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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Enumeration of MOLS of small order
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by Judith Egan and Ian M. Wanless PDF
Math. Comp. 85 (2016), 799-824

Abstract:

We report the results of a computer investigation of sets of mutually orthogonal Latin squares (MOLS) of small order. For $n\leqslant 9$ 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.

References
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Additional Information
  • Judith Egan
  • Affiliation: School of Mathematical Sciences, Monash University, VIC 3800 Australia
  • MR Author ID: 300990
  • Email: judith.egan@monash.edu
  • Ian M. Wanless
  • Affiliation: School of Mathematical Sciences, Monash University, VIC 3800 Australia
  • Email: ian.wanless@monash.edu
  • Received by editor(s): June 14, 2014
  • Received by editor(s) in revised form: September 18, 2014
  • Published electronically: July 14, 2015
  • © Copyright 2015 by the authors
  • Journal: Math. Comp. 85 (2016), 799-824
  • MSC (2010): Primary 05B15; Secondary 62K99
  • DOI: https://doi.org/10.1090/mcom/3010
  • MathSciNet review: 3434882