Gröbner 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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Vydáno v:Journal of symbolic computation Ročník 42; číslo 11; s. 1142 - 1154
Hlavní autoři: Falcón, R.M., Martín-Morales, J.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.11.2007
Témata:
Autotopism group
Gröbner basis
Latin square
Gröbner basis
Autotopism group
Latin square
ISSN:0747-7171, 1095-855X
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Popis
Shrnutí: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.
ISSN:0747-7171
1095-855X
DOI:10.1016/j.jsc.2007.07.004