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Transversals in m × n Arrays

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Abstract

An m by n array consists of mn cells in m rows and n columns, where 2 < m < n. A partial transversal in an m by n array is a set of m cells, one from each row and no two from the same column. A transversal in an m by n array is a partial transversal in which m symbols are distinct. Define L(m, n) as the largest integer such that if each symbol in an m by n array appears at most L(m, n) times, then the array must have a transversal. In this article, we first obtain a better lower bound of L(tm, n) by using a probabilistic method and then find L(m, n) for certain positive integers m and n.

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Authors and Affiliations

  1. Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan

    Hung-Lin Fu & Chang-Chun Lee

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  1. Hung-Lin Fu
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  2. Chang-Chun Lee
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Correspondence to Hung-Lin Fu.

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Fu, HL., Lee, CC. Transversals in m × n Arrays. J Stat Theory Pract 6, 139–146 (2012). https://doi.org/10.1080/15598608.2012.647554

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  • DOI: https://doi.org/10.1080/15598608.2012.647554

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