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

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.