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

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  • Yordzhev, Krasimir

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.

Suggested Citation

  • Yordzhev, Krasimir, 2014. "On the probability of two randomly generated S-permutation matrices to be disjoint," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 47-51.
    • Handle: RePEc:eee:stapro:v:91:y:2014:i:c:p:47-51
    DOI: 10.1016/j.spl.2014.04.006
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    Cited by:

    1. Yordzhev, Krasimir, 2015. "Calculation of the number of all pairs of disjoint S-permutation matrices," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1-11.

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