Latin squares with a unique intercalate

Mahamendige Jayama Lalani Mendis, Ian M. Wanless

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

Suppose that n≡±1 mod 6 and n≥7. We construct a Latin square Ln of order n with the following properties: Ln has no proper subsquares of order 3 or more. Ln has exactly one intercalate (subsquare of order 2). When the intercalate is replaced by the other possible subsquare on the same symbols, the resulting Latin square is in the same species as Ln. Hence Ln generalizes the square that Sade famously found to complete Norton's enumeration of Latin squares of order 7. In particular, Ln is what is known as a self-switching Latin square and possesses a near-autoparatopism.

Original languageEnglish
Pages (from-to)279-293
Number of pages15
JournalJournal of Combinatorial Designs
Volume24
Issue number6
DOIs
Publication statusPublished - 1 Jun 2016

Keywords

  • autoparatopism
  • intercalate
  • Latin square
  • self-switching
  • subsquare

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