Tactical decompositions of designs.
The (16,6,2) designs.
The algebraic multiplicity of the number zero in the spectrum of a bipartite graph
The Bruhat rank of a binary symmetric staircase pattern
In this work we show that the Bruhat rank of a symmetric (0,1)-matrix of order n with a staircase pattern, total support, and containing In, is at most 2. Several other related questions are also discussed. Some illustrative examples are presented.
The calculation of α-sets of representatives
The check positions of Hamming codes and the construction of a 2EC-AUED code.
The difference matrices of the classes of a Sharma-Kaushik partition
Sharma-Kaushik partitions have been used to define distances between vectors with -coordinates. In this paper, “difference matrices” for the partitioning classes have been introduced and investigated. It has been shown that the difference matrices are circulant and that the entries of a product of matrices is an extended intersection number of a distance scheme. The sum of the entries of each row or columns of the product matrix has been obtained. The algebra of matrices generated by the difference...
The maximum number of odd submatrices in -matrices.
The Moore-Penrose inverse of a free matrix.
Thin Lehman matrices and their graphs.
Two improvements of a result concerning a problem of K. Zarankiewicz
Two-level Cretan matrices constructed using SBIBD
Two-level Cretan matrices are orthogonal matrices with two elements, x and y. At least one element per row and column is 1 and the other element has modulus ≤ 1. These have been studied in the Russian literature for applications in image processing and compression. Cretan matrices have been found by both mathematical and computational methods but this paper concentrates on mathematical solutions for the first time. We give, for the first time, families of Cretan matrices constructed using the incidence...