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.Comment: arXiv admin note: text overlap with arXiv:1211.162