Enumeration of MOLS of small order

J. Egan, I.M. Wanless

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We report the results of a computer investigation of sets of mutually orthogonal Latin squares (MOLS) of small order. For n ≤ 9 we: (1) determine the number of orthogonal mates for each species of Latin square of order n; (2) calculate the proportion of Latin squares of order n that have an orthogonal mate, and the expected number of mates when a square is chosen uniformly at random; (3) classify all sets of MOLS of order n up to various different notions of equivalence. We also provide a triple of Latin squares of order 10 that is the closest to being a set of MOLS so far found. © 2015 American Mathematical Society.
Original languageEnglish
Pages (from-to)799-824
Number of pages26
JournalMathematics of Computation
Volume85
Issue number298
DOIs
Publication statusPublished - 2016
Externally publishedYes

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Mutually Orthogonal Latin Squares
Enumeration
Magic square
Proportion
Classify
Equivalence
Calculate

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Egan, J. ; Wanless, I.M. / Enumeration of MOLS of small order. In: Mathematics of Computation. 2016 ; Vol. 85, No. 298. pp. 799-824.
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Egan, J & Wanless, IM 2016, 'Enumeration of MOLS of small order', Mathematics of Computation, vol. 85, no. 298, pp. 799-824. https://doi.org/10.1090/mcom/3010

Enumeration of MOLS of small order. / Egan, J.; Wanless, I.M.

In: Mathematics of Computation, Vol. 85, No. 298, 2016, p. 799-824.

Research output: Contribution to journalArticleResearchpeer-review

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