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IMI/Publicaţii/BASM/Ediţii/BASM n.3 (52), 2006/

A new method for computing the number of n-quasigroups.

Authors: S. Markovski, V. Dimitrova, A. Mileva

Abstract

We use the isotopy classes of quasigroups for computing the numbers of finite n-quasigroups (n=1,2,3,...). The computation is based on the property that every two isotopic n-quasigroups are substructures of the same number of n+1-quasigroups. This is a new method for computing the number of n-quasigroups and in an enough easy way we could compute the numbers of ternary quasigroups of orders up to and including 5 and of quaternary quasigroups of orders up to and including 4.

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