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This paper delves into the study of critical sets of Latin squares having a given isotopism in their autotopism group. Particularly, we prove that the sizes of these critical sets only depend on both the main class of the Latin square and the cycle structure of the isotopism under consideration. Keeping then in mind that the autotopism group of a Latin square acts faithfully on the set of entries of the latter, we enumerate all the critical sets based on autotopisms of Latin squares of order up to five.
Original languageEnglish
Pages (from-to)261-295
Number of pages34
JournalAIMS Mathematics
Volume6
Issue number1
DOIs
Publication statusPublished - 10 Oct 2020

    Research areas

  • Latin square, autotopism, cycle structure, critical set, enumeration

ID: 4284687