The enumeration of cyclic mutually nearly orthogonal Latin squares

Fatih Demirkale, Diane M. Donovan, Janne I. Kokkala, Trent G. Marbach*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

In this paper, we study collections of mutually nearly orthogonal Latin squares (MNOLS), which come from a modification of the orthogonality condition for mutually orthogonal Latin squares. In particular, we find the maximum μ such that there exists a set of μ cyclic MNOLS of order n for n≤18, as well as providing a full enumeration of sets and lists of μ cyclic MNOLS of order n under a variety of equivalences with n≤18. This resolves in the negative a conjecture that proposed that the maximum μ for which a set of μ cyclic MNOLS of order n exists is [n/4]+1.

Original languageEnglish
Pages (from-to)265-276
Number of pages12
JournalJournal of Combinatorial Designs
Volume27
Issue number5
Early online date1 Jan 2019
DOIs
Publication statusPublished - 1 May 2019
MoE publication typeA1 Journal article-refereed

Keywords

  • latin square
  • MNOLS
  • nearly orthogonal
  • NUMBER

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