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On the number of mutually disjoint pairs of S-permutation matrices (1604.02712v2)
Published 10 Apr 2016 in math.CO and cs.DM
Abstract: This work examines the concept of S-permutation matrices, namely $n2 \times n2$ 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 $n2 \times n2$ 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.