
[ −1, 0,−1,
[ −1, 0,−1,
[ −1, 0, 0,
[ −1, 0, 0,
[ −1, 0, 0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
∗
6
7
4
5
• I ≡ P133 :
3
2
1





CI =








b I =
Cox




1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
−1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
−1
−1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
−1
















bI =
C




1
1
1
1
1
1
1
0
















BI =



0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0











1
1
1
0
1
0
1
−1
Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −2, 0, 0,
[ −1,−1,−1,
[ −1,−1,−1,
[ −1,−1, 0,
[ −1,−1, 0,
[ −1, 0,−1,
[ −1, 0,−1,
[ −1, 0, 0,
[ −1, 0, 0,
1,
0,
0,
0,
1,
0,
1,
0,
0,
1,
1,
2,
1,
1,
1,
1,
0,
0,
1,
2,
2,
1,
1,
1,
1,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1 ],
0 ],
1 ],
0 ],
1 ],
0 ],
1 ],
0 ],
1 ],
[ −1,−1,−1,−1,
[ −1,−1,−1, 0,
[ −1,−1, 0, 0,
[ −1,−1, 0, 0,
[ −1, 0,−1, 0,
[ −1, 0,−1, 0,
[ −1, 0, 0, 0,
[ −1, 0, 0, 0,
[ −1, 0, 0, 0,
1,
1,
0,
1,
0,
1,
0,
0,
1,
248
2,
2,
1,
1,
1,
1,
0,
1,
0,
1, 0 ],
1, 1 ],
1, 0 ],
1, 1 ],
1, 0 ],
1, 1 ],
0,−1 ],
0, 0 ],
0, 0 ],
1,
1,
1,
1,
1,
1,
0,
0,
1,
1,
2,
1,
2,
1,
2,
0,
1,
1,
1,
2,
0,
1,
0,
1,
0,
1,
0,
0 ],
1 ],
0 ],
1 ],
0 ],
1 ],
0 ],
0 ],
0 ],
1
1
1
1
1
1
0
−1











[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ −1, 0, 0, 1, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 1, 0, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 0, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 0, 1 ],
[ −1, 1, 1, 1,−1,−1, 0, 0 ],
[ −1, 1, 1, 1, 0,−1, 0, 1 ],
[ 0,−2,−1,−1, 1, 2, 1, 0 ],
[ 0,−1,−1,−1, 0, 1, 1,−1 ],
[ 0,−1,−1,−1, 1, 1, 0,−1 ],
[ 0,−1,−1,−1, 1, 2, 0, 0 ],
[ 0,−1,−1, 0, 0, 1, 1, 0 ],
[ 0,−1,−1, 0, 1, 1, 1, 1 ],
[ 0,−1, 0,−1, 0, 1, 0,−1 ],
[ 0,−1, 0,−1, 1, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 1, 0 ],
[ 0,−1, 0, 0, 0, 1, 1, 1 ],
[ 0,−1, 0, 0, 1, 1, 0, 1 ],
[ 0, 0,−1,−1, 0, 0, 0,−1 ],
[ 0, 0,−1,−1, 0, 1, 1, 0 ],
[ 0, 0,−1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1, 0, 0, 1, 1, 0 ],
[ 0, 0,−1, 0, 1, 1, 0, 0 ],
[ 0, 0, 0,−1,−1, 0, 0,−1 ],
[ 0, 0, 0,−1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0,−1 ],
[ 0, 0, 0, 0, 0,−1,−1,−1 ],
[ 0, 0, 0, 0, 0, 0,−1,−1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0,−1, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 0,−1,−1,−1,−1 ],
[ 0, 0, 1, 0,−1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0,−1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0,−1, 0, 0 ],
[ 0, 1,−1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0,−1,−1, 0, 0 ],
[ 0, 1, 0, 0, 0,−1,−1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0,−1,−1, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 1, 0,−1,−1,−1, 0 ],
[ 0, 1, 1, 1,−1,−2,−1,−1 ],
[ 0, 1, 1, 1,−1,−1,−1, 0 ],
[ 0, 1, 1, 1, 0,−2,−1, 0 ],
[ 0, 1, 1, 1, 0,−1, 0, 1 ],
[ 1,−1,−1,−2, 0, 1, 0,−1 ],
[ 1,−1,−1,−1, 0, 1, 0, 0 ],
[ 1,−1, 0,−1,−1, 0, 0,−1 ],
[ 1,−1, 0,−1, 0, 0, 0, 0 ],
[ 1, 0,−1,−1,−1, 0, 0,−1 ],
[ 1, 0,−1,−1, 0, 0, 0, 0 ],
[ 1, 0, 0,−1,−1,−1,−1,−2 ],
[ 1, 0, 0,−1,−1, 0,−1,−1 ],
[ 1, 0, 0,−1, 0,−1,−1,−1 ],
[ 1, 0, 0,−1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0,−1,−1, 0, 0 ],
[ 1, 0, 0, 0, 0,−1,−1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0,−1,−2,−1,−1 ],
[ 1, 0, 1, 0,−1,−1, 0, 0 ],
[ 1, 1, 0, 0,−1,−2,−1,−1 ],
[ 1, 1, 0, 0,−1,−1, 0, 0 ],
[ 1, 1, 1, 0,−1,−2,−2,−1 ],
[ 1, 1, 1, 0,−1,−1,−1, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 1, 0, 0, 1, 1 ],
[ −1, 0, 0, 1, 1, 0, 0, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 1 ],
[ −1, 0, 1, 1, 0,−1, 0, 0 ],
[ −1, 0, 1, 1, 0, 0, 1, 1 ],
[ −1, 1, 0, 1, 0,−1, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 1, 1 ],
[ −1, 1, 1, 1, 0,−1,−1, 0 ],
[ −1, 1, 1, 1, 0, 0, 0, 1 ],
[ 0,−1,−2,−1, 1, 2, 1, 0 ],
[ 0,−1,−1,−1, 0, 1, 1, 0 ],
[ 0,−1,−1,−1, 1, 1, 0, 0 ],
[ 0,−1,−1,−1, 1, 2, 1, 0 ],
[ 0,−1,−1, 0, 1, 1, 0, 0 ],
[ 0,−1,−1, 0, 1, 2, 1, 1 ],
[ 0,−1, 0,−1, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
[ 0,−1, 0, 0, 0, 1, 0, 0 ],
[ 0,−1, 0, 0, 1, 0, 0, 0 ],
[ 0,−1, 0, 0, 1, 1, 1, 1 ],
[ 0, 0,−1,−1, 0, 1, 0,−1 ],
[ 0, 0,−1,−1, 1, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 1, 0 ],
[ 0, 0,−1, 0, 0, 1, 1, 1 ],
[ 0, 0,−1, 0, 1, 1, 0, 1 ],
[ 0, 0, 0,−1, 0, 0,−1,−1 ],
[ 0, 0, 0,−1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0,−1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0,−1, 0,−1 ],
[ 0, 0, 0, 0, 0, 0,−1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0,−1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, 0,−1,−1, 0,−1 ],
[ 0, 0, 1, 0, 0,−1,−1,−1 ],
[ 0, 0, 1, 0, 0, 0,−1, 0 ],
[ 0, 0, 1, 1,−1,−1, 0, 0 ],
[ 0, 0, 1, 1, 0,−1, 0, 1 ],
[ 0, 1, 0, 0,−1,−1,−1,−1 ],
[ 0, 1, 0, 0,−1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0,−1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0,−1, 0, 0 ],
[ 0, 1, 1, 0,−1,−2,−1,−1 ],
[ 0, 1, 1, 0,−1,−1, 0, 0 ],
[ 0, 1, 1, 1,−1,−2,−1, 0 ],
[ 0, 1, 1, 1,−1,−1, 0, 0 ],
[ 0, 1, 1, 1, 0,−1,−1, 0 ],
[ 0, 1, 2, 1,−1,−2,−1, 0 ],
[ 1,−1,−1,−1, 0, 0, 0,−1 ],
[ 1,−1,−1,−1, 0, 1, 1, 0 ],
[ 1,−1, 0,−1, 0, 0,−1,−1 ],
[ 1,−1, 0,−1, 0, 1, 0, 0 ],
[ 1, 0,−1,−1, 0, 0,−1,−1 ],
[ 1, 0,−1,−1, 0, 1, 0, 0 ],
[ 1, 0, 0,−1,−1,−1,−1,−1 ],
[ 1, 0, 0,−1,−1, 0, 0,−1 ],
[ 1, 0, 0,−1, 0, 0,−1,−1 ],
[ 1, 0, 0, 0,−1,−1,−1,−1 ],
[ 1, 0, 0, 0,−1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0,−1, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 1, 0,−1,−1,−1,−1 ],
[ 1, 0, 1, 0, 0,−1,−1, 0 ],
[ 1, 1, 0, 0,−1,−1,−1,−1 ],
[ 1, 1, 0, 0, 0,−1,−1, 0 ],
[ 1, 1, 1, 0,−1,−2,−1,−1 ],
[ 1, 1, 1, 1,−1,−2,−1, 0 ],
249
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 1, 0, 1, 1, 1 ],
[ −1, 0, 0, 1, 1, 0, 1, 1 ],
[ −1, 0, 0, 1, 1, 1, 1, 2 ],
[ −1, 0, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ −1, 1, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 1, 0, 0, 1 ],
[ −1, 1, 1, 1, 0,−1, 0, 0 ],
[ −1, 1, 1, 2, 0,−1, 0, 1 ],
[ 0,−1,−1,−1, 0, 1, 0,−1 ],
[ 0,−1,−1,−1, 0, 2, 1, 0 ],
[ 0,−1,−1,−1, 1, 1, 1, 0 ],
[ 0,−1,−1,−1, 1, 2, 1, 1 ],
[ 0,−1,−1, 0, 1, 1, 1, 0 ],
[ 0,−1, 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 0, 1, 1, 0 ],
[ 0,−1, 0, 0, 0, 0, 0, 0 ],
[ 0,−1, 0, 0, 0, 1, 1, 0 ],
[ 0,−1, 0, 0, 1, 1, 0, 0 ],
[ 0,−1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0,−1,−1, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 0, 0, 0,−1 ],
[ 0, 0,−1, 0, 0, 1, 0, 0 ],
[ 0, 0,−1, 0, 1, 0, 0, 0 ],
[ 0, 0,−1, 0, 1, 1, 1, 1 ],
[ 0, 0, 0,−1, 0, 0, 0,−1 ],
[ 0, 0, 0, 0,−1,−1, 0,−1 ],
[ 0, 0, 0, 0,−1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0,−1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0,−1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, 0,−1,−1, 0, 0 ],
[ 0, 0, 1, 0, 0,−1,−1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0,−1,−1, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 0,−1,−1, 0,−1 ],
[ 0, 1, 0, 0, 0,−1,−1,−1 ],
[ 0, 1, 0, 0, 0, 0,−1, 0 ],
[ 0, 1, 0, 1,−1,−1, 0, 0 ],
[ 0, 1, 0, 1, 0,−1, 0, 1 ],
[ 0, 1, 1, 0,−1,−1,−1,−1 ],
[ 0, 1, 1, 0, 0,−1,−1, 0 ],
[ 0, 1, 1, 1,−1,−2, 0, 0 ],
[ 0, 1, 1, 1,−1,−1, 0, 1 ],
[ 0, 1, 1, 1, 0,−1,−1, 1 ],
[ 0, 2, 1, 1,−1,−2,−1, 0 ],
[ 1,−1,−1,−1, 0, 1, 0,−1 ],
[ 1,−1,−1,−1, 1, 1, 0, 0 ],
[ 1,−1, 0,−1, 0, 0, 0,−1 ],
[ 1,−1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0,−1,−1, 0, 0, 0,−1 ],
[ 1, 0,−1, 0, 0, 0, 0, 0 ],
[ 1, 0, 0,−1,−1,−1, 0,−1 ],
[ 1, 0, 0,−1,−1, 0, 0, 0 ],
[ 1, 0, 0,−1, 0, 0,−1, 0 ],
[ 1, 0, 0, 0,−1,−1, 0,−1 ],
[ 1, 0, 0, 0, 0,−1,−1,−1 ],
[ 1, 0, 0, 0, 0, 0,−1, 0 ],
[ 1, 0, 1,−1,−1,−1,−1,−1 ],
[ 1, 0, 1, 0,−1,−1,−1, 0 ],
[ 1, 1, 0,−1,−1,−1,−1,−1 ],
[ 1, 1, 0, 0,−1,−1,−1, 0 ],
[ 1, 1, 1, 0,−2,−2,−1,−1 ],
[ 1, 1, 1, 0,−1,−2,−1, 0 ],
[ 2, 0, 0,−1,−1,−1,−1,−1 ]
∗
7
• I ≡ P134 :
3
6
2
5
4
1





CI =








b
CoxI =



0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
−1
0
0
−1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1
















bI =
C




1
1
1
1
1
1
1
0
















BI =



0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
−1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
−1
−1
0
0
−1
−1
−1
−1
−1
−1
−1
1











