On automorphisms of strongly regular graphs with parameters (243,66,9,21).
On automorphisms of strongly regular graphs with and . II.
On averages of randomized class functions on the symmetric groups and their asymptotics
The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices ( points). In this paper, we generalize many aspects of this situation. We introduce random shifts of the eigenvalues of the permutation matrices, in two different ways: independently or not for each subset of eigenvalues associated to the same cycle. We also consider vastly more general functions than the characteristic polynomial of a permutation matrix, by...
On Averaging Sets.
On Baer Subspaces of Finite Projective Spaces.
On Balanced Room Squares and Complete Balanced Howell Rotations
On balancing of hypergraphs
On bandwidth, cutwidth, and quotient graphs
On base partitions and cover partitions of skew characters.
On betweenness-uniform graphs
The betweenness centrality of a vertex of a graph is the fraction of shortest paths between all pairs of vertices passing through that vertex. In this paper, we study properties and constructions of graphs whose vertices have the same value of betweenness centrality (betweenness-uniform graphs); we show that this property holds for distance-regular graphs (which include strongly regular graphs) and various graphs obtained by graph cloning and local join operation. In addition, we show that, for...
On bicritical snarks
On biembeddings of Latin squares.
On binary representations of integers with digits .
On binary trees and Dyck paths
A bijection between the set of binary trees with n vertices and the set of Dyck paths of length 2n is obtained. Two constructions are given which enable to pass from a Dyck path to a binary tree and from a binary tree to a Dyck path.
On binary trees and permutations
Every binary tree is associated to a permutation with repetitions, which determines it uniquely. Two operations are introduced and used for the construction of the set of all binary trees. The set of all permutations which correspond to a given binary tree is determined and its cardinal number is evaluated.
On bounded paradoxical subsets of the plane
On Brooks' theorem and some related results.
On cardinalities of row spaces of Boolean matrices.
On Catalan trees and the Jacobian conjecture.
On Cayley graphs of completely 0-simple semigroups
We give necessary and sufficient conditions for various vertex-transitivity of Cayley graphs of the class of completely 0-simple semigroups and its several subclasses. Moreover, the question when the Cayley graphs of completely 0-simple semigroups are undirected is considered.