Calculation of the Number of all Pairs of Disjoint S-permutation Matrices

Abstract

The concept of S-permutation matrix is considered. A general formula for counting all disjoint pairs of $n^2\times n^2$ S-permutation matrices as a function of the positive integer $n$ is formulated and proven in this paper. To do that, the graph theory techniques have been used. It has been shown that to count the number of disjoint pairs of $n^2\times n^2$ S-permutation matrices, it is sufficient to obtain some numerical characteristics of all $n\times n$ bipartite graphs.

arXiv admin note: text overlap with arXiv:1211.1628

References in corpus (2)

• On the Number of Disjoint Pairs of S-permutation Matrices
• Random Permutations, Random Sudoku Matrices and Randomized Algorithms