1
0
0
0
0
0
0
0
Number of sincere Tits roots of poset I sI = 0.
Table of roots of qbI
[ −2, 1,
[ −1,−1,
[ −1,−1,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 1,
[ −1, 1,
[ −1, 1,
[ −1, 1,
[ −1, 1,
[ −1, 1,
[ −1, 1,
[ −1, 2,
[ −1, 2,
[ 0,−2,
[ 0,−2,
[ 0,−2,
[ 0,−1,
[ 0,−1,
[ 0,−1,
[ 0,−1,
[ 0,−1,
1, 1, 1, 0, 0, 1 ],
1, 0, 0, 0, 1, 0 ],
1, 0, 0, 1, 1, 1 ],
0, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0 ],
1, 0, 0, 0, 1, 0 ],
1, 0, 0, 1, 0, 1 ],
1, 0, 1, 0, 0, 1 ],
1, 1, 0, 0, 0, 0 ],
1, 1, 0, 1, 0, 1 ],
0, 0, 1,−1, 0, 0 ],
0, 0, 1, 0, 0, 1 ],
0, 1, 0, 0, 0, 0 ],
0, 1, 1,−1, 0, 0 ],
0, 1, 1, 0,−1, 1 ],
1, 1, 0, 0, 0, 1 ],
1, 1, 1, 0, 0, 1 ],
0, 1, 1,−1,−1, 0 ],
0, 1, 1, 0,−1, 1 ],
0,−1,−1, 1, 1,−1 ],
1,−1,−1, 1, 2, 0 ],
1, 0,−1, 1, 1, 0 ],
0,−1,−1, 1, 1,−1 ],
0,−1, 0, 0, 1,−1 ],
0,−1, 0, 1, 0, 0 ],
0, 0,−1, 0, 1,−1 ],
0, 0,−1, 1, 0, 0 ],
[ −1,−1,
[ −1,−1,
[ −1,−1,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 0,
[ −1, 1,
[ −1, 1,
[ −1, 1,
[ −1, 1,
[ −1, 1,
[ −1, 1,
[ −1, 1,
[ −1, 2,
[ −1, 2,
[ 0,−2,
[ 0,−2,
[ 0,−1,
[ 0,−1,
[ 0,−1,
[ 0,−1,
[ 0,−1,
[ 0,−1,
1,−1, 0, 1, 1, 0 ],
1, 0, 0, 1, 0, 0 ],
2, 0, 0, 1, 1, 1 ],
0, 0, 0, 0, 1, 0 ],
0, 1, 0, 0, 0, 0 ],
1, 0, 0, 0, 1, 1 ],
1, 0, 0, 1, 1, 1 ],
1, 0, 1, 0, 1, 1 ],
1, 1, 0, 0, 0, 1 ],
1, 1, 1, 0, 0, 1 ],
0, 0, 1, 0,−1, 0 ],
0, 1, 0,−1, 0, 0 ],
0, 1, 0, 0, 0, 1 ],
0, 1, 1,−1, 0, 1 ],
0, 1, 1, 0, 0, 1 ],
1, 1, 1,−1, 0, 1 ],
1, 1, 1, 0, 0, 2 ],
0, 1, 1,−1,−1, 1 ],
0, 1, 2,−1,−1, 1 ],
1,−1,−1, 1, 1,−1 ],
1,−1,−1, 2, 1, 0 ],
0,−1,−1, 0, 1,−1 ],
0,−1,−1, 1, 1, 0 ],
0,−1, 0, 0, 1, 0 ],
0,−1, 0, 1, 1, 0 ],
0, 0,−1, 0, 1, 0 ],
0, 0,−1, 1, 1, 0 ],
250
[ −1,−1, 1, 0,−1, 1, 1, 0 ],
[ −1,−1, 1, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0,−1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 1, 0, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0,−1, 0 ],
[ −1, 1, 0, 1, 1,−1,−1, 0 ],
[ −1, 1, 0, 1, 1, 0,−1, 0 ],
[ −1, 1, 1, 0, 1, 0, 0, 1 ],
[ −1, 1, 1, 1, 1, 0,−1, 1 ],
[ −1, 2,−1, 1, 1,−1,−1, 0 ],
[ −1, 2, 0, 1, 1,−1, 0, 1 ],
[ −1, 2, 0, 2, 1,−1,−1, 1 ],
[ 0,−2, 1,−1,−1, 1, 1, 0 ],
[ 0,−2, 1,−1, 0, 1, 1, 0 ],
[ 0,−1, 0,−1,−1, 1, 0,−1 ],
[ 0,−1, 0,−1, 0, 0, 0,−1 ],
[ 0,−1, 0,−1, 0, 1, 0,−1 ],
[ 0,−1, 0, 0,−1, 0, 0,−1 ],
[ 0,−1, 0, 0,−1, 1, 0,−1 ],
[ 0,−1, 0, 0, 0, 0, 0,−1 ],
1
1
0
1
1
1
1
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,−1, 0, 0, 0, 0, 0, 0 ],
0,−1, 1,−1,−1, 1, 1, 0 ],
0,−1, 1,−1, 0, 1, 1, 0 ],
0,−1, 1, 0,−1, 1, 0, 0 ],
0,−1, 1, 0, 0, 0, 0, 0 ],
0,−1, 1, 0, 0, 1, 0, 0 ],
0, 0,−1,−1, 0, 0, 0,−1 ],
0, 0,−1, 0, 0, 0,−1,−1 ],
0, 0, 0,−1, 0, 0, 0,−1 ],
0, 0, 0,−1, 0, 1, 0, 0 ],
0, 0, 0, 0,−1, 0, 0, 0 ],
0, 0, 0, 0, 0,−1, 0,−1 ],
0, 0, 0, 0, 0, 0,−1,−1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1,−1, 0 ],
0, 0, 0, 0, 1,−1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0,−1, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 1, 0, 1 ],
0, 1,−1, 0, 0,−1,−1,−1 ],
0, 1,−1, 0, 0, 0,−1,−1 ],
0, 1,−1, 0, 1,−1,−1,−1 ],
0, 1,−1, 0, 1, 0,−1, 0 ],
0, 1,−1, 1, 0,−1, 0, 0 ],
0, 1, 0, 0, 0,−1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 1,−1, 0, 1 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
0, 1, 0, 1, 0,−1, 0, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
0, 1, 0, 1, 1,−1, 0, 1 ],
0, 2,−1, 1, 0,−1,−1, 0 ],
0, 2,−1, 1, 1,−1,−1, 0 ],
1,−2, 0,−2,−1, 1, 1,−1 ],
1,−2, 0,−1,−1, 1, 0,−1 ],
1,−2, 1,−1,−1, 1, 1, 0 ],
1,−1,−1,−1,−1, 0, 1,−1 ],
1,−1,−1, 0,−1, 0, 0,−1 ],
1,−1, 0,−1,−1, 0, 1, 0 ],
1,−1, 0,−1,−1, 1, 1, 0 ],
1,−1, 0,−1, 0, 0, 1, 0 ],
1,−1, 0, 0,−1, 0, 0, 0 ],
1,−1, 0, 0, 0, 0, 0, 0 ],
1, 0,−1,−1, 0, 0,−1,−1 ],
1, 0,−1, 0,−1,−1, 0,−1 ],
1, 0,−1, 0,−1, 0, 0, 0 ],
1, 0,−1, 0, 0,−1, 0, 0 ],
1, 0,−1, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0,−1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 1,−1, 0, 0,−1,−1, 0 ],
1, 1,−1, 0, 1,−1,−1, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,−1, 0, 0, 0, 0, 1, 0 ],
0,−1, 1,−1, 0, 0, 1, 0 ],
0,−1, 1,−1, 0, 1, 1, 1 ],
0,−1, 1, 0,−1, 1, 1, 0 ],
0,−1, 1, 0, 0, 0, 1, 0 ],
0,−1, 1, 0, 0, 1, 0, 1 ],
0, 0,−1, 0,−1, 0, 0,−1 ],
0, 0,−1, 0, 0, 0, 0,−1 ],
0, 0, 0,−1, 0, 0, 0, 0 ],
0, 0, 0,−1, 1, 0, 0, 0 ],
0, 0, 0, 0,−1, 0, 1, 0 ],
0, 0, 0, 0, 0,−1, 0, 0 ],
0, 0, 0, 0, 0, 0,−1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0,−1, 0 ],
0, 0, 0, 1,−1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 1,−1, 0, 0,−1, 0,−1 ],
0, 1,−1, 0, 0, 0,−1, 0 ],
0, 1,−1, 0, 1,−1,−1, 0 ],
0, 1,−1, 1, 0,−1,−1,−1 ],
0, 1,−1, 1, 0, 0,−1, 0 ],
0, 1, 0, 0, 0, 0,−1, 0 ],
0, 1, 0, 0, 1,−1,−1, 0 ],
0, 1, 0, 0, 1, 0,−1, 0 ],
0, 1, 0, 1, 0,−1,−1, 0 ],
0, 1, 0, 1, 0, 0,−1, 0 ],
0, 1, 0, 1, 1,−1,−1, 0 ],
0, 1, 0, 1, 1, 0,−1, 1 ],
0, 2,−1, 1, 1,−2,−1, 0 ],
0, 2,−1, 1, 1,−1,−1, 1 ],
1,−2, 0,−1,−2, 1, 1,−1 ],
1,−2, 0,−1,−1, 1, 1,−1 ],
1,−1,−1,−1,−1, 0, 0,−2 ],
1,−1,−1,−1,−1, 1, 0,−1 ],
1,−1, 0,−1,−1, 0, 0,−1 ],
1,−1, 0,−1,−1, 1, 0,−1 ],
1,−1, 0,−1, 0, 0, 0,−1 ],
1,−1, 0,−1, 0, 1, 0, 0 ],
1,−1, 0, 0,−1, 0, 1, 0 ],
1, 0,−1,−1,−1, 0, 0,−1 ],
1, 0,−1,−1, 0, 0, 0,−1 ],
1, 0,−1, 0,−1, 0,−1,−1 ],
1, 0,−1, 0, 0,−1,−1,−1 ],
1, 0,−1, 0, 0, 0,−1,−1 ],
1, 0, 0,−1, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 0,−1, 0 ],
1, 1,−2, 0, 0,−1,−1,−1 ],
1, 1,−1, 0, 0,−1, 0, 0 ],
1, 1,−1, 1, 0,−1,−1, 0 ],
∗
• I ≡ P135 :
5
6
7
2
3
4
1
251
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,−1, 0, 0, 0, 1, 0, 0 ],
0,−1, 1,−1, 0, 1, 0, 0 ],
0,−1, 1, 0,−1, 0, 1, 0 ],
0,−1, 1, 0,−1, 1, 1, 1 ],
0,−1, 1, 0, 0, 0, 1, 1 ],
0,−1, 1, 0, 0, 1, 1, 1 ],
0, 0,−1, 0, 0,−1, 0,−1 ],
0, 0,−1, 0, 0, 0, 0, 0 ],
0, 0, 0,−1, 0, 0, 1, 0 ],
0, 0, 0, 0,−1, 0, 0,−1 ],
0, 0, 0, 0,−1, 1, 0, 0 ],
0, 0, 0, 0, 0,−1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0,−1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0,−1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, 0, 1, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 1,−1, 0, 0,−1, 0, 0 ],
0, 1,−1, 0, 0, 0, 0, 0 ],
0, 1,−1, 0, 1,−1, 0, 0 ],
0, 1,−1, 1, 0,−1,−1, 0 ],
0, 1,−1, 1, 1,−1,−1, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 1,−1, 0, 0 ],
0, 1, 0, 0, 1, 0,−1, 1 ],
0, 1, 0, 1, 0,−1, 0, 0 ],
0, 1, 0, 1, 0, 0,−1, 1 ],
0, 1, 0, 1, 1,−1,−1, 1 ],
0, 2,−1, 0, 1,−1,−1, 0 ],
0, 2,−1, 1, 1,−1,−2, 0 ],
0, 2, 0, 1, 1,−1,−1, 1 ],
1,−2, 0,−1,−1, 0, 1,−1 ],
1,−2, 0,−1,−1, 1, 1, 0 ],
1,−1,−1,−1,−1, 0, 0,−1 ],
1,−1,−1,−1, 0, 0, 0,−1 ],
1,−1, 0,−1,−1, 0, 1,−1 ],
1,−1, 0,−1,−1, 1, 0, 0 ],
1,−1, 0,−1, 0, 0, 0, 0 ],
1,−1, 0, 0,−1, 0, 0,−1 ],
1,−1, 0, 0,−1, 1, 0, 0 ],
1, 0,−1,−1, 0,−1, 0,−1 ],
1, 0,−1,−1, 0, 0, 0, 0 ],
1, 0,−1, 0,−1, 0, 0,−1 ],
1, 0,−1, 0, 0,−1, 0,−1 ],
1, 0,−1, 0, 0, 0,−1, 0 ],
1, 0, 0, 0,−1, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 1,−1, 0, 0,−1,−1,−1 ],
1, 1,−1, 0, 0, 0,−1, 0 ],
2,−1,−1,−1,−1, 0, 0,−1 ]





CI =








b I =
Cox




0
0
1
1
0
0
1
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
−1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
−1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
−1
0
0
−1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
−1
−1
0
0
−1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
















BI =



1
1
1
0
1
1
0
−1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
−1
















bI =
C




1
1
1
1
1
1
1
−1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
−1
0
0
−1
0
0
0
0
−1
−1
0
0
−1
0
0











