On the number of mutually disjoint pairs of S-permutation matrices

Abstract

This work examines the concept of S-permutation matrices, namely $n^2\times n^2$ permutation matrices containing a single 1 in each canonical $n\times n$ subsquare (block). The article suggests a formula for counting mutually disjoint pairs of $n^2\times n^2$ S-permutation matrices in the general case by restricting this task to the problem of finding some numerical characteristics of the elements of specially defined for this purpose factor-set of the set of $n\times n$ binary matrices. The paper describe an algorithm that solves the main problem. To do that, every $n\times n$ binary matrix is represented uniquely as a n-tuple of integers.

arXiv admin note: substantial text overlap with arXiv:1501.03395; text overlap with arXiv:1604.02691

References in corpus (1)

• Random Permutations, Random Sudoku Matrices and Randomized Algorithms