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

This work examines the concept of S-permutation matrices, namely n2×n2 permutation matrices containing a single 1 in each canonical n×n subsquare (block). The article suggests a formula for counting mutually disjoint pairs of n2×n2S-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×n binary matrices. The paper describes an algorithm that solves the main problem. To do that, every n×n binary matrix is represented uniquely as a n-tuple of integers.