... The Number of Solutions of X
2
=0 in Triangular Matrices Over GF(q)
Shalosh B. EKHAD
1
and Doron ZEILBERGER
1
Abstract: We prove an explicit formula for the number of n × n upper triangular matrices, ... matrix, is given by the polynomial C
n
(q), where,
C
2n
(q )=
j
2n
n − 3j
−
2n
n − 3j − 1
· q
n
2
−3j
2
−j
,
C
2n+1
(q )=
j
2n +1
n − 3...
... M´exico,
Circuito Exterior, C.U. Coyoac´an 04 5 10, M´exico D.F.
merino@matem.unam.mx
Submitted: Nov 21 , 20 07 ; Accepted: Jul 11, 20 08 ; Published: Jul 21 , 20 08
Mathematics Subject Classifications: 05 A19
Abstract
If ... that
n 0
J
n +2
(−1)( 2)
n
t
n
n!
=
1
(cos(t) + sin(t))
2
. (5)
Taking x = 2 and y = −1 in Equation (3), we get the following identiti...
... become
f
[00 ]
w
= 1 + f
[00 ]
w
(zf
[00 ]
w−1
+ z
3 /2
f
[01 ]
w−1
+ z
3 /2
f
[ 10]
w−1
+ z
2
f
[11]
w−1
) (16)
f
[01 ]
w
= f
[00 ]
w
(z
1 /2
f
[00 ]
w−1
+ zf
[01 ]
w−1
) (17)
f
[ 10]
w
= f
[00 ]
w
(z
1 /2
f
[00 ]
w−1
+ ... zf
[ 10]
w−1
) (18)
f
[11]
w
= f
[00 ]
w−1
+ f
[01 ]
w
(z
1 /2
f
[00 ]
w−1
+ zf
[01 ]
w−1
). (19)
We clean up our notation now. Le...
... Then
i
d
i
= n. Draw a punctured polygon with n
the electronic journal of combinatorics 16 ( 20 09 ), #R49 14
n d(n)
3 4
4 6
5 26
6 80
7 24 6
n d(n)
8 8 10
9 27 04
10 925 2
11 3 20 66
12 1 127 20
Table 1: ... ICRA,
Torun ( 20 07 ).
[V] Vatne D. F. The mutation class of D
n
quivers, arXiv :08 10. 4789v1 ( 20 08 ).
the electronic journal of combinatorics 16 ( 20 09...
... Jun 28 , 20 10; Accepted: Jan 27 , 20 11; Published: Feb 14, 20 11
Mathematics Subject Classification: 05 C 30; 05 A16, 05 C05, 05 C69, 92E 10
Abstract
For graphs F and G an F -matching in G is a subgraph of ... with
integer coefficients g(r) =
d
i=1
c
i
g(r − i). Assume that g (0) = 0 and c
d
= 1. Then for
every positive integer m > 0 there exists an index r...