0
0
−1
0
0
0
−1
0
0
0
1
0
0
0
0
−1
Number of sincere Tits roots of poset I sI = 10.
Table of roots of qbI
[ −2,−1,−2,−1, 1, 2, 1,−1 ],
[ −1,−1,−2,−1, 1, 2, 1,−1 ],
[ 1, 1, 2, 1,−1,−2,−1, 1 ],
[ 2, 1, 2, 1,−1,−2,−1, 1 ],
[ −1, −1, −2, −1, 0, 1, 1, −2 ],
[ −1, −1, −2, −1, 1, 2, 1, 0 ],
[ −1, −1, −1, −1, 0, 0, 0, −2 ],
[ −1, −1, −1, −1, 0, 1, 1, −1 ],
[ −1, −1, −1, −1, 1, 2, 1, 0 ],
[ −1, −1, −1, 0, 1, 1, 0, 0 ],
[ −1, −1, −1, 0, 1, 2, 1, 0 ],
[ −1, −1, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, −1, −1, 0, 0, 0, −2 ],
[ −1, 0, −1, −1, 0, 1, 0, −1 ],
[ −1, 0, −1, −1, 1, 1, 1, 0 ],
[ −1, 0, −1, 0, 0, 1, 0, 0 ],
[ −1, 0, −1, 0, 1, 1, 1, 0 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 1, 1, 0, 1 ],
[ 0, −1, −1, −1, −1, 0, 0, −2 ],
[ 0, −1, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 1, 0 ],
[ 0, −1, −1, 0, 0, 1, 0, −1 ],
[ 0, −1, −1, 0, 1, 1, 0, 0 ],
[ 0, −1, −1, 0, 1, 2, 1, 1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, −1, −1, −1, 0, 0, −2 ],
[ 0, 0, −1, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, −1, 0, 1, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 1, 1, 0 ],
[ 0, 0, 0, −1, −1, −1, −1, −2 ],
[ 0, 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, −1, −1, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ −1,−2,−2,−1, 1, 2, 1,−1 ],
[ −1,−1,−1,−1, 1, 1, 1,−1 ],
[ 1, 1, 2, 1,−1,−1,−1, 1 ],
[ −1, −1, −2, −2, 0, 1, 1, −2 ],
[ −1, −1, −2, −1, 0, 1, 1, −1 ],
[ −1, −1, −2, −1, 1, 2, 2, 0 ],
[ −1, −1, −1, −1, 0, 1, 0, −2 ],
[ −1, −1, −1, −1, 1, 1, 0, −1 ],
[ −1, −1, −1, 0, 0, 1, 0, −1 ],
[ −1, −1, −1, 0, 1, 1, 1, 0 ],
[ −1, −1, −1, 0, 1, 2, 1, 1 ],
[ −1, 0, −2, −1, 0, 1, 1, −1 ],
[ −1, 0, −1, −1, 0, 0, 0, −1 ],
[ −1, 0, −1, −1, 0, 1, 1, −1 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, 1, 1, 0 ],
[ −1, 0, −1, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 0, 0, 0, −1, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, 0, 0, 0, −2 ],
[ 0, −1, −1, −1, 0, 1, 0, −1 ],
[ 0, −1, −1, −1, 1, 1, 1, 0 ],
[ 0, −1, −1, 0, 0, 1, 0, 0 ],
[ 0, −1, −1, 0, 1, 1, 1, 0 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 0, 0 ],
[ 0, −1, 0, 1, 1, 1, 0, 1 ],
[ 0, 0, −1, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, −1, 0, 0, 1, −1 ],
[ 0, 0, −1, 0, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, −1, −1, −1, 0, −2 ],
[ 0, 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
252
[ −1,−1,−2,−1, 1, 1, 1,−1 ],
[ 1, 1, 1, 1,−1,−1,−1, 1 ],
[ 1, 2, 2, 1,−1,−2,−1, 1 ],
[ −1, −1, −2, −1, 0, 1, 0, −2 ],
[ −1, −1, −2, −1, 0, 2, 1, −1 ],
[ −1, −1, −2, 0, 1, 2, 1, 0 ],
[ −1, −1, −1, −1, 0, 1, 0, −1 ],
[ −1, −1, −1, −1, 1, 1, 1, 0 ],
[ −1, −1, −1, 0, 1, 1, 0, −1 ],
[ −1, −1, −1, 0, 1, 2, 0, 0 ],
[ −1, −1, −1, 0, 2, 2, 1, 1 ],
[ −1, 0, −1, −1, −1, 0, 0, −2 ],
[ −1, 0, −1, −1, 0, 0, 1, −1 ],
[ −1, 0, −1, −1, 0, 1, 1, 0 ],
[ −1, 0, −1, 0, 0, 1, 0, −1 ],
[ −1, 0, −1, 0, 1, 1, 0, 0 ],
[ −1, 0, −1, 0, 1, 2, 1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ 0, −1, −2, −1, 0, 1, 1, −1 ],
[ 0, −1, −1, −1, 0, 0, 0, −1 ],
[ 0, −1, −1, −1, 0, 1, 1, −1 ],
[ 0, −1, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, −1, 0, 0, 1, 1, 0 ],
[ 0, −1, −1, 0, 1, 1, 1, 1 ],
[ 0, −1, 0, 0, 0, 0, −1, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, −1, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, −1, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, 1, 1, 1, 1 ],
[ 0, 0, 0, −1, −1, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1, −2 ],
[ 0, 0, 0, 0, −1, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
0, 0, 1, 0, 0, 1 ],
0, 0, 1, 1, 1, 1 ],
0, 1, 0, 0, 0, 0 ],
0, 1, 1, 0, 0, 1 ],
0, 1, 1, 1, 1, 2 ],
1, 0, 0, −1, −1, 0 ],
1, 0, 0, 0, 0, 0 ],
1, 1, 0, −1, −1, 0 ],
1, 1, 0, 0, 0, 1 ],
1, 1, 1, 0, 0, 2 ],
0, 0, −1, −1, −1, −1 ],
0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, 1 ],
1, 0, −1, −2, −1, −1 ],
1, 0, −1, −1, 0, 0 ],
1, 0, 0, −1, 0, 1 ],
1, 1, 0, −1, −1, 0 ],
1, 1, 0, 0, −1, 1 ],
1, 1, 1, 0, 0, 2 ],
0, −1, −1, −1, 0, −1 ],
0, 0, −1, −1, 0, 0 ],
0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 1 ],
1, 0, −1, −1, −1, 0 ],
1, 0, 0, −1, 0, 0 ],
1, 1, −1, −1, −1, 0 ],
1, 1, 0, −1, 0, 1 ],
1, 1, 0, 0, 0, 2 ],
0, 0, −1, −1, 0, 0 ],
1, 0, −1, −2, −1, 0 ],
1, 0, −1, −1, 0, 0 ],
1, 1, −1, −2, −1, 0 ],
1, 1, 0, −1, −1, 1 ],
1, 1, 0, 0, 0, 2 ],
2, 1, −1, −2, −1, 0 ],
2, 1, 0, −1, −1, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
0,
0,
0,
1,
1,
1,
1,
1,
2,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
2,
2,
0, 1, 0, 1, 1 ],
0, 1, 1, 1, 2 ],
1, 0, 0, 0, 1 ],
1, 1, 1, 0, 1 ],
0, −1, −1, −1, −1 ],
0, 0, −1, 0, 0 ],
0, 0, 0, 0, 1 ],
1, 0, 0, −1, 0 ],
1, 1, 0, −1, 1 ],
1, 1, 1, 0, 2 ],
0, −1, −1, 0, −1 ],
0, 0, −1, 0, 0 ],
0, 0, 0, 1, 1 ],
0, −1, −1, −1, −1 ],
0, 0, −1, −1, 0 ],
0, 0, 0, 0, 1 ],
1, 0, −1, −1, 1 ],
1, 0, 0, 0, 1 ],
1, 0, −1, −1, 1 ],
0, −1, −1, −1, −1 ],
0, −1, 0, 0, 0 ],
0, 0, 0, 0, 1 ],
0, −1, −2, −1, −1 ],
0, −1, −1, 0, 0 ],
0, 0, −1, 0, 1 ],
1, 0, −1, −1, 0 ],
1, 0, 0, −1, 1 ],
1, 1, 0, 0, 2 ],
0, −2, −2, −1, −1 ],
0, −1, −2, 0, 0 ],
0, −1, −1, 0, 1 ],
1, −1, −1, −1, 0 ],
1, 0, −1, 0, 1 ],
0, −1, −2, −1, 0 ],
1, 0, −2, −1, 1 ],
1, 0, −1, 0, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
1, −1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
0, 0, 1, 1, 0, 1 ],
0, 1, 0, 0, −1, 0 ],
0, 1, 0, 1, 0, 1 ],
0, 1, 1, 1, 0, 2 ],
1, 0, 0, −1, −1, −1 ],
1, 0, 0, 0, −1, 0 ],
1, 0, 1, 0, 0, 1 ],
1, 1, 0, 0, −1, 1 ],
1, 1, 1, 0, 0, 1 ],
0, −1, −1, −1, 0, −1 ],
0, 0, −1, −1, 0, 0 ],
0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 1 ],
1, 0, −1, −1, −1, 0 ],
1, 0, 0, −1, 0, 0 ],
1, 1, −1, −1, −1, 0 ],
1, 1, 0, −1, 0, 1 ],
1, 1, 0, 0, 0, 2 ],
0, 0, 0, 0, 0, 0 ],
0, 0, −1, −1, 0, −1 ],
0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 1, 1 ],
1, 0, −1, −1, −1, −1 ],
1, 0, 0, −1, −1, 0 ],
1, 0, 0, 0, 0, 1 ],
1, 1, 0, −1, −1, 1 ],
1, 1, 0, 0, 0, 1 ],
2, 1, 0, −1, −1, 1 ],
1, 0, −1, −2, −1, −1 ],
1, 0, −1, −1, −1, 0 ],
1, 0, 0, −1, 0, 1 ],
1, 1, −1, −1, 0, 1 ],
1, 1, 0, −1, 0, 2 ],
2, 1, −1, −2, −2, 0 ],
2, 1, 0, −1, −1, 1 ],
2, 2, 0, −1, −1, 2 ]
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
−1
1
0
1
1
0
1
0
0
0
0
−1
−1
0
−1
0
0
∗
7
• I ≡ P136 :
2
4
6
1
3
5





CI =








b
CoxI =



0
0
1
0
1
1
1
−1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
−1
0
0
1
0
0
0
0
0
0
0
0
0
−1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
−1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
−1
−1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1
















bI =
C




1
1
0
1
0
0
0
0
















BI =



Number of sincere Tits roots of poset I sI = 10.
253
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
1
0
1
1
1
1
1
−1
−1
0
0
−1
0
0
0
0











0
0
−1
0
0
−1
−1
0
1
0
1
1
0
0
0
−1











Table of roots of qbI
[ −1, 1,−2, 2,−1, 1, 1, 1 ],
[ −1, 1,−1, 1,−1, 1, 1, 1 ],
[ 1,−1, 1,−1, 1,−1,−1,−1 ],
[ 1,−1, 2,−2, 1,−1,−1,−1 ],
[ −1, 0, −2, 1, −2, 1, 1, −1 ],
[ −1, 0, −2, 1, −1, 1, 1, −1 ],
[ −1, 0, −1, 0, −1, 0, 0, −2 ],
[ −1, 0, −1, 0, −1, 1, 0, −1 ],
[ −1, 0, −1, 1, −1, 0, 1, −1 ],
[ −1, 0, −1, 1, −1, 1, 0, 0 ],
[ −1, 0, −1, 1, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 1, −2, 1, −1, 1, 1, 0 ],
[ −1, 1, −1, 1, −1, 0, 1, 0 ],
[ −1, 1, −1, 1, 0, 0, 0, 0 ],
[ −1, 1, −1, 1, 0, 1, 0, 0 ],
[ −1, 1, −1, 2, 0, 0, 1, 1 ],
[ −1, 1, −1, 2, 0, 1, 1, 2 ],
[ −1, 1, 0, 1, 0, 0, 0, 1 ],
[ −1, 1, 0, 1, 1, 0, 0, 1 ],
[ 0, −1, −1, 0, −1, 0, 0, −2 ],
[ 0, −1, −1, 0, −1, 1, 0, −1 ],
[ 0, −1, 0, −1, −1, 0, −1, −2 ],
[ 0, −1, 0, −1, 0, −1, −1, −2 ],
[ 0, −1, 0, −1, 0, 0, −1, −2 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 1, −1, 0, −1, −1, −2 ],
[ 0, −1, 1, −1, 0, 0, −1, −1 ],
[ 0, 0, −1, 0, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, −1, 1, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, 1, −1, 1, 1, 0 ],
[ 0, 0, −1, 1, 0, 0, 1, 0 ],
[ 0, 0, −1, 1, 0, 1, 0, 1 ],
[ 0, 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, −1, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 1, −1, 0, −1, 0, −1 ],
[ 0, 0, 1, −1, 0, 0, −1, 0 ],
[ 0, 0, 1, −1, 1, −1, −1, 0 ],
[ 0, 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 0, 1, −1, 0, 1 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 1, −1, 1, 0, 0, 1, 1 ],
[ 0, 1, −1, 1, 0, 1, 1, 2 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 0, 1, 2 ],
[ 0, 1, 0, 1, 0, 1, 1, 2 ],
[ 0, 1, 0, 1, 1, 0, 1, 2 ],
[ 0, 1, 1, 0, 1, −1, 0, 1 ],
[ 0, 1, 1, 0, 1, 0, 0, 2 ],
[ 1, −1, 0, −1, −1, 0, 0, −1 ],
[ 1, −1, 0, −1, 0, 0, 0, −1 ],
[ 1, −1, 1, −2, 0, −1, −1, −2 ],
[ 1, −1, 1, −2, 0, 0, −1, −1 ],
[ −1, 1,−2, 2,−1, 1, 2, 1 ],
[ −1, 1,−1, 2,−1, 1, 1, 1 ],
[ 1,−1, 2,−2, 1,−2,−1,−1 ],
[ −2, 1, −2, 2, −1, 1, 1, 0 ],
[ −1, 0, −2, 1, −1, 0, 1, −1 ],
[ −1, 0, −2, 1, −1, 1, 1, 0 ],
[ −1, 0, −1, 0, −1, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, −1, 1, −1, 0, 1, 0 ],
[ −1, 0, −1, 1, −1, 1, 1, 0 ],
[ −1, 0, −1, 1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, −2, 2, −1, 1, 1, 0 ],
[ −1, 1, −1, 1, −1, 1, 0, 0 ],
[ −1, 1, −1, 1, 0, 0, 1, 0 ],
[ −1, 1, −1, 1, 0, 1, 0, 1 ],
[ −1, 1, −1, 2, 0, 1, 0, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 1, 1 ],
[ −1, 2, −1, 2, 0, 1, 1, 2 ],
[ 0, −1, −1, 0, −1, 0, 0, −1 ],
[ 0, −1, −1, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, −1, 0, 0, −2 ],
[ 0, −1, 0, −1, 0, −1, 0, −2 ],
[ 0, −1, 0, −1, 0, 0, −1, −1 ],
[ 0, −1, 0, 0, 0, −1, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 1, −1, 0, −1, −1, −1 ],
[ 0, −1, 1, −1, 1, −1, −1, −1 ],
[ 0, 0, −1, 0, −1, 0, 1, −1 ],
[ 0, 0, −1, 0, −1, 1, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 1, −1, 0, 1, 0 ],
[ 0, 0, −1, 1, −1, 1, 1, 1 ],
[ 0, 0, −1, 1, 0, 0, 1, 1 ],
[ 0, 0, −1, 1, 0, 1, 1, 1 ],
[ 0, 0, 0, −1, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 1, −1, 0, −1, 0, 0 ],
[ 0, 0, 1, −1, 0, 0, 0, 0 ],
[ 0, 0, 1, −1, 1, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 0, 1, 0, 1, −1, −1, 0 ],
[ 0, 0, 1, 0, 1, 0, −1, 0 ],
[ 0, 0, 2, −1, 1, −1, −1, 0 ],
[ 0, 1, −1, 1, 0, 1, 0, 1 ],
[ 0, 1, −1, 2, 0, 1, 1, 2 ],
[ 0, 1, 0, 0, 0, 0, 1, 1 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 1, 0, 1 ],
[ 0, 1, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 1, 1, 1, 0, 2 ],
[ 0, 1, 1, 0, 1, 0, −1, 1 ],
[ 0, 1, 1, 1, 1, 0, 0, 2 ],
[ 1, −1, 0, −1, 0, −1, 0, −1 ],
[ 1, −1, 0, −1, 0, 0, 0, 0 ],
[ 1, −1, 1, −2, 0, −1, −1, −1 ],
[ 1, −1, 1, −1, 0, −1, −1, −1 ],
254
[ −1, 1,−2, 2,−1, 2, 1, 1 ],
[ 1,−1, 1,−2, 1,−1,−1,−1 ],
[ 1,−1, 2,−2, 1,−1,−2,−1 ],
[ −1, −1, −1, 0, −1, 0, 0, −2 ],
[ −1, 0, −2, 1, −1, 1, 0, −1 ],
[ −1, 0, −2, 2, −1, 1, 1, 0 ],
[ −1, 0, −1, 0, −1, 0, 1, −1 ],
[ −1, 0, −1, 1, −1, 0, 0, −1 ],
[ −1, 0, −1, 1, −1, 1, 0, −1 ],
[ −1, 0, −1, 1, 0, 0, 0, −1 ],
[ −1, 0, −1, 1, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, −1, −1 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, −2, 2, 0, 1, 1, 1 ],
[ −1, 1, −1, 1, −1, 1, 1, 0 ],
[ −1, 1, −1, 1, 0, 0, 1, 1 ],
[ −1, 1, −1, 1, 0, 1, 1, 1 ],
[ −1, 1, −1, 2, 0, 1, 1, 1 ],
[ −1, 1, 0, 1, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 1, 0, 1 ],
[ 0, −1, −1, −1, −1, 0, 0, −2 ],
[ 0, −1, −1, 0, −1, 0, 1, −1 ],
[ 0, −1, 0, −1, −1, −1, 0, −2 ],
[ 0, −1, 0, −1, −1, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, −1, 0, −1 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, −1, −1 ],
[ 0, −1, 1, −2, 0, −1, −1, −2 ],
[ 0, −1, 1, −1, 0, −1, 0, −1 ],
[ 0, 0, −2, 1, −1, 1, 1, 0 ],
[ 0, 0, −1, 0, −1, 0, 1, 0 ],
[ 0, 0, −1, 0, −1, 1, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 1, −1, 1, 0, 0 ],
[ 0, 0, −1, 1, 0, 0, 0, 0 ],
[ 0, 0, −1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, −1, 0 ],
[ 0, 0, 0, 0, 1, −1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, −1, 0, −1, −1, −1 ],
[ 0, 0, 1, −1, 0, 0, −1, −1 ],
[ 0, 0, 1, −1, 1, −1, −1, −1 ],
[ 0, 0, 1, −1, 1, 0, −1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 1, −1, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, −1, 1 ],
[ 0, 1, −1, 1, −1, 1, 1, 1 ],
[ 0, 1, −1, 1, 0, 1, 1, 1 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 1, 0, 1, 0, 2 ],
[ 0, 1, 0, 1, 1, 0, 0, 2 ],
[ 0, 1, 1, 0, 0, 0, 0, 1 ],
[ 0, 1, 1, 0, 1, 0, 0, 1 ],
[ 1, −2, 1, −2, 0, −1, −1, −2 ],
[ 1, −1, 0, −1, 0, 0, −1, −1 ],
[ 1, −1, 0, 0, 0, 0, 0, 0 ],
[ 1, −1, 1, −2, 0, −1, 0, −1 ],
[ 1, −1, 1, −1, 0, −1, 0, −1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
1, −1,
1, −1,
1, −1,
1, −1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, −1,
1, −1,
1, −1,
2, −1,
0, 0,
0, 0,
1, −1,
1, −1,
1, −1,
1, 0,
1, 0,
2, −1,
2, −1,
0, −1, 0,
0, 0, 0,
1, 0, −1,
1, −1, −1,
0, 0, 0,
1, 0, 0,
0, 0, 0,
1, −1, 0,
1, 0, −1,
1, −1, 0,
1, 0, 0,
1, −1, −1,
2, −1, −1,
0 ],
0 ],
0 ],
0 ],
1 ],
1 ],
0 ],
0 ],
1 ],
1 ],
2 ],
1 ],
1 ],
1, −1,
1, −1,
1, −1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
[
[
[
[
[
[
[
[
[
[
[
[
[
1, −1,
1, −1,
2, −2,
0, −1,
0, 0,
1, −1,
1, −1,
1, −1,
1, −1,
1, 0,
2, −2,
2, −1,
1, 0,
0, 0, −1, −1 ],
1, −1, −1, 0 ],
0, −1, −1, −1 ],
0, 0, 0, 0 ],
0, 0, 1, 1 ],
0, −1, 0, 0 ],
0, 0, 0, 1 ],
1, −1, 0, 1 ],
1, 0, 0, 1 ],
1, 0, −1, 1 ],
1, −1, −1, 0 ],
1, −1, 0, 1 ],
1, 0, 0, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
1, −1,
1, −1,
1, −1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
2, −1,
1, −1,
1, −1,
2, −2,
0, 0,
0, 0,
1, −1,
1, −1,
1, −1,
1, 0,
1, 0,
2, −1,
2, −1,
2, −2,
0, 0, −1,
1, −1, 0,
1, −1, −1,
0, 0, 0,
0, 1, 0,
0, 0, −1,
1, −1, −1,
1, 0, −1,
0, 0, 0,
1, 0, 0,
1, −1, −1,
1, 0, −1,
1, −1, −1,
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
−1
0
0
0
0
0
1
0
0
0
0
0
0
0
−1
−1
0
0 ],
0 ],
0 ],
0 ],
1 ],
0 ],
0 ],
0 ],
1 ],
1 ],
0 ],
1 ],
0]
∗
7
6
• I ≡ P137 :
5
2
4
1
3





