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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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

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spelling	doaj-c9d21e01729f4a3f9c43f3cb62a205ad2020-11-25T03:57:08ZengAIMS PressAIMS Mathematics2473-69882021-10-016126129510.3934/math.2021017A census of critical sets based on non-trivial autotopisms of Latin squares of order up to fiveRaúl M. Falcón0Laura Johnson1Stephanie Perkins21 Department of Applied Mathematics I. Universidad de Sevilla, Spain2 School of Computing and Mathematics. University of South Wales, United Kingdom2 School of Computing and Mathematics. University of South Wales, United KingdomThis 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.https://www.aimspress.com/article/10.3934/math.2021017/fulltext.htmllatin squareautotopismcycle structurecritical setenumeration
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Raúl M. Falcón Laura Johnson Stephanie Perkins
spellingShingle	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 AIMS Mathematics latin square autotopism cycle structure critical set enumeration
author_facet	Raúl M. Falcón Laura Johnson Stephanie Perkins
author_sort	Raúl M. Falcón
title	A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five
title_short	A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five
title_full	A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five
title_fullStr	A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five
title_full_unstemmed	A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five
title_sort	census of critical sets based on non-trivial autotopisms of latin squares of order up to five
publisher	AIMS Press
series	AIMS Mathematics
issn	2473-6988
publishDate	2021-10-01
description	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.
topic	latin square autotopism cycle structure critical set enumeration
url	https://www.aimspress.com/article/10.3934/math.2021017/fulltext.html
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A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five

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