Grobner Bases and the Number of Latin Squares Related to Autotopisms of Order <= 7

Latin squares can be seen as multiplication tables of quasigroups, which are, in general, non-commutative and non-associative algebraic structures. The number of Latin squares having a fixed isotopism in their autotopism group is at the moment an open problem. In this paper, we use Gröbner bases to...

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Detalles Bibliográficos
Autores: Falcon, R. M., Martin-Morales, J.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2007
País:España
Institución:Universidad de Zaragoza
Repositorio:Zaguán. Repositorio Digital de la Universidad de Zaragoza
OAI Identifier:oai:zaguan.unizar.es:132068
Acceso en línea:http://zaguan.unizar.es/record/132068
Access Level:acceso abierto
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spelling Grobner Bases and the Number of Latin Squares Related to Autotopisms of Order <= 7Falcon, R. M.Martin-Morales, J.Latin squares can be seen as multiplication tables of quasigroups, which are, in general, non-commutative and non-associative algebraic structures. The number of Latin squares having a fixed isotopism in their autotopism group is at the moment an open problem. In this paper, we use Gröbner bases to describe an algorithm that allows one to obtain the previous number. Specifically, this algorithm is implemented in Singular to obtain the number of Latin squares related to any autotopism of Latin squares of order up to 7.2007info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://zaguan.unizar.es/record/132068reponame:Zaguán. Repositorio Digital de la Universidad de Zaragozainstname:Universidad de ZaragozaInglésinfo:eu-repo/semantics/openAccessoai:zaguan.unizar.es:1320682026-05-29T13:59:51Z
dc.title.none.fl_str_mv Grobner Bases and the Number of Latin Squares Related to Autotopisms of Order <= 7
title Grobner Bases and the Number of Latin Squares Related to Autotopisms of Order <= 7
spellingShingle Grobner Bases and the Number of Latin Squares Related to Autotopisms of Order <= 7
Falcon, R. M.
title_short Grobner Bases and the Number of Latin Squares Related to Autotopisms of Order <= 7
title_full Grobner Bases and the Number of Latin Squares Related to Autotopisms of Order <= 7
title_fullStr Grobner Bases and the Number of Latin Squares Related to Autotopisms of Order <= 7
title_full_unstemmed Grobner Bases and the Number of Latin Squares Related to Autotopisms of Order <= 7
title_sort Grobner Bases and the Number of Latin Squares Related to Autotopisms of Order <= 7
dc.creator.none.fl_str_mv Falcon, R. M.
Martin-Morales, J.
author Falcon, R. M.
author_facet Falcon, R. M.
Martin-Morales, J.
author_role author
author2 Martin-Morales, J.
author2_role author
description Latin squares can be seen as multiplication tables of quasigroups, which are, in general, non-commutative and non-associative algebraic structures. The number of Latin squares having a fixed isotopism in their autotopism group is at the moment an open problem. In this paper, we use Gröbner bases to describe an algorithm that allows one to obtain the previous number. Specifically, this algorithm is implemented in Singular to obtain the number of Latin squares related to any autotopism of Latin squares of order up to 7.
publishDate 2007
dc.date.none.fl_str_mv 2007
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.none.fl_str_mv http://zaguan.unizar.es/record/132068
url http://zaguan.unizar.es/record/132068
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
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dc.source.none.fl_str_mv reponame:Zaguán. Repositorio Digital de la Universidad de Zaragoza
instname:Universidad de Zaragoza
instname_str Universidad de Zaragoza
reponame_str Zaguán. Repositorio Digital de la Universidad de Zaragoza
collection Zaguán. Repositorio Digital de la Universidad de Zaragoza
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