CI =








b I =
Cox




0
0
1
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
−1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
−1
0
0
−1
−1
0
0
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
1
1
0
1
1
1
1
0
















BI =



0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
1
0
0
0
0
0











0
0
−1
−1
0
0
0
0
1
0
1
1
1
1
0
−1
Number of sincere Tits roots of poset I sI = 12.
Table of roots of qbI
[ −2, 2,−1, 1, 1, 1,−1, 1 ],
[ −2, 2,−1, 2, 1, 1,−1, 1 ],
[ 1,−2, 1,−1,−1,−1, 1,−1 ],
[ 2,−2, 1,−1,−2,−1, 1,−1 ],
[ −2, 1, −2, 1, 1, 1, 0, 0 ],
[ −2, 1, −1, 1, 1, 0, 0, 0 ],
[ −2, 1, −1, 1, 1, 1, 0, 1 ],
[ −2, 2, 0, 1, 1, 1, −1, 1 ],
[ −1, 0, −1, 0, 0, 0, 1, −1 ],
[ −1, 0, −1, 0, 0, 1, 0, 0 ],
[ −1, 0, −1, 0, 1, 0, 0, 0 ],
[ −1, 0, −1, 1, 0, 0, 0, −1 ],
[ −2, 2,−1, 1, 1, 2,−1, 1 ],
[ −1, 1,−1, 1, 1, 1,−1, 1 ],
[ 1,−1, 1,−1,−1,−1, 1,−1 ],
[ 2,−2, 1,−1,−1,−2, 1,−1 ],
[ −2, 1, −1, 0, 1, 1, 0, 0 ],
[ −2, 1, −1, 1, 1, 1, −1, 0 ],
[ −2, 2, −1, 1, 1, 1, −1, 0 ],
[ −1, −1, −1, 0, 0, 0, 1, −1 ],
[ −1, 0, −1, 0, 0, 0, 1, 0 ],
[ −1, 0, −1, 0, 0, 1, 1, 0 ],
[ −1, 0, −1, 0, 1, 0, 1, 0 ],
[ −1, 0, −1, 1, 0, 0, 0, 0 ],
255
[ −2, 2,−1, 1, 2, 1,−1, 1 ],
[ −1, 2,−1, 1, 1, 1,−1, 1 ],
[ 2,−2, 1,−2,−1,−1, 1,−1 ],
[ 2,−2, 1,−1,−1,−1, 1,−1 ],
[ −2, 1, −1, 1, 0, 1, 0, 0 ],
[ −2, 1, −1, 1, 1, 1, 0, 0 ],
[ −2, 2, −1, 1, 1, 1, 0, 1 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, 1, 0, −1 ],
[ −1, 0, −1, 0, 1, 0, 0, −1 ],
[ −1, 0, −1, 0, 1, 1, 0, 0 ],
[ −1, 0, −1, 1, 0, 0, 1, 0 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, −1, 1, 0, 1, 0, 0 ],
−1, 0, 0, 0, 0, 0, 0, 0 ],
−1, 0, 0, 0, 1, 0, 0, 0 ],
−1, 1, −1, 0, 1, 0, 0, 0 ],
−1, 1, −1, 0, 1, 1, 0, 1 ],
−1, 1, −1, 1, 0, 1, 0, 0 ],
−1, 1, −1, 1, 1, 0, 0, 0 ],
−1, 1, −1, 1, 1, 1, 0, 1 ],
−1, 1, 0, 0, 0, 1, 0, 0 ],
−1, 1, 0, 0, 1, 0, 0, 0 ],
−1, 1, 0, 0, 1, 1, −1, 1 ],
−1, 1, 0, 1, 0, 0, 0, 0 ],
−1, 1, 0, 1, 0, 1, −1, 1 ],
−1, 1, 0, 1, 1, 0, −1, 1 ],
−1, 2, 0, 0, 1, 1, −1, 1 ],
−1, 2, 0, 1, 1, 1, −2, 1 ],
0, −1, −1, −1, 0, 0, 1, −1 ],
0, −1, −1, 0, 0, 0, 0, −1 ],
0, −1, 0, −1, −1, 0, 1, −1 ],
0, −1, 0, −1, 0, 0, 1, −1 ],
0, −1, 0, 0, −1, 0, 0, −1 ],
0, −1, 0, 0, 0, −1, 0, −1 ],
0, −1, 0, 0, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 1, 0, 0 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 1, 0, 0 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1, −1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 1, −1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 0, 0, 0, 1, −1, 0 ],
0, 1, 0, 0, 1, 0, −1, 0 ],
0, 1, 0, 0, 1, 1, −1, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
0, 1, 1, 0, 0, 0, −1, 0 ],
0, 1, 1, 0, 0, 1, −1, 1 ],
1, −2, 0, −1, −1, −1, 1, −2 ],
1, −2, 0, −1, −1, 0, 1, −1 ],
1, −1, 0, −1, −1, −1, 1, −1 ],
1, −1, 0, −1, −1, 0, 1, 0 ],
1, −1, 0, −1, 0, −1, 1, 0 ],
1, −1, 0, −1, 0, 0, 1, 0 ],
1, −1, 0, 0, −1, −1, 1, 0 ],
1, −1, 0, 0, −1, 0, 1, 0 ],
1, −1, 0, 0, 0, −1, 1, 0 ],
1, −1, 1, −1, −1, −1, 1, 0 ],
1, −1, 1, −1, −1, 0, 1, 0 ],
1, −1, 1, −1, 0, −1, 1, 0 ],
1, −1, 1, 0, −1, −1, 0, 0 ],
1, −1, 1, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 1, −1, 0, 0, −1, 0 ],
1, 0, 1, 0, −1, −1, 0, 0 ],
1, 0, 1, 0, −1, 0, 0, 1 ],
1, 0, 1, 0, 0, −1, 0, 1 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
2, −2, 1, −1, −1, −1, 0, −1 ],
2, −1, 1, −1, −1, −1, 0, 0 ],
2, −1, 1, −1, 0, −1, 0, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, −1, 1, 1, 0, 0, 0 ],
−1, 0, 0, 0, 0, 0, 1, 0 ],
−1, 0, 0, 1, 0, 0, 0, 0 ],
−1, 1, −1, 0, 1, 1, −1, 0 ],
−1, 1, −1, 1, 0, 0, 0, 0 ],
−1, 1, −1, 1, 0, 1, 0, 1 ],
−1, 1, −1, 1, 1, 0, 0, 1 ],
−1, 1, 0, 0, 0, 0, 0, 0 ],
−1, 1, 0, 0, 0, 1, 0, 1 ],
−1, 1, 0, 0, 1, 0, 0, 1 ],
−1, 1, 0, 0, 1, 1, 0, 1 ],
−1, 1, 0, 1, 0, 0, 0, 1 ],
−1, 1, 0, 1, 0, 1, 0, 1 ],
−1, 1, 0, 1, 1, 0, 0, 1 ],
−1, 2, 0, 1, 0, 1, −1, 1 ],
−1, 2, 0, 1, 1, 1, −1, 1 ],
0, −1, −1, 0, −1, 0, 1, −1 ],
0, −1, −1, 0, 0, 0, 1, −1 ],
0, −1, 0, −1, 0, −1, 1, −1 ],
0, −1, 0, −1, 0, 0, 1, 0 ],
0, −1, 0, 0, −1, 0, 1, −1 ],
0, −1, 0, 0, 0, −1, 1, −1 ],
0, −1, 0, 0, 0, 0, 0, 0 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, −1, 0, 1, 0, 0, 0 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, −1, 1, 0, 0, 0 ],
0, 0, 0, 0, −1, 0, 1, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 1, −1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 0, −1, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, 1, −1, 1 ],
0, 1, 0, 0, 1, 0, −1, 1 ],
0, 1, 0, 1, 0, 0, −1, 0 ],
0, 1, 0, 1, 0, 1, −1, 1 ],
0, 1, 1, 0, 0, 0, −1, 1 ],
0, 1, 1, 0, 1, 0, −1, 1 ],
1, −2, 0, −1, −1, −1, 1, −1 ],
1, −2, 0, −1, 0, −1, 1, −1 ],
1, −1, 0, −1, −1, 0, 0, −1 ],
1, −1, 0, −1, 0, −1, 0, −1 ],
1, −1, 0, −1, 0, 0, 0, −1 ],
1, −1, 0, 0, −1, −1, 0, −1 ],
1, −1, 0, 0, −1, 0, 0, −1 ],
1, −1, 0, 0, 0, −1, 0, −1 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, −1, 1, −1, −1, 0, 0, −1 ],
1, −1, 1, −1, 0, −1, 0, −1 ],
1, −1, 1, −1, 0, 0, 0, 0 ],
1, −1, 1, 0, −1, −1, 1, 0 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, −1, 0 ],
1, 0, 1, −1, −1, 0, 0, 0 ],
1, 0, 1, −1, 0, 0, 0, 0 ],
1, 0, 1, 0, −1, 0, −1, 0 ],
1, 0, 1, 0, 0, −1, −1, 0 ],
1, 0, 1, 0, 0, 0, −1, 0 ],
1, 1, 1, 0, 0, 0, −1, 1 ],
2, −2, 1, −1, −1, −1, 1, 0 ],
2, −1, 1, −1, −1, −1, 1, 0 ],
2, −1, 1, 0, −1, −1, 0, 0 ],
256
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, 0, 0, 0, 0, 0, −1 ],
−1, 0, 0, 0, 0, 1, 0, 0 ],
−1, 1, −1, 0, 0, 1, 0, 0 ],
−1, 1, −1, 0, 1, 1, 0, 0 ],
−1, 1, −1, 1, 0, 1, −1, 0 ],
−1, 1, −1, 1, 1, 0, −1, 0 ],
−1, 1, −1, 1, 1, 1, −1, 0 ],
−1, 1, 0, 0, 0, 1, −1, 0 ],
−1, 1, 0, 0, 1, 0, −1, 0 ],
−1, 1, 0, 0, 1, 1, −1, 0 ],
−1, 1, 0, 1, 0, 0, −1, 0 ],
−1, 1, 0, 1, 0, 1, −1, 0 ],
−1, 1, 0, 1, 1, 0, −1, 0 ],
−1, 1, 0, 1, 1, 1, −1, 1 ],
−1, 2, 0, 1, 1, 0, −1, 1 ],
−1, 2, 0, 1, 1, 1, −1, 2 ],
0, −1, −1, 0, 0, −1, 1, −1 ],
0, −1, −1, 0, 0, 0, 1, 0 ],
0, −1, 0, −1, 0, 0, 0, −1 ],
0, −1, 0, 0, −1, −1, 1, −1 ],
0, −1, 0, 0, −1, 0, 1, 0 ],
0, −1, 0, 0, 0, −1, 1, 0 ],
0, −1, 0, 0, 0, 0, 1, 0 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, −1, 1, 0, 0, 0, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, −1, 1, 0, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, −1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 0, 1, 0, 1 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
0, 1, 0, 1, 0, 0, −1, 1 ],
0, 1, 0, 1, 1, 0, −1, 1 ],
0, 1, 1, 0, 0, 0, 0, 1 ],
0, 1, 1, 1, 0, 0, −1, 1 ],
1, −2, 0, −1, −1, −1, 2, −1 ],
1, −2, 0, 0, −1, −1, 1, −1 ],
1, −1, 0, −1, −1, 0, 1, −1 ],
1, −1, 0, −1, 0, −1, 1, −1 ],
1, −1, 0, −1, 0, 0, 0, 0 ],
1, −1, 0, 0, −1, −1, 1, −1 ],
1, −1, 0, 0, −1, 0, 0, 0 ],
1, −1, 0, 0, 0, −1, 0, 0 ],
1, −1, 1, −1, −1, −1, 0, −1 ],
1, −1, 1, −1, −1, 0, 0, 0 ],
1, −1, 1, −1, 0, −1, 0, 0 ],
1, −1, 1, 0, −1, −1, 0, −1 ],
1, −1, 1, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 1, −1, 0, −1, 0, 0 ],
1, 0, 1, −1, 0, 0, 0, 1 ],
1, 0, 1, 0, −1, 0, 0, 0 ],
1, 0, 1, 0, 0, −1, 0, 0 ],
1, 0, 1, 0, 0, 0, −1, 1 ],
2, −2, 0, −1, −1, −1, 1, −1 ],
2, −1, 1, −1, −1, −1, 0, −1 ],
2, −1, 1, −1, −1, 0, 0, 0 ],
2, −1, 2, −1, −1, −1, 0, 0 ]
∗
7
• I ≡ P138 :
1
6
3
5
2
4





CI =








b I =
Cox




0
1
1
1
1
1
1
−1
1
0
0
1
0
0
0
−1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
−1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
−1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
















b
CI =



1
1
1
1
1
1
1
−1
















BI =



1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
−1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
1
1
2
1
1
−1
0
0
0
1
1
1
1
0
0
−1
−1
0
−1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
−1
0
0
0
0
0
0
1
0
0
−1
−1
−1
−1
−1
−1
1
−1
−1
−1
−1
−1
−1
−1
1
0
−1
0
0
−1
−1
0
0











