... at least 4 letters co ntains a square. A. S. Fraenkel and J. Simp-
son [2, 1] studied the number of distinct squares in binary word; see also Ilie [4], where it
was shown that a binary word can ... in this list of length 29.
the electronic journal of combinatorics 18 (2011), #P6 7
The Number of Positions Starting a Square
in Binary Words
Tero Harju
Depart...
... The Number of Solutions of X
2
= 0in 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, ... over
GF(q), whose square is the zero matrix. This formula was recently conjectured by Sasha Kirillov
and Anna Melnikov [KM].
Theorem. The number of n × n upper-triangular mat...
... edges.Since
a single graph may have many embeddings, there are generally fewer planar graphs
than there are maps. In this paper, we study the number of labeled 2-connected
planar graphs with a given ... Gao
∗
School of Mathematics and Statistics
Carleton University
Ottawa K1S 5B6, Canada
zgao@math.carleton.ca
Nicholas C. Wormald
†
Department of Mathematics and Statistics
Univers...
... binomials,
Proceedings of the American Mathematical Society 134 (2006), no 1, 15-22.
[2] A. Akbary and Q. Wang, On some permutation polynomials over finite fields, Inter-
national Journal of Mathematics and Mathematical ... journal of combinatorics 13 (2006), #R65 8
The Number of Permutation Binomials
Over F
4p+1
where p and 4p + 1 are Primes
A. Masuda, D. Panario
∗
and Q. Wang
∗
Sc...
... For a spanning tree A of
K
n
, an inversion in A is a pair of vertices labelled i,j such that i > j and i is on the
unique path from 1 to j in A. Let invA be the number of inversions in A. ... present an algebraic proof of a result
with the same flavour as the latter: T
n+2
(1, −1) = T
n
(2, −1), where T
n
(1, −1) has
the combinatorial interpretation of being t...
... the Catalan numbers [St].
3 The Main Result - Basketball Games
Definition 1 An [ij] walk is a walk that starts at the line y = i and ends at the line
y = j.
Definition 2 An irreducible [ij] walk ... journal of combinatorics 14 (2007), #R19 3
The Number of [Old-Time] Basketball Games with
Final Score n:n where the Home Team was never
losing but also never ahead by more than w Points
Arvi...
... can use the number of planar graphs and the number of
triangulations as lower bounds. Determining the number (of graphs of sub-classes) of planar
graphs has attracted considerable attention [1, ... not in the
case of maximal K
3,3
-minor-free graphs as one condition requires that two disjoint copies
of a graph of the class in question form again a graph of the c...
... mutation class of a quiver
of type D
n
and triangulations up to rotation and
inverting tags
Here we adapt the methods and ideas of [T] to obtain a bijection between the mutation
class of a quiver ... in B, and we want this to
commute with mutation o f triangulations. Mutating a triangulation at a given diagonal
is defined as removing this diagonal and replacing it with anot...
... set of F -matchings
not covering v being a separate cla ss C
0
. We argue that the number of F -matchings in
each such class is a zero residue. Indeed, the number of F -matchings in a given class ... −1) starting vertices in W
t
. To see this
recall that 1 is always a starting vertex, and each copy but the la st adds d − 1 starting
vertices; also, the last copy...
... that k ≥ k
0
= n/2.(5)
the electronic journal of combinatorics 4 (1997), #R3 2
1. Introduction
Almost all the familiar concepts of linear algebra, such as dimension and linear
independence, are ... O(q
−2t
)
=exp
O(q
−k
)
=1+O(q
−n/2
),
(9)
the electronic journal of combinatorics 4 (1997), #R3 4
ratioofthetwoversionsofλapproach 1, the inequality in (2) follows from that in
(...