Latin squares with restricted transversals

Judith Egan, Ian Murray Wanless

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7 Citations (Scopus)

Abstract

We prove that for all odd m >= 3 there exists a latin square of order 3 m that contains an (m - 1) x m latin subrectangle consisting of entries not in any transversal. We prove that for all even n >= 10 there exists a latin square of order n in which there is at least one transversal, but all transversals coincide on a single entry. A corollary is a new proof of the existence of a latin square without an orthogonal mate, for all odd orders n >= 11. Finally, we report on an extensive computational study of transversal-free entries and sets of disjoint transversals in the latin squares of order n
Original languageEnglish
Pages (from-to)124 - 141
Number of pages18
JournalJournal of Combinatorial Designs
Volume20
Issue number2
DOIs
Publication statusPublished - 2012

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