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TitleGröbner bases and the number of Latin squares related to autotopisms of order ≤7
Author(s) R.M. Falcón, J. Martín-Morales
TypeArticle in Journal
AbstractLatin 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.
KeywordsAutotopism group, Gröbner basis, Latin square
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717107001009
LanguageEnglish
JournalJournal of Symbolic Computation
Volume42
Number11–12
Pages1142 - 1154
Year2007
NoteNon-commutative Gröbner bases and applications
Edition0
Translation No
Refereed No
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