Cycle structure of autotopisms of quasigroups and Latin squares

Douglas Stuart Stones, Petr Vojtechovsky, Ian Murray Wanless

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27 Citations (Scopus)


An autotopism of a Latin square is a triple (alpha, beta, gamma) of permutations such that the Latin square is mapped to itself by permuting its rows by alpha, columns by beta, and symbols by gamma. Let Atp(n) be the set of all autotopisms of Latin squares of order n. Whether a triple (alpha, beta, gamma) of permutations belongs to Atp(n) depends only on the cycle structures of alpha, beta, and gamma. We establish a number of necessary conditions for (alpha, beta, gamma) to be in Atp(n), and use them to determine Atp(n) for n
Original languageEnglish
Pages (from-to)227 - 263
Number of pages37
JournalJournal of Combinatorial Designs
Issue number5
Publication statusPublished - 2012

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