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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Detalhes bibliográficos
Autores: Falcon, R. M., Martin-Morales, J.
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2007
País:España
Recursos:Universidad de Zaragoza
Repositorio:Zaguán. Repositorio Digital de la Universidad de Zaragoza
OAI Identifier:oai:zaguan.unizar.es:132068
Acesso em linha:http://zaguan.unizar.es/record/132068
Access Level:acceso abierto
Descrição
Resumo: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.