0
0
0
−1
−1
0
0
0
Number of sincere Tits roots of poset I sI = 18.
Table of roots of qbI
[ −1, 1,−2, 1,−1,−1,−1,−2 ],
[ −1, 2,−2, 1,−2,−1,−1,−2 ],
[ −1, 2,−2, 1,−1,−1,−1,−2 ],
[ 1,−2, 1,−1, 1, 1, 1, 1 ],
[ 1,−2, 2,−1, 1, 1, 2, 2 ],
[ 1,−1, 1,−1, 1, 1, 1, 1 ],
[ −2, 1, −2, 0, −1, −1, −1, −3 ],
[ −1, −1, 0, −1, 0, 0, 0, −1 ],
[ −1, −1, 0, −1, 1, 0, 0, −1 ],
[ −1, 0, −1, −1, 0, −1, 0, −2 ],
[ −1, 0, −1, −1, 0, 0, 0, −1 ],
[ −1, 0, −1, 0, −1, 0, 0, −2 ],
[ −1, 0, −1, 0, 0, −1, 0, −2 ],
[ −1, 0, −1, 0, 0, 0, −1, −1 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 1, −2, 0, −1, −1, −1, −2 ],
[ −1, 1, −2, 0, 0, −1, −1, −2 ],
[ −1, 1, −1, 0, −1, −1, 0, −1 ],
[ −1, 1, −1, 0, −1, 0, 0, −1 ],
[ −1, 1, −1, 0, 0, −1, 0, −1 ],
[ −1, 1, −1, 1, −1, 0, −1, −1 ],
[ 0, −2, 1, −2, 1, 1, 1, 0 ],
[ 0, −2, 1, −1, 1, 1, 0, 0 ],
[ 0, −2, 2, −1, 1, 1, 1, 1 ],
[ 0, −1, 0, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, −1, 1, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ −1, 1,−1, 1,−1,−1,−1,−2 ],
[ −1, 2,−2, 1,−1,−2,−1,−2 ],
[ −1, 2,−2, 1,−1,−1,−1,−1 ],
[ 1,−2, 2,−1, 1, 1, 1, 1 ],
[ 1,−2, 2,−1, 1, 2, 1, 2 ],
[ 1,−1, 1,−1, 1, 1, 1, 2 ],
[ −1, −1, −1, −1, 0, 0, 0, −2 ],
[ −1, −1, 0, −1, 0, 0, 1, −1 ],
[ −1, −1, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, −1, −1, 0, 0, −1, −2 ],
[ −1, 0, −1, 0, −1, −1, 0, −2 ],
[ −1, 0, −1, 0, −1, 0, 0, −1 ],
[ −1, 0, −1, 0, 0, −1, 0, −1 ],
[ −1, 0, −1, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, −1, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, −2, 0, −1, −1, 0, −2 ],
[ −1, 1, −1, 0, −1, −1, −1, −2 ],
[ −1, 1, −1, 0, −1, 0, −1, −2 ],
[ −1, 1, −1, 0, 0, −1, −1, −2 ],
[ −1, 1, −1, 0, 0, 0, −1, −1 ],
[ −1, 1, −1, 1, 0, −1, −1, −1 ],
[ 0, −2, 1, −1, 0, 1, 1, 0 ],
[ 0, −2, 1, −1, 1, 1, 1, 0 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 1, 0, −1 ],
[ 0, −1, 0, −1, 1, 0, 0, −1 ],
[ 0, −1, 0, −1, 1, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 1, −1, 0, 0, 1, 0 ],
257
[ −1, 1,−1, 1,−1,−1,−1,−1 ],
[ −1, 2,−2, 1,−1,−1,−2,−2 ],
[ −1, 2,−1, 1,−1,−1,−1,−1 ],
[ 1,−2, 2,−1, 1, 1, 1, 2 ],
[ 1,−2, 2,−1, 2, 1, 1, 2 ],
[ 1,−1, 2,−1, 1, 1, 1, 2 ],
[ −1, −1, 0, −1, 0, 0, 0, −2 ],
[ −1, −1, 0, −1, 0, 1, 0, −1 ],
[ −1, 0, −1, −1, −1, 0, 0, −2 ],
[ −1, 0, −1, −1, 0, 0, 0, −2 ],
[ −1, 0, −1, 0, −1, 0, −1, −2 ],
[ −1, 0, −1, 0, 0, −1, −1, −2 ],
[ −1, 0, −1, 0, 0, 0, −1, −2 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, −1, −1 ],
[ −1, 1, −2, 0, −1, −1, −1, −3 ],
[ −1, 1, −2, 0, −1, 0, −1, −2 ],
[ −1, 1, −1, 0, −1, −1, 0, −2 ],
[ −1, 1, −1, 0, −1, 0, −1, −1 ],
[ −1, 1, −1, 0, 0, −1, −1, −1 ],
[ −1, 1, −1, 1, −1, −1, 0, −1 ],
[ −1, 2, −2, 0, −1, −1, −1, −2 ],
[ 0, −2, 1, −1, 1, 0, 1, 0 ],
[ 0, −2, 1, −1, 1, 1, 1, 1 ],
[ 0, −1, 0, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 1, 0, 0 ],
[ 0, −1, 0, −1, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 1, −1, 0, 1, 0, 0 ],
0
0
0
0
0
0
0
−1











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 1, −1, 0, 1, 1, 0 ],
0, −1, 1, −1, 1, 0, 1, 0 ],
0, −1, 1, −1, 1, 1, 0, 1 ],
0, −1, 1, 0, 0, 0, 1, 0 ],
0, −1, 1, 0, 0, 1, 0, 1 ],
0, −1, 1, 0, 1, 0, 0, 1 ],
0, 0, −1, −1, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 0, −1, −1 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 1, 0, 0 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1, −1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 1, 0, 1 ],
0, 1, −1, 0, −1, −1, 0, −1 ],
0, 1, −1, 0, −1, 0, 0, 0 ],
0, 1, −1, 0, 0, −1, 0, 0 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, −1, 1, −1, −1, 0, 0 ],
0, 1, −1, 1, −1, 0, 0, 0 ],
0, 1, −1, 1, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 1, −1, 0, 0, 0 ],
0, 1, 0, 1, 0, −1, 0, 0 ],
0, 1, 0, 1, 0, 0, −1, 1 ],
0, 2, −1, 1, −1, −1, −1, −1 ],
0, 2, −1, 1, −1, 0, −1, 0 ],
1, −2, 2, 0, 1, 1, 1, 2 ],
1, −1, 1, −1, 1, 1, 0, 1 ],
1, −1, 1, 0, 0, 1, 1, 1 ],
1, −1, 1, 0, 1, 0, 1, 1 ],
1, −1, 1, 0, 1, 1, 0, 2 ],
1, −1, 2, 0, 1, 0, 1, 2 ],
1, −1, 2, 0, 1, 1, 1, 3 ],
1, 0, 0, 0, 0, 0, 1, 1 ],
1, 0, 0, 1, 0, 0, 0, 1 ],
1, 0, 1, 0, 0, 0, 1, 2 ],
1, 0, 1, 0, 0, 1, 1, 2 ],
1, 0, 1, 0, 1, 0, 1, 2 ],
1, 0, 1, 1, 0, 0, 0, 2 ],
1, 0, 1, 1, 1, 0, 0, 2 ],
1, 1, 0, 1, 0, −1, 0, 1 ],
1, 1, 0, 1, 0, 0, 0, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 1, −1, 0, 1, 1, 1 ],
0, −1, 1, −1, 1, 0, 1, 1 ],
0, −1, 1, −1, 1, 1, 1, 1 ],
0, −1, 1, 0, 0, 0, 1, 1 ],
0, −1, 1, 0, 0, 1, 1, 1 ],
0, −1, 1, 0, 1, 0, 1, 1 ],
0, 0, −1, 0, −1, 0, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, −1, 1, 0, 0, 0 ],
0, 0, 0, 0, −1, 0, 1, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 1, −1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 1, −1, 0, −1, 0, −1, −1 ],
0, 1, −1, 0, 0, −1, −1, −1 ],
0, 1, −1, 0, 0, 0, −1, −1 ],
0, 1, −1, 1, −1, −1, −1, −1 ],
0, 1, −1, 1, −1, 0, −1, −1 ],
0, 1, −1, 1, 0, −1, −1, −1 ],
0, 1, −1, 1, 0, 0, −1, 0 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 0, 1, −1, −1, 0, 0 ],
0, 1, 0, 1, −1, 0, 0, 1 ],
0, 1, 0, 1, 0, −1, 0, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
0, 2, −1, 1, −1, −1, −1, 0 ],
0, 2, −1, 1, 0, −1, −1, 0 ],
1, −1, 1, −1, 0, 1, 1, 1 ],
1, −1, 1, 0, 0, 0, 1, 1 ],
1, −1, 1, 0, 0, 1, 1, 2 ],
1, −1, 1, 0, 1, 0, 1, 2 ],
1, −1, 1, 0, 1, 1, 1, 2 ],
1, −1, 2, 0, 1, 1, 0, 2 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 1, 0, 1 ],
1, 0, 1, 0, 0, 0, 0, 1 ],
1, 0, 1, 0, 0, 1, 0, 1 ],
1, 0, 1, 0, 1, 0, 0, 1 ],
1, 0, 1, 0, 1, 1, 0, 2 ],
1, 0, 1, 1, 0, 0, 1, 2 ],
1, 1, 0, 0, 0, 0, 0, 1 ],
1, 1, 0, 1, 0, 0, −1, 1 ],
1, 1, 1, 1, 0, 0, 0, 2 ],
∗
7
• I ≡ P139 :
6
5
4
3
2
1
258
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 1, −1, 1, 0, 0, 0 ],
0, −1, 1, −1, 1, 1, 0, 0 ],
0, −1, 1, 0, 0, 0, 0, 0 ],
0, −1, 1, 0, 0, 1, 0, 0 ],
0, −1, 1, 0, 1, 0, 0, 0 ],
0, −1, 1, 0, 1, 1, 0, 1 ],
0, 0, −1, 0, 0, −1, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, −1, 1, 0, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, 0, 1, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 1, −1, 0, −1, 0, 0, −1 ],
0, 1, −1, 0, 0, −1, 0, −1 ],
0, 1, −1, 0, 0, 0, −1, 0 ],
0, 1, −1, 1, −1, −1, 0, −1 ],
0, 1, −1, 1, −1, 0, −1, 0 ],
0, 1, −1, 1, 0, −1, −1, 0 ],
0, 1, 0, 0, −1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 1, −1, 0, −1, 0 ],
0, 1, 0, 1, 0, −1, −1, 0 ],
0, 1, 0, 1, 0, 0, −1, 0 ],
0, 2, −2, 1, −1, −1, −1, −1 ],
0, 2, −1, 1, −1, −1, 0, 0 ],
0, 2, −1, 2, −1, −1, −1, 0 ],
1, −1, 1, −1, 1, 0, 1, 1 ],
1, −1, 1, 0, 0, 1, 0, 1 ],
1, −1, 1, 0, 1, 0, 0, 1 ],
1, −1, 1, 0, 1, 1, 0, 1 ],
1, −1, 2, 0, 0, 1, 1, 2 ],
1, −1, 2, 0, 1, 1, 1, 2 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 0, 0, 0, 1, 0, 0, 1 ],
1, 0, 1, 0, 0, 0, 1, 1 ],
1, 0, 1, 0, 0, 1, 0, 2 ],
1, 0, 1, 0, 1, 0, 0, 2 ],
1, 0, 1, 1, 0, 0, 0, 1 ],
1, 0, 1, 1, 0, 1, 0, 2 ],
1, 1, 0, 1, −1, 0, 0, 1 ],
1, 1, 0, 1, 0, 0, 0, 1 ],
2, −1, 2, 0, 1, 1, 1, 3 ]





CI =








b I =
Cox




0
0
0
1
0
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
−1
0
0
1
0
0
1
0
0
−1
−1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
−1
0
0
0
0
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
1
1
1
0
1
1
1
0
















BI =



0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
−1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
−1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
−1
0
−1
0
0
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
−1
−1
0
−1
0
0











0
−1
0
0
0
0
0
0
0
0
0
1
0
0
0
−1
Number of sincere Tits roots of poset I sI = 12.
Table of roots of qbI
[ −2,−1,−1,−2, 1, 2, 1,−1 ],
[ −1,−1,−1,−2, 1, 1, 1,−1 ],
[ 1, 1, 1, 1,−1,−1,−1, 1 ],
[ 1, 1, 2, 2,−1,−2,−1, 1 ],
[ −1, −1, −1, −2, 0, 1, 1, −2 ],
[ −1, −1, −1, −2, 0, 2, 1, −1 ],
[ −1, −1, −1, −1, 0, 1, 1, −1 ],
[ −1, −1, −1, −1, 1, 2, 0, −1 ],
[ −1, −1, −1, −1, 2, 2, 0, 0 ],
[ −1, −1, 0, −1, 0, 1, 0, −1 ],
[ −1, −1, 0, −1, 1, 1, 0, −1 ],
[ −1, −1, 0, −1, 1, 2, 0, 0 ],
[ −1, 0, −1, −1, 0, 0, 1, −1 ],
[ −1, 0, −1, −1, 0, 1, 1, 0 ],
[ −1, 0, −1, −1, 1, 1, 1, 0 ],
[ −1, 0, 0, −1, −1, 0, 1, −1 ],
[ −1, 0, 0, −1, 0, 0, 1, 0 ],
[ −1, 0, 0, −1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, −1, −1, −2, 0, 1, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 1, −1 ],
[ 0, −1, −1, −1, 1, 1, 0, 0 ],
[ 0, −1, −1, 0, 1, 1, 0, 0 ],
[ 0, −1, 0, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 0, 0 ],
[ 0, 0, −1, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, −1, 0, 0, 1, 0 ],
[ 0, 0, −1, −1, 0, 1, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 0, 0, 0 ],
[ 0, 0, −1, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, −1, −1, 0, 1, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, −1, 0 ],
[ −1,−2,−1,−2, 1, 2, 1,−1 ],
[ −1,−1,−1,−2, 1, 2, 1,−1 ],
[ 1, 1, 1, 2,−1,−2,−1, 1 ],
[ 1, 2, 1, 2,−1,−2,−1, 1 ],
[ −1, −1, −1, −2, 0, 1, 1, −1 ],
[ −1, −1, −1, −2, 1, 2, 0, −1 ],
[ −1, −1, −1, −1, 1, 1, 0, −1 ],
[ −1, −1, −1, −1, 1, 2, 0, 0 ],
[ −1, −1, 0, −2, 0, 1, 1, −1 ],
[ −1, −1, 0, −1, 0, 1, 1, −1 ],
[ −1, −1, 0, −1, 1, 1, 0, 0 ],
[ −1, −1, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, −1, −1, 0, 1, 0, −1 ],
[ −1, 0, −1, −1, 1, 1, 0, −1 ],
[ −1, 0, −1, −1, 1, 2, 0, 0 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, −1, 0, 1, 0, −1 ],
[ −1, 0, 0, −1, 1, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 1, 1, −1, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 1, 0 ],
[ 0, −1, −1, −1, 1, 1, 1, 0 ],
[ 0, −1, 0, −1, −1, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, −1, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, −1, 0, 1, 0, −1 ],
[ 0, 0, −1, −1, 1, 1, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 1, 1, −1, 0 ],
[ 0, 0, 0, −1, −1, −1, 1, −1 ],
[ 0, 0, 0, −1, −1, 0, 1, 0 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, −1, 1, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
259
[ −1,−1,−2,−2, 1, 2, 1,−1 ],
[ −1,−1,−1,−1, 1, 1, 1,−1 ],
[ 1, 1, 1, 2,−1,−1,−1, 1 ],
[ 2, 1, 1, 2,−1,−2,−1, 1 ],
[ −1, −1, −1, −2, 0, 1, 2, −1 ],
[ −1, −1, −1, −2, 1, 2, 1, 0 ],
[ −1, −1, −1, −1, 1, 1, 1, 0 ],
[ −1, −1, −1, −1, 1, 2, 1, 0 ],
[ −1, −1, 0, −1, 0, 0, 1, −1 ],
[ −1, −1, 0, −1, 0, 1, 1, 0 ],
[ −1, −1, 0, −1, 1, 1, 1, 0 ],
[ −1, 0, −1, −2, 0, 1, 1, −1 ],
[ −1, 0, −1, −1, 0, 1, 1, −1 ],
[ −1, 0, −1, −1, 1, 1, 0, 0 ],
[ −1, 0, −1, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, −1, 0, 0, 1, −1 ],
[ −1, 0, 0, −1, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 0 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, 0, 1, 0, −1 ],
[ 0, −1, −1, −1, 1, 1, 0, −1 ],
[ 0, −1, −1, −1, 1, 2, 0, 0 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 1, 0, −1 ],
[ 0, −1, 0, −1, 1, 1, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, 1, 1, −1, 0 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, 0, 0, 1, −1 ],
[ 0, 0, −1, −1, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, 1, 1, 0, 0 ],
[ 0, 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, −1, −1, 1, 0 ],
[ 0, 0, 0, 0, −1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, −1, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],











