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

S. Markovski, V. Dimitrova, A