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AIMS Mathematics

2021, Volume 6, Issue 1: 261-295. doi: 10.3934/math.2021017
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A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five

  • 1.
    Department of Applied Mathematics I. Universidad de Sevilla, Spain
  • 2.
    School of Computing and Mathematics. University of South Wales, United Kingdom
  • Received: 14 August 2020 Accepted: 07 October 2020 Published: 10 October 2020

  • MSC : 05B15

  • 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.

    Citation: Raúl M. Falcón, Laura Johnson, Stephanie Perkins. A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five[J]. AIMS Mathematics, 2021, 6(1): 261-295. doi: 10.3934/math.2021017

    Related Papers:

  • 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.


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