Calculation of the number of all pairs of disjoint S-permutation matrices

Krasimir Yordzhev

Applied Mathematics and Computation, 2015, vol. 268, issue C, 1-11

Abstract: The concept of S-permutation matrix is considered. A general formula for counting all disjoint pairs of n2 × n2 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 n2 × n2 S-permutation matrices, it is sufficient to obtain some numerical characteristics of all n × n bipartite graphs.

Keywords: Binary matrix; S-permutation matrix; Sudoku matrix; Disjoint matrices; Bipartite graph (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:268:y:2015:i:c:p:1-11

DOI: 10.1016/j.amc.2015.06.054

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