Grobner Bases and the Number of Latin Squares Related to Autotopisms of Order <= 7
Falcon, R. M. ; Martin-Morales, J.
Resumen: 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.
Idioma: Inglés
DOI: 10.1016/j.jsc.2007.07.004
Año: 2007
Publicado en: JOURNAL OF SYMBOLIC COMPUTATION 42, 11-12 (2007), 1142-1154
ISSN: 0747-7171
Factor impacto JCR: 0.658 (2007)
Categ. JCR: MATHEMATICS, APPLIED rank: 91 / 165 = 0.552 (2007) - Q3 - T2
Categ. JCR: COMPUTER SCIENCE, THEORY & METHODS rank: 49 / 78 = 0.628 (2007) - Q3 - T2
Tipo y forma: Article (Published version)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material.
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Idioma: Inglés
DOI: 10.1016/j.jsc.2007.07.004
Año: 2007
Publicado en: JOURNAL OF SYMBOLIC COMPUTATION 42, 11-12 (2007), 1142-1154
ISSN: 0747-7171
Factor impacto JCR: 0.658 (2007)
Categ. JCR: MATHEMATICS, APPLIED rank: 91 / 165 = 0.552 (2007) - Q3 - T2
Categ. JCR: COMPUTER SCIENCE, THEORY & METHODS rank: 49 / 78 = 0.628 (2007) - Q3 - T2
Tipo y forma: Article (Published version)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material. Exportado de SIDERAL (2024-03-11-10:22:31)
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Record created 2024-03-01, last modified 2024-03-11