Autoparatopisms of Quasigroups and Latin Squares

Mahamendige Jayama Lalani Mendis, Ian Wanless

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

Abstract

Paratopism is a well-known action of the wreath product Sn  S3 on Latin squares of order n. A paratopism that maps a Latin square to itself is an autoparatopism of that Latin square. Let Par(n) denote the set of paratopisms that are an autoparatopism of at least one Latin square of order n. We prove a number of general properties of autoparatopisms. Applying these results, we determine Par(n) for n ≤ 17. We also study the proportion of all paratopisms that are in Par(n) as n → ∞.

Original languageEnglish
Pages (from-to)51-74
Number of pages24
JournalJournal of Combinatorial Designs
Volume25
Issue number2
DOIs
Publication statusPublished - 1 Feb 2017

Keywords

  • automorphism
  • autoparatopism
  • autotopism
  • Latin square
  • quasigroup

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