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Journal of Statistical Theory and Practice

, Volume 6, Issue 1, pp 139–146 | Cite as

Transversals in m × n Arrays

  • Hung-Lin Fu
  • Chang-Chun Lee
Article

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.

05B15 

Keywords

Transversal m × n arrays 

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Copyright information

© Grace Scientific Publishing 2012

Authors and Affiliations

  1. 1.Department of Applied MathematicsNational Chiao Tung UniversityHsinchuTaiwan

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