| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 1152626 | Statistics & Probability Letters | 2014 | 5 Pages |
•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.
