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

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

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. Kee...

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Bibliographic Details
Main Authors: Raúl M. Falcón, Laura Johnson, Stephanie Perkins
Format: Article
Language:English
Published: AIMS Press 2021-10-01
Series:AIMS Mathematics
Subjects:
latin square
autotopism
cycle structure
critical set
enumeration
Online Access:https://www.aimspress.com/article/10.3934/math.2021017/fulltext.html
Description
Summary: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.
ISSN:2473-6988

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