[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, 0, 0,
0, 0, 0,
0, 0, 0,
0, 0, 0,
0, 0, 0,
0, 0, 1,
0, 0, 1,
0, 0, 1,
0, 0, 1,
0, 0, 1,
0, 1, −1,
0, 1, 0,
0, 1, 0,
0, 1, 0,
0, 1, 0,
0, 1, 0,
0, 1, 1,
0, 1, 1,
0, 1, 1,
1, −1, 0,
1, 0, 0,
1, 0, 0,
1, 0, 0,
1, 0, 0,
1, 0, 0,
1, 0, 1,
1, 0, 1,
1, 0, 1,
1, 0, 1,
1, 1, 0,
1, 1, 0,
1, 1, 0,
1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1, 1,
0, 1, 0, −1,
0, 1, 1, −1,
1, 0, −1, 0,
1, 0, 0, 0,
1, 1, 0, 0,
0, −1, −1, 0,
0, 0, −1, 0,
0, 0, 0, 0,
1, 0, −1, 0,
1, 0, 0, −1,
0, 0, 0, 0,
0, −1, −1, 1,
0, 0, 0, −1,
1, −1, −1, 0,
1, 0, −1, 0,
1, 0, 0, 0,
1, −1, −2, 0,
1, −1, −1, 0,
1, 0, −1, 0,
0, 0, 0, 0,
0, −1, −1, 0,
0, 0, −1, 0,
0, 0, 0, 0,
1, 0, −1, 0,
1, 0, 0, −1,
0, −1, −1, 0,
1, −1, −1, 0,
1, 0, −1, −1,
2, 0, −1, −1,
1, −1, −1, −1,
1, 0, −1, −1,
1, 0, 0, −1,
1, −1, −2, −1,
1, −1, −1, −1,
2, −1, −2, −1,
2, 0, −1, −2,
0 ],
0 ],
0 ],
1 ],
1 ],
0 ],
0 ],
1 ],
0 ],
1 ],
0 ],
0 ],
0 ],
0 ],
1 ],
1 ],
0 ],
1 ],
1 ],
0 ],
0 ],
0 ],
1 ],
0 ],
1 ],
0 ],
0 ],
1 ],
1 ],
0 ],
0 ],
1 ],
0 ],
0 ],
0 ],
1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 1,
0, 1,
0, 1,
0, 1,
0, 1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
1, 1,
0, −1,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 1,
0, 1,
0, 1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
1, 1,
1, 1,
0, 1, 0, 0, 0 ],
0, 1, 1, −1, 1 ],
1, 0, 0, −1, 0 ],
1, 1, 0, −1, 0 ],
1, 1, 1, −1, 1 ],
0, −1, −1, 1, 0 ],
0, 0, 0, −1, 0 ],
1, −1, −1, 0, 0 ],
1, 0, −1, 0, 1 ],
1, 0, 0, 0, 1 ],
0, −1, −1, 0, −1 ],
0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0 ],
1, 0, −1, −1, 0 ],
1, 0, 0, −1, 0 ],
1, 1, 0, −1, 1 ],
1, −1, −1, −1, 0 ],
1, 0, −1, −1, 0 ],
1, 0, 0, −1, 1 ],
0, 0, 0, 0, 0 ],
0, −1, −1, 1, 0 ],
0, 0, 0, −1, 0 ],
1, −1, −1, 0, 0 ],
1, 0, −1, 0, 1 ],
1, 0, 0, 0, 1 ],
1, −1, −2, 0, 0 ],
1, −1, −1, 0, 1 ],
1, 0, −1, 0, 1 ],
0, −1, −1, 0, 0 ],
1, −1, −1, 0, 0 ],
1, 0, −1, −1, 1 ],
2, 0, −1, −1, 1 ],
1, −1, −2, 0, 0 ],
1, −1, −1, 0, 1 ],
2, −1, −2, 0, 1 ],
2, 0, −1, −1, 1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
1,
1,
1,
0,
0,
0,
1,
1,
1,
1,
1,
0, 1, 0, 0, 1 ],
0, 1, 1, 0, 1 ],
1, 0, 0, 0, 0 ],
1, 1, 0, −1, 1 ],
0, −1, −1, 0, −1 ],
0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0 ],
1, 0, −1, −1, 0 ],
1, 0, 0, −1, 0 ],
1, 1, 0, −1, 1 ],
0, −1, −1, 0, 0 ],
0, 0, −1, 0, 0 ],
0, 0, 0, 0, 1 ],
1, 0, −1, 0, 0 ],
1, 0, 0, −1, 1 ],
0, −1, −1, 0, 0 ],
1, −1, −1, 0, 0 ],
1, 0, −1, −1, 1 ],
2, 0, −1, −1, 1 ],
0, −1, −1, 0, −1 ],
0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0 ],
1, 0, −1, −1, 0 ],
1, 0, 0, −1, 0 ],
1, 1, 0, −1, 1 ],
1, −1, −1, −1, 0 ],
1, 0, −1, −1, 0 ],
1, 0, 0, −1, 1 ],
1, −1, −2, 0, 0 ],
1, −1, −1, 0, 1 ],
1, 0, −1, 0, 1 ],
1, −2, −2, 0, 0 ],
1, −1, −2, 0, 1 ],
1, 0, −1, −1, 1 ],
2, 0, −2, −1, 1 ],
2, 0, −1, −1, 2 ]
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
∗
• I ≡ P140 :
7
6
4
3
5
2
1





CI =








b I =
Cox




0
0
0
1
1
0
0
−1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
−1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
1
−1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
−1
−1
0
0
−1
0
0
1
1
1
1
1
1
1
1
1
















b
CI =



1
1
1
1
1
1
1
−1
1
1
1
0
0
1
1
0
















BI =



260
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
−1
1
1
1
0
0
1
0
−1
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
0
0
1
0
0
−1











−1
−1
−1
0
0
0
−1
0
1
1
1
0
0
0
0
−1











Number of sincere Tits roots of poset I sI = 18.
Table of roots of qbI
[ −2,−1,−1,−2,−1, 1, 2,−2 ],
[ −1,−1,−1,−2,−1, 1, 1,−2 ],
[ −1,−1,−1,−1,−1, 1, 1,−2 ],
[ 1, 1, 1, 1, 1,−1,−2, 1 ],
[ 1, 1, 1, 2, 1,−1,−2, 1 ],
[ 1, 1, 2, 2, 1,−1,−2, 2 ],
[ −1, −1, −1, −2, −2, 0, 1, −3 ],
[ −1, −1, −1, −2, −1, 0, 2, −2 ],
[ −1, −1, −1, −1, 0, 1, 1, −1 ],
[ −1, −1, −1, −1, 0, 2, 2, 0 ],
[ −1, −1, 0, −1, −1, 0, 1, −2 ],
[ −1, −1, 0, −1, 0, 0, 1, −1 ],
[ −1, −1, 0, −1, 0, 1, 2, 0 ],
[ −1, 0, −1, −1, −1, 0, 0, −2 ],
[ −1, 0, −1, −1, −1, 1, 1, −1 ],
[ −1, 0, −1, −1, 0, 1, 1, 0 ],
[ −1, 0, 0, −1, −1, −1, 0, −2 ],
[ −1, 0, 0, −1, −1, 0, 1, −1 ],
[ −1, 0, 0, −1, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
[ 0, −1, −1, −2, −1, 0, 1, −2 ],
[ 0, −1, −1, −1, −1, 0, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 1, −1 ],
[ 0, −1, −1, 0, 0, 1, 1, 0 ],
[ 0, −1, 0, −1, −1, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, 0, −1, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, −1, −1, −1, −1, 0, −2 ],
[ 0, 0, −1, −1, −1, 0, 1, −1 ],
[ 0, 0, −1, −1, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 1, 0, 0 ],
[ 0, 0, −1, 0, 1, 1, 1, 1 ],
[ 0, 0, 0, −1, −1, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, −1, −1, −1, −2 ],
[ 0, 0, 0, 0, −1, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, −1, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, −1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, −1, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 0, 2 ],
[ 0, 0, 1, 0, 0, −1, −1, −1 ],
[ 0, 0, 1, 0, 0, 0, −1, 0 ],
[ 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, −1, 1 ],
[ 0, 0, 1, 1, 1, 0, 0, 1 ],
[ 0, 1, −1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, −1, −1, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, −1, −1, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 1, 0, 0, 2 ],
[ 0, 1, 1, 1, 0, −1, −2, 0 ],
[ 0, 1, 1, 1, 0, 0, −1, 1 ],
[ 0, 1, 1, 1, 1, 0, −1, 2 ],
[ −1,−2,−1,−2,−1, 1, 2,−2 ],
[ −1,−1,−1,−2,−1, 1, 2,−2 ],
[ −1,−1,−1,−1,−1, 1, 1,−1 ],
[ 1, 1, 1, 1, 1,−1,−1, 1 ],
[ 1, 1, 1, 2, 1,−1,−2, 2 ],
[ 1, 2, 1, 2, 1,−1,−2, 2 ],
[ −1, −1, −1, −2, −1, 0, 1, −3 ],
[ −1, −1, −1, −2, 0, 1, 2, −1 ],
[ −1, −1, −1, −1, 0, 1, 2, −1 ],
[ −1, −1, 0, −2, −1, 0, 1, −2 ],
[ −1, −1, 0, −1, −1, 0, 1, −1 ],
[ −1, −1, 0, −1, 0, 1, 1, −1 ],
[ −1, −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, −1, −1, −1, 0, 1, −2 ],
[ −1, 0, −1, −1, 0, 0, 1, −1 ],
[ −1, 0, −1, −1, 0, 1, 2, 0 ],
[ −1, 0, 0, −1, −1, 0, 0, −2 ],
[ −1, 0, 0, −1, 0, 0, 0, −1 ],
[ −1, 0, 0, −1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, −1, 0, 0, −2 ],
[ 0, −1, −1, −1, −1, 1, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, −1, −1, −1, 0, −2 ],
[ 0, −1, 0, −1, −1, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[ 0, −1, 0, 0, 0, 1, 0, 0 ],
[ 0, −1, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, −1, −1, −1, 0, 0, −2 ],
[ 0, 0, −1, −1, 0, 0, 0, −1 ],
[ 0, 0, −1, −1, 0, 1, 1, 0 ],
[ 0, 0, −1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, 0, 0, 1, 1, 0 ],
[ 0, 0, 0, −1, −1, −1, −1, −2 ],
[ 0, 0, 0, −1, −1, 0, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, −1, −1, −1, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, −1, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, −1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 1, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 1, 2 ],
[ 0, 0, 1, 0, 0, −1, −1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, −1, −1, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 1, 0, 0, 2 ],
[ 0, 1, 0, 0, −1, −1, −1, −1 ],
[ 0, 1, 0, 0, 0, −1, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 0, −1, 0 ],
[ 0, 1, 0, 1, 1, 0, −1, 1 ],
[ 0, 1, 0, 1, 1, 1, 0, 2 ],
[ 0, 1, 1, 1, 0, −1, −1, 0 ],
[ 0, 1, 1, 1, 1, −1, −1, 1 ],
[ 0, 1, 1, 1, 1, 0, 0, 2 ],
261
[ −1,−1,−2,−2,−1, 1, 2,−2 ],
[ −1,−1,−1,−2,−1, 1, 2,−1 ],
[ −1,−1,−1,−1,−1, 1, 2,−1 ],
[ 1, 1, 1, 1, 1,−1,−1, 2 ],
[ 1, 1, 1, 2, 1,−1,−1, 2 ],
[ 2, 1, 1, 2, 1,−1,−2, 2 ],
[ −1, −1, −1, −2, −1, 0, 1, −2 ],
[ −1, −1, −1, −1, −1, 0, 1, −2 ],
[ −1, −1, −1, −1, 0, 1, 2, 0 ],
[ −1, −1, 0, −1, −1, 0, 0, −2 ],
[ −1, −1, 0, −1, −1, 1, 1, −1 ],
[ −1, −1, 0, −1, 0, 1, 1, 0 ],
[ −1, 0, −1, −2, −1, 0, 1, −2 ],
[ −1, 0, −1, −1, −1, 0, 1, −1 ],
[ −1, 0, −1, −1, 0, 1, 1, −1 ],
[ −1, 0, −1, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, −1, −1, 0, 0, −1 ],
[ −1, 0, 0, −1, 0, 0, 1, −1 ],
[ −1, 0, 0, 0, −1, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, −1, −1, −1, 0, 1, −2 ],
[ 0, −1, −1, −1, 0, 0, 1, −1 ],
[ 0, −1, −1, −1, 0, 1, 2, 0 ],
[ 0, −1, 0, −1, −1, 0, 0, −2 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 1, 1, 0 ],
[ 0, −1, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, −1, −1, −1, 0, 0, −1 ],
[ 0, 0, −1, −1, 0, 0, 1, −1 ],
[ 0, 0, −1, 0, −1, 0, 0, −1 ],
[ 0, 0, −1, 0, 0, 0, 1, 0 ],
[ 0, 0, −1, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, −1, −1, −1, 0, −2 ],
[ 0, 0, 0, −1, 0, −1, 0, −1 ],
[ 0, 0, 0, −1, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, −1, −1, 0, −1 ],
[ 0, 0, 0, 0, −1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, −1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, −1 ],
[ 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 1, 1 ],
[ 0, 0, 0, 0, 1, 1, 1, 2 ],
[ 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 0, 1, 0, −1, −1, −1, −1 ],
[ 0, 0, 1, 0, 0, −1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 0, −1, 0 ],
[ 0, 0, 1, 1, 1, 0, −1, 1 ],
[ 0, 0, 1, 1, 1, 1, 0, 2 ],
[ 0, 1, 0, 0, 0, −1, −1, −1 ],
[ 0, 1, 0, 0, 0, 0, −1, 0 ],
[ 0, 1, 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 1, 0, 0, −1, 1 ],
[ 0, 1, 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 1, 0, 0, −1, −1, 0 ],
[ 0, 1, 1, 1, 0, −1, −1, 1 ],
[ 0, 1, 1, 1, 1, 0, −1, 1 ],
[ 0, 1, 1, 2, 1, 0, −1, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
1, −1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
1, 1,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
0,
0,
0,
1,
1,
1,
0,
0,
0,
0,
1,
1,
0,
1,
1,
2,
1,
1,
1,
1,
1,
2,
0, 0, 0, 0 ],
0, −1, −1, −1 ],
0, 0, −1, 0 ],
1, 0, 0, 1 ],
0, 0, −1, 1 ],
1, 0, 0, 1 ],
0, −1, −1, 0 ],
0, −1, −1, 1 ],
1, 0, −1, 1 ],
1, 0, −1, 2 ],
0, −1, −1, 0 ],
1, −1, −1, 1 ],
1, 0, 0, 2 ],
0, −1, −2, 0 ],
1, 0, −1, 2 ],
1, 0, −1, 2 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1,
0, 0,
0, 0,
0, 0,
0, 0,
0, 0,
0, 1,
0, 1,
0, 1,
1, 0,
1, 0,
1, 0,
1, 0,
1, 1,
1, 1,
1, 1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
1,
1,
1,
1,
1,
1,
0,
1,
1,
2,
1,
2,
2,
0, 0, 0,
0, −1, −1,
0, 0, 0,
0, −1, −1,
0, 0, 0,
1, 0, 0,
0, −1, −2,
0, 0, −1,
1, 0, −1,
0, −1, −1,
0, −1, −1,
1, 0, −1,
1, 0, −1,
0, −1, −2,
0, −1, −2,
1, 0, −1,
0 ],
0 ],
0 ],
0 ],
1 ],
2 ],
0 ],
1 ],
2 ],
0 ],
1 ],
1 ],
2 ],
1 ],
1 ],
3 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
0,
1,
1,
1,
0,
0,
0,
1,
1,
1,
1,
0, −1, −1, −1, −1 ],
0, 0, −1, 0, 0 ],
0, 0, 0, 0, 1 ],
1, 0, 0, −1, 0 ],
1, 1, 0, −1, 1 ],
1, 1, 1, 0, 2 ],
1, 0, −1, −1, 0 ],
1, 1, −1, −1, 1 ],
1, 1, 0, 0, 2 ],
1, 0, −1, −2, 0 ],
1, 0, 0, −1, 1 ],
1, 1, 0, −1, 2 ],
1, 0, −2, −2, 0 ],
1, 0, −1, −1, 1 ],
2, 1, 0, −2, 2 ],
2, 2, 0, −1, 3 ]
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
−1
−1
−1
−1
−1
−1
−1
1
1
1
1
1
1
0
1
−1
1
0
0
0
0
0
0
0
0
−1
−1
−1
0
0
−1
0
∗
7
6
5
4
• I ≡ P141 :
3
2
1





