On the probability of two randomly generated SS-permutation matrices to be disjoint

• A lower band of the number of all disjoint with an arbitrary n2×n2n2×n2   SS-permutation matrix is found.
• A lower band of the number of all non-ordered pairs of disjoint n2×n2n2×n2   SS-permutation matrices is found.
• A lower band of the probability of two randomly generated SS-permutation matrices to be disjoint is found.
• A relevant point of Roberto Fontana’s algorithm is discussed.
• The cases when n=2n=2 and n=3n=3 are discussed in detail.

The concept of SS-permutation matrix is considered in this paper. It defines when two binary matrices are disjoint. For an arbitrary n2×n2n2×n2   SS-permutation matrix, a lower band of the number of all disjoint with its SS-permutation matrices is found. A formula for counting a lower band of the number of all disjoint pairs of n2×n2n2×n2SS-permutation matrices is formulated and proven. As a consequence, a lower band of the probability of two randomly generated SS-permutation matrices to be disjoint is found. In particular, a different proof of a known assertion is obtained in the work. The cases when n=2n=2 and n=3n=3 are discussed in detail.