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

AIMS Mathematics

Raúl M. Falcón¹  Laura Johnson²  Stephanie Perkins² 

[1] 1 Department of Applied Mathematics I. Universidad de Sevilla, Spain;2 School of Computing and Mathematics. University of South Wales, United Kingdom;

关键词: latin square;    autotopism;    cycle structure;    critical set;    enumeration;   

DOI  :  10.3934/math.2021017

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown