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

Krasimir Yordzhev

Statistics & Probability Letters, 2014, vol. 91, issue C, 47-51

Abstract: The concept of S-permutation matrix is considered in this paper. It defines when two binary matrices are disjoint. For an arbitrary n2×n2 S-permutation matrix, a lower band of the number of all disjoint with its S-permutation matrices is found. A formula for counting a lower band of the number of all disjoint pairs of n2×n2S-permutation matrices is formulated and proven. As a consequence, a lower band of the probability of two randomly generated S-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=2 and n=3 are discussed in detail.

Keywords: S-permutation matrix; Disjoint binary matrices; Rencontre; Derangement; Sudoku (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2014.04.006

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