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Gröbner bases and the number of Latin squares related to autotopisms of order ≤7

 

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Opened Access Gröbner bases and the number of Latin squares related to autotopisms of order ≤7
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Author: Falcón Ganfornina, Raúl Manuel
Martín Morales, Jorge
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2007
Published in: Journal of symbolic computation, 42 (11), 1142-1154.
Document type: Article
Abstract: Latin squares can be seen as multiplication tables of quasigroups, which are, in general, noncommutativeand non-associative algebraic structures. The number of Latin squares having a fixed isotopismin their autotopism group is at the moment an open problem. In this paper, we use Gröbner bases todescribe 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 oforder up to 7.
Cite: Falcón Ganfornina, R.M. y Martín Morales, J. (2007). Gröbner bases and the number of Latin squares related to autotopisms of order ≤7. Journal of symbolic computation, 42 (11), 1142-1154.
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