Transversals in m × n arrays

Hung-Lin Fu*, Chang Chun Lee

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 as the largest integer such that if each symbol in an m by n array appears at most times, then the array must have a transversal. In this article, we first obtain a better lower bound of by using a probabilistic method and then find for certain positive integers m and n.

Original languageEnglish
Pages (from-to)139-146
Number of pages8
JournalJournal of Statistical Theory and Practice
Volume6
Issue number1
DOIs
StatePublished - 1 Mar 2012

Keywords

  • m n arrays
  • Transversal

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