Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

   
 

 

Enumeration of MOLS of small order


Authors: Judith Egan and Ian M. Wanless
Journal: Math. Comp. 85 (2016), 799-824
MSC (2010): Primary 05B15; Secondary 62K99
DOI: https://doi.org/10.1090/mcom/3010
Published electronically: July 14, 2015
MathSciNet review: 3434882
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We report the results of a computer investigation of sets of mutually orthogonal Latin squares (MOLS) of small order. For $ n\le 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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 05B15, 62K99

Retrieve articles in all journals with MSC (2010): 05B15, 62K99


Additional Information

Judith Egan
Affiliation: School of Mathematical Sciences, Monash University, VIC 3800 Australia
Email: judith.egan@monash.edu

Ian M. Wanless
Affiliation: School of Mathematical Sciences, Monash University, VIC 3800 Australia
Email: ian.wanless@monash.edu

DOI: https://doi.org/10.1090/mcom/3010
Keywords: Latin square, MOLS, transversal, plex, orthogonal mate
Received by editor(s): June 14, 2014
Received by editor(s) in revised form: September 18, 2014
Published electronically: July 14, 2015
Article copyright: © Copyright 2015 by the authors