CI =








b I =
Cox




0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
−1
−1
−1
0
0
0
0
0
1
1
1
1
1
1
1
1
















bI =
C




1
1
1
1
1
1
1
−1
















BI =



0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0











1
1
1
1
0
1
0
−1











Number of sincere Tits roots of poset I sI = 12.
Table of roots of qbI
[ −1, 1, 1, 1, 1,−1,−1, 1 ],
[ −1, 1, 1, 2, 2,−1,−2, 1 ],
[ 1,−2,−1,−1,−2, 1, 2,−1 ],
[ 1,−1,−1,−1,−2, 1, 1,−1 ],
[ −2, 1, 1, 1, 2, 0, −1, 1 ],
[ −1, 0, 0, −1, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 1 ],
[ −1, 0, 0, 0, 1, 1, 0, 1 ],
[ −1, 1, 1, 1, 2,−1,−2, 1 ],
[ −1, 1, 2, 1, 2,−1,−2, 1 ],
[ 1,−1,−2,−1,−2, 1, 2,−1 ],
[ 1,−1,−1,−1,−2, 1, 2,−1 ],
[ −1, −1, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 1, 1, 1 ],
262
[ −1, 1, 1, 1, 2,−1,−1, 1 ],
[ −1, 2, 1, 1, 2,−1,−2, 1 ],
[ 1,−1,−1,−2,−2, 1, 2,−1 ],
[ 1,−1,−1,−1,−1, 1, 1,−1 ],
[ −1, 0, −1, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 0, 1, 1, 0 ],
[ −1, 0, 0, 0, 1, 1, 0, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, 0, 1, 1, 0, −1, 0 ],
−1, 0, 0, 1, 1, 1, 0, 1 ],
−1, 0, 1, 0, 1, 0, 0, 0 ],
−1, 0, 1, 1, 1, −1, −1, 0 ],
−1, 0, 1, 1, 1, 0, 0, 1 ],
−1, 1, 0, 0, 1, 0, −1, 0 ],
−1, 1, 0, 0, 1, 1, 0, 1 ],
−1, 1, 0, 1, 1, 0, −1, 1 ],
−1, 1, 1, 0, 1, −1, −1, 0 ],
−1, 1, 1, 0, 1, 0, 0, 1 ],
−1, 1, 1, 1, 1, −1, −1, 0 ],
−1, 1, 1, 1, 2, 0, −2, 1 ],
0, −1, −1, −1, −2, 1, 2, −1 ],
0, −1, −1, −1, −1, 1, 2, 0 ],
0, −1, −1, 0, −1, 1, 1, −1 ],
0, −1, −1, 0, 0, 1, 1, 0 ],
0, −1, 0, −1, −1, 1, 1, 0 ],
0, −1, 0, 0, −1, 0, 0, −1 ],
0, −1, 0, 0, −1, 1, 1, 0 ],
0, −1, 0, 0, 0, 0, 1, 0 ],
0, −1, 0, 0, 0, 1, 1, 1 ],
0, 0, −1, −1, −1, 0, 1, −1 ],
0, 0, −1, −1, −1, 1, 2, 0 ],
0, 0, −1, 0, −1, 0, 1, −1 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 1, 0, 0 ],
0, 0, −1, 1, 0, 0, 0, 0 ],
0, 0, 0, −1, −1, 0, 1, 0 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, −1, 0, 1, 1, 0 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, 0, −1, −1, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 0, 1, 1, 0, 1 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 0, 1, 1, 0, −1, 1 ],
0, 0, 1, 0, 0, −1, −1, −1 ],
0, 0, 1, 0, 0, 0, −1, 0 ],
0, 0, 1, 0, 1, −1, −1, 0 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 0, 1, 1, 1, −1, −1, 0 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, −1, −1, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 0, 1, 0, −1, 0 ],
0, 1, 0, 1, 0, −1, −1, 0 ],
0, 1, 0, 1, 1, −1, −1, 1 ],
0, 1, 1, 0, 1, −1, −2, 0 ],
0, 1, 1, 0, 1, 0, −1, 1 ],
0, 1, 1, 1, 1, −1, −2, 1 ],
1, −1, −1, −1, −2, 0, 1, −2 ],
1, −1, −1, −1, −2, 1, 2, 0 ],
1, −1, −1, −1, −1, 1, 2, 0 ],
1, −1, −1, 0, −1, 0, 1, −1 ],
1, −1, 0, −1, −2, 0, 1, −1 ],
1, −1, 0, −1, −1, 0, 1, 0 ],
1, −1, 0, 0, −1, 0, 0, −1 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, −1, −1, −1, 0, 1, −1 ],
1, 0, −1, 0, −1, −1, 0, −1 ],
1, 0, −1, 0, −1, 0, 1, 0 ],
1, 0, 0, −1, −1, 0, 0, −1 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, −1, −1, 0, 0 ],
1, 0, 0, 0, 0, −1, −1, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 0, 1, 0, 0, −1, −1, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
−1, 0, 0, 1, 1, 0, 0, 0 ],
−1, 0, 1, 0, 0, 0, 0, 0 ],
−1, 0, 1, 0, 1, 0, 0, 1 ],
−1, 0, 1, 1, 1, 0, −1, 0 ],
−1, 0, 1, 1, 2, 0, −1, 1 ],
−1, 1, 0, 0, 1, 0, 0, 0 ],
−1, 1, 0, 1, 1, −1, −1, 0 ],
−1, 1, 0, 1, 1, 0, 0, 1 ],
−1, 1, 1, 0, 1, 0, −1, 0 ],
−1, 1, 1, 0, 2, 0, −1, 1 ],
−1, 1, 1, 1, 1, 0, −1, 1 ],
−1, 1, 1, 1, 2, 0, −1, 1 ],
0, −1, −1, −1, −1, 1, 1, −1 ],
0, −1, −1, −1, −1, 2, 2, 0 ],
0, −1, −1, 0, −1, 1, 1, 0 ],
0, −1, 0, −1, −1, 0, 1, −1 ],
0, −1, 0, −1, −1, 1, 2, 0 ],
0, −1, 0, 0, −1, 0, 1, −1 ],
0, −1, 0, 0, 0, 0, 0, −1 ],
0, −1, 0, 0, 0, 1, 0, 0 ],
0, −1, 0, 1, 0, 0, 0, 0 ],
0, 0, −1, −1, −1, 1, 1, −1 ],
0, 0, −1, −1, 0, 1, 1, 0 ],
0, 0, −1, 0, −1, 0, 1, 0 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, −1, 0, 0, 1, 1, 0 ],
0, 0, 0, −1, −1, 0, 0, −1 ],
0, 0, 0, −1, −1, 1, 1, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, −1, 0, 1, 1, 1 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, −1, −1, −1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 0, 1, 1, −1, −1, 0 ],
0, 0, 0, 1, 1, 0, 0, 1 ],
0, 0, 1, 0, 0, −1, −1, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 1, 0, −1, 0 ],
0, 0, 1, 1, 0, −1, −1, 0 ],
0, 0, 1, 1, 1, −1, −1, 1 ],
0, 1, 0, −1, 0, 0, 0, 0 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 0, 1, 0, −1, 1 ],
0, 1, 0, 1, 1, −1, −2, 0 ],
0, 1, 0, 1, 1, 0, −1, 1 ],
0, 1, 1, 0, 1, −1, −1, 0 ],
0, 1, 1, 1, 1, −2, −2, 0 ],
0, 1, 1, 1, 1, −1, −1, 1 ],
1, −1, −1, −1, −2, 0, 1, −1 ],
1, −1, −1, −1, −1, 0, 1, −1 ],
1, −1, −1, 0, −2, 0, 1, −1 ],
1, −1, −1, 0, −1, 0, 1, 0 ],
1, −1, 0, −1, −1, 0, 0, −1 ],
1, −1, 0, −1, −1, 1, 1, 0 ],
1, −1, 0, 0, −1, 0, 0, 0 ],
1, 0, −1, −1, −2, 0, 1, −1 ],
1, 0, −1, −1, −1, 0, 1, 0 ],
1, 0, −1, 0, −1, 0, 0, −1 ],
1, 0, −1, 0, 0, 0, 0, 0 ],
1, 0, 0, −1, −1, 0, 0, 0 ],
1, 0, 0, 0, −1, −1, −1, −1 ],
1, 0, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 1, 0, 0, 0, −1, −1, 0 ],
263
[
[
[
[
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[
[
[
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[
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[
[
[
[
[
[
−1, 0, 0, 1, 1, 0, 0, 1 ],
−1, 0, 1, 0, 1, 0, −1, 0 ],
−1, 0, 1, 0, 1, 1, 0, 1 ],
−1, 0, 1, 1, 1, 0, −1, 1 ],
−1, 1, 0, 0, 0, 0, 0, 0 ],
−1, 1, 0, 0, 1, 0, 0, 1 ],
−1, 1, 0, 1, 1, 0, −1, 0 ],
−1, 1, 0, 1, 2, 0, −1, 1 ],
−1, 1, 1, 0, 1, 0, −1, 1 ],
−1, 1, 1, 1, 1, −1, −2, 0 ],
−1, 1, 1, 1, 2, −1, −2, 0 ],
−1, 1, 1, 1, 2, 0, −1, 2 ],
0, −1, −1, −1, −1, 1, 2, −1 ],
0, −1, −1, 0, −1, 0, 1, −1 ],
0, −1, −1, 0, −1, 1, 2, 0 ],
0, −1, 0, −1, −1, 1, 1, −1 ],
0, −1, 0, −1, 0, 1, 1, 0 ],
0, −1, 0, 0, −1, 0, 1, 0 ],
0, −1, 0, 0, 0, 0, 0, 0 ],
0, −1, 0, 0, 0, 1, 1, 0 ],
0, −1, 1, 0, 0, 0, 0, 0 ],
0, 0, −1, −1, −1, 1, 1, 0 ],
0, 0, −1, 0, −1, 0, 0, −1 ],
0, 0, −1, 0, −1, 1, 1, 0 ],
0, 0, −1, 0, 0, 0, 1, 0 ],
0, 0, −1, 0, 0, 1, 1, 1 ],
0, 0, 0, −1, −1, 0, 1, −1 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 1, 0, 0 ],
0, 0, 0, 0, −1, −1, 0, −1 ],
0, 0, 0, 0, −1, 0, 1, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 1, 1 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, −1, −1, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 0, 1, 1, 0, −1, 0 ],
0, 0, 1, −1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, −1, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 1, 0, −1, 1 ],
0, 0, 1, 1, 1, −1, −2, 0 ],
0, 0, 1, 1, 1, 0, −1, 1 ],
0, 1, 0, 0, 0, −1, −1, −1 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 0, 0, 1, −1, −1, 0 ],
0, 1, 0, 0, 1, 0, 0, 1 ],
0, 1, 0, 1, 1, −1, −1, 0 ],
0, 1, 1, 0, 0, −1, −1, 0 ],
0, 1, 1, 0, 1, −1, −1, 1 ],
0, 1, 1, 1, 1, −1, −2, 0 ],
0, 1, 1, 1, 2, −1, −2, 1 ],
1, −1, −1, −1, −2, 0, 2, −1 ],
1, −1, −1, −1, −1, 1, 1, 0 ],
1, −1, −1, 0, −1, 0, 0, −1 ],
1, −1, −1, 0, −1, 1, 1, 0 ],
1, −1, 0, −1, −1, 0, 1, −1 ],
1, −1, 0, 0, −1, −1, 0, −1 ],
1, −1, 0, 0, −1, 0, 1, 0 ],
1, 0, −1, −1, −1, 0, 0, −1 ],
1, 0, −1, −1, −1, 1, 1, 0 ],
1, 0, −1, 0, −1, 0, 0, 0 ],
1, 0, 0, −1, −1, −1, 0, −1 ],
1, 0, 0, −1, −1, 0, 1, 0 ],
1, 0, 0, 0, −1, −1, 0, −1 ],
1, 0, 0, 0, 0, −1, −1, −1 ],
1, 0, 0, 0, 0, 0, −1, 0 ],
1, 0, 0, 1, 0, −1, −1, 0 ],
2, −1, −1, −1, −2, 0, 1, −1 ]
∗
7
6
• I ≡ P142 :
3
5
2
4
1





