A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five

Raúl M. Falcón, Laura Johnson, Stephanie Perkins

    Research output: Contribution to journalArticlepeer-review

    9 Downloads (Pure)

    Abstract

    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

    Keywords

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

    Fingerprint

    Dive into the research topics of 'A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five'. Together they form a unique fingerprint.

    Cite this