CI =








b
CoxI =



0
0
0
0
0
0
0
−1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
−1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
−1
















bI =
C




1
1
1
1
1
1
1
0
















BI =



0
1
1
0
1
1
1
0
0
−1
0
0
−1
0
0
0
0
0
1
0
0
0
0
0
−1
0
0
−1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
−1
−1
−1
−1
−1
−1
−1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0











1
1
0
1
1
1
1
−1
1
1
1
1
1
1
0
−1











Number of sincere Tits roots of poset I sI = 12.
Table of roots of qbI
[ −1,−2, 2,−1, 1, 1, 1, 1 ],
[ −1,−2, 2,−1, 2, 1, 1, 1 ],
[ 1, 1,−2, 1,−1,−1,−1,−1 ],
[ 1, 2,−2, 1,−1,−2,−1,−1 ],
[ −2, −1, 2, 0, 1, 1, 1, 1 ],
[ −1, −2, 2, 0, 1, 1, 1, 1 ],
[ −1, −1, 1, −1, 1, 1, 0, 0 ],
[ −1, −1, 1, 0, 0, 1, 0, 0 ],
[ −1, −1, 1, 0, 1, 0, 0, 0 ],
[ −1, −1, 1, 0, 1, 1, 0, 0 ],
[ −1, −1, 2, 0, 0, 1, 1, 1 ],
[ −1, −1, 2, 0, 1, 1, 1, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, 0 ],
[ −1, 0, 0, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 1, 0 ],
[ −1, 0, 1, 0, 0, 1, 0, 1 ],
[ −1, 0, 1, 0, 1, 0, 0, 1 ],
[ −1, 0, 1, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 1, 0, 1, 0, 1 ],
[ −1, 1, 0, 1, −1, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 0, 0 ],
[ 0, −2, 1, −2, 1, 1, 1, 0 ],
[ 0, −2, 1, −1, 1, 1, 0, 0 ],
[ 0, −2, 2, −1, 1, 1, 1, 1 ],
[ 0, −1, 0, −1, 0, 0, 1, 0 ],
[ 0, −1, 0, −1, 0, 1, 1, 0 ],
[ 0, −1, 0, −1, 1, 0, 1, 0 ],
[ −1,−2, 2,−1, 1, 1, 2, 1 ],
[ −1,−1, 1,−1, 1, 1, 1, 1 ],
[ 1, 1,−1, 1,−1,−1,−1,−1 ],
[ 1, 2,−2, 1,−1,−1,−2,−1 ],
[ −1, −2, 1, −1, 1, 1, 1, 0 ],
[ −1, −1, 1, −1, 0, 1, 1, 0 ],
[ −1, −1, 1, −1, 1, 1, 1, 0 ],
[ −1, −1, 1, 0, 0, 1, 1, 0 ],
[ −1, −1, 1, 0, 1, 0, 1, 0 ],
[ −1, −1, 1, 0, 1, 1, 0, 1 ],
[ −1, −1, 2, 0, 1, 0, 1, 1 ],
[ −1, −1, 2, 0, 1, 1, 1, 2 ],
[ −1, 0, 0, 0, 0, 0, 1, 0 ],
[ −1, 0, 0, 1, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 1, 1 ],
[ −1, 0, 1, 0, 0, 1, 1, 1 ],
[ −1, 0, 1, 0, 1, 0, 1, 1 ],
[ −1, 0, 1, 1, 0, 0, 0, 1 ],
[ −1, 0, 1, 1, 1, 0, 0, 1 ],
[ −1, 1, 0, 1, 0, −1, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, 0, 1 ],
[ 0, −2, 1, −1, 0, 1, 1, 0 ],
[ 0, −2, 1, −1, 1, 1, 1, 0 ],
[ 0, −1, 0, −1, 0, 0, 0, −1 ],
[ 0, −1, 0, −1, 0, 1, 0, −1 ],
[ 0, −1, 0, −1, 1, 0, 0, −1 ],
[ 0, −1, 0, −1, 1, 1, 0, 0 ],
264
[ −1,−2, 2,−1, 1, 2, 1, 1 ],
[ −1,−1, 2,−1, 1, 1, 1, 1 ],
[ 1, 2,−2, 1,−2,−1,−1,−1 ],
[ 1, 2,−2, 1,−1,−1,−1,−1 ],
[ −1, −2, 2, −1, 1, 1, 1, 0 ],
[ −1, −1, 1, −1, 1, 0, 1, 0 ],
[ −1, −1, 1, 0, 0, 0, 1, 0 ],
[ −1, −1, 1, 0, 0, 1, 1, 1 ],
[ −1, −1, 1, 0, 1, 0, 1, 1 ],
[ −1, −1, 1, 0, 1, 1, 1, 1 ],
[ −1, −1, 2, 0, 1, 1, 0, 1 ],
[ −1, 0, 0, 0, 0, 0, 0, −1 ],
[ −1, 0, 0, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 0, 0, 0, 0 ],
[ −1, 0, 1, 0, 0, 1, 0, 0 ],
[ −1, 0, 1, 0, 1, 0, 0, 0 ],
[ −1, 0, 1, 0, 1, 1, 0, 1 ],
[ −1, 0, 1, 1, 0, 0, 1, 1 ],
[ −1, 1, 0, 0, 0, 0, 0, 0 ],
[ −1, 1, 0, 1, 0, 0, −1, 0 ],
[ −1, 1, 1, 1, 0, 0, 0, 1 ],
[ 0, −2, 1, −1, 1, 0, 1, 0 ],
[ 0, −2, 1, −1, 1, 1, 1, 1 ],
[ 0, −1, 0, −1, 0, 0, 1, −1 ],
[ 0, −1, 0, −1, 0, 1, 0, 0 ],
[ 0, −1, 0, −1, 1, 0, 0, 0 ],
[ 0, −1, 0, 0, 0, 0, 0, −1 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 0, 0, 0, 0, 0, 0 ],
0, −1, 0, 0, 1, 0, 0, 0 ],
0, −1, 1, −1, 0, 1, 1, 0 ],
0, −1, 1, −1, 1, 0, 1, 0 ],
0, −1, 1, −1, 1, 1, 0, 1 ],
0, −1, 1, 0, 0, 0, 1, 0 ],
0, −1, 1, 0, 0, 1, 0, 1 ],
0, −1, 1, 0, 1, 0, 0, 1 ],
0, 0, −1, −1, 0, 0, 0, −1 ],
0, 0, −1, 0, 0, 0, −1, −1 ],
0, 0, 0, −1, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 1, 0, 0 ],
0, 0, 0, 0, −1, 0, 0, 0 ],
0, 0, 0, 0, 0, −1, 0, −1 ],
0, 0, 0, 0, 0, 0, −1, −1 ],
0, 0, 0, 0, 0, 0, 0, 1 ],
0, 0, 0, 0, 0, 1, −1, 0 ],
0, 0, 0, 0, 1, −1, 0, 0 ],
0, 0, 0, 0, 1, 0, 0, 1 ],
0, 0, 0, 1, 0, 0, −1, 0 ],
0, 0, 1, 0, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 1, 0, 1 ],
0, 1, −1, 0, −1, −1, 0, −1 ],
0, 1, −1, 0, −1, 0, 0, 0 ],
0, 1, −1, 0, 0, −1, 0, 0 ],
0, 1, −1, 0, 0, 0, 0, 0 ],
0, 1, −1, 1, −1, −1, 0, 0 ],
0, 1, −1, 1, −1, 0, 0, 0 ],
0, 1, −1, 1, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, −1, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 1 ],
0, 1, 0, 1, −1, 0, 0, 0 ],
0, 1, 0, 1, 0, −1, 0, 0 ],
0, 1, 0, 1, 0, 0, −1, 1 ],
0, 2, −1, 1, −1, −1, −1, −1 ],
0, 2, −1, 1, −1, 0, −1, 0 ],
1, −1, −1, −1, 0, 0, 0, −1 ],
1, −1, 0, −1, 0, 0, 1, 0 ],
1, −1, 0, 0, 0, 0, 0, 0 ],
1, 0, −1, −1, 0, 0, −1, −1 ],
1, 0, −1, 0, −1, −1, 0, −1 ],
1, 0, −1, 0, −1, 0, 0, 0 ],
1, 0, −1, 0, 0, −1, 0, 0 ],
1, 0, −1, 0, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, −1, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 1 ],
1, 1, −2, 0, −1, −1, 0, −1 ],
1, 1, −1, 0, −1, −1, −1, −1 ],
1, 1, −1, 0, −1, 0, −1, −1 ],
1, 1, −1, 0, 0, −1, −1, −1 ],
1, 1, −1, 0, 0, 0, −1, 0 ],
1, 1, −1, 1, −1, 0, −1, 0 ],
1, 2, −2, 1, −1, −1, −1, 0 ],
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 0, 0, 0, 0, 1, 0 ],
0, −1, 1, −1, 0, 0, 1, 0 ],
0, −1, 1, −1, 0, 1, 1, 1 ],
0, −1, 1, −1, 1, 0, 1, 1 ],
0, −1, 1, −1, 1, 1, 1, 1 ],
0, −1, 1, 0, 0, 0, 1, 1 ],
0, −1, 1, 0, 0, 1, 1, 1 ],
0, −1, 1, 0, 1, 0, 1, 1 ],
0, 0, −1, 0, −1, 0, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, −1 ],
0, 0, 0, −1, 0, 0, 0, 0 ],
0, 0, 0, −1, 1, 0, 0, 0 ],
0, 0, 0, 0, −1, 0, 1, 0 ],
0, 0, 0, 0, 0, −1, 0, 0 ],
0, 0, 0, 0, 0, 0, −1, 0 ],
0, 0, 0, 0, 0, 0, 1, 0 ],
0, 0, 0, 0, 0, 1, 0, 0 ],
0, 0, 0, 0, 1, 0, −1, 0 ],
0, 0, 0, 1, −1, 0, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 0 ],
0, 0, 1, 0, 0, 0, 0, 1 ],
0, 0, 1, 0, 1, 0, 0, 1 ],
0, 1, −1, 0, −1, 0, −1, −1 ],
0, 1, −1, 0, 0, −1, −1, −1 ],
0, 1, −1, 0, 0, 0, −1, −1 ],
0, 1, −1, 1, −1, −1, −1, −1 ],
0, 1, −1, 1, −1, 0, −1, −1 ],
0, 1, −1, 1, 0, −1, −1, −1 ],
0, 1, −1, 1, 0, 0, −1, 0 ],
0, 1, 0, 0, 0, 0, −1, 0 ],
0, 1, 0, 1, −1, −1, 0, 0 ],
0, 1, 0, 1, −1, 0, 0, 1 ],
0, 1, 0, 1, 0, −1, 0, 1 ],
0, 1, 0, 1, 0, 0, 0, 1 ],
0, 2, −1, 1, −1, −1, −1, 0 ],
0, 2, −1, 1, 0, −1, −1, 0 ],
1, −1, 0, −1, 0, 0, 0, −1 ],
1, −1, 0, −1, 0, 1, 0, 0 ],
1, 0, −1, −1, −1, 0, 0, −1 ],
1, 0, −1, −1, 0, 0, 0, −1 ],
1, 0, −1, 0, −1, 0, −1, −1 ],
1, 0, −1, 0, 0, −1, −1, −1 ],
1, 0, −1, 0, 0, 0, −1, −1 ],
1, 0, 0, −1, 0, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, −1, 0 ],
1, 1, −2, 0, −1, −1, −1, −2 ],
1, 1, −2, 0, −1, 0, −1, −1 ],
1, 1, −1, 0, −1, −1, 0, −1 ],
1, 1, −1, 0, −1, 0, −1, 0 ],
1, 1, −1, 0, 0, −1, −1, 0 ],
1, 1, −1, 1, −1, −1, −1, 0 ],
1, 1, −1, 1, 0, −1, −1, 0 ],
1, 2, −1, 1, −1, −1, −1, 0 ],
∗
• I ≡ P143 :
7
6
4
3
2
1
5
265
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
0, −1, 0, 0, 0, 1, 0, 0 ],
0, −1, 1, −1, 0, 1, 0, 0 ],
0, −1, 1, −1, 1, 0, 0, 0 ],
0, −1, 1, −1, 1, 1, 0, 0 ],
0, −1, 1, 0, 0, 0, 0, 0 ],
0, −1, 1, 0, 0, 1, 0, 0 ],
0, −1, 1, 0, 1, 0, 0, 0 ],
0, −1, 1, 0, 1, 1, 0, 1 ],
0, 0, −1, 0, 0, −1, 0, −1 ],
0, 0, −1, 0, 0, 0, 0, 0 ],
0, 0, 0, −1, 0, 0, 1, 0 ],
0, 0, 0, 0, −1, 0, 0, −1 ],
0, 0, 0, 0, −1, 1, 0, 0 ],
0, 0, 0, 0, 0, −1, 1, 0 ],
0, 0, 0, 0, 0, 0, 0, −1 ],
0, 0, 0, 0, 0, 0, 1, 1 ],
0, 0, 0, 0, 0, 1, 0, 1 ],
0, 0, 0, 0, 1, 0, 0, 0 ],
0, 0, 0, 1, 0, −1, 0, 0 ],
0, 0, 0, 1, 0, 0, 0, 1 ],
0, 0, 1, 0, 0, 0, 1, 1 ],
0, 0, 1, 1, 0, 0, 0, 1 ],
0, 1, −1, 0, −1, 0, 0, −1 ],
0, 1, −1, 0, 0, −1, 0, −1 ],
0, 1, −1, 0, 0, 0, −1, 0 ],
0, 1, −1, 1, −1, −1, 0, −1 ],
0, 1, −1, 1, −1, 0, −1, 0 ],
0, 1, −1, 1, 0, −1, −1, 0 ],
0, 1, 0, 0, −1, 0, 0, 0 ],
0, 1, 0, 0, 0, 0, 0, 0 ],
0, 1, 0, 1, −1, 0, −1, 0 ],
0, 1, 0, 1, 0, −1, −1, 0 ],
0, 1, 0, 1, 0, 0, −1, 0 ],
0, 2, −2, 1, −1, −1, −1, −1 ],
0, 2, −1, 1, −1, −1, 0, 0 ],
0, 2, −1, 2, −1, −1, −1, 0 ],
1, −1, 0, −1, 0, 0, 0, 0 ],
1, −1, 0, −1, 1, 0, 0, 0 ],
1, 0, −1, −1, 0, −1, 0, −1 ],
1, 0, −1, −1, 0, 0, 0, 0 ],
1, 0, −1, 0, −1, 0, 0, −1 ],
1, 0, −1, 0, 0, −1, 0, −1 ],
1, 0, −1, 0, 0, 0, −1, 0 ],
1, 0, 0, 0, −1, 0, 0, 0 ],
1, 0, 0, 0, 0, 0, 0, 0 ],
1, 1, −2, 0, −1, −1, −1, −1 ],
1, 1, −2, 0, 0, −1, −1, −1 ],
1, 1, −1, 0, −1, −1, 0, 0 ],
1, 1, −1, 0, −1, 0, 0, 0 ],
1, 1, −1, 0, 0, −1, 0, 0 ],
1, 1, −1, 1, −1, −1, 0, 0 ],
1, 2, −2, 0, −1, −1, −1, −1 ],
2, 1, −2, 0, −1, −1, −1, −1 ]





CI =








b I =
Cox




0
1
0
1
0
0
1
−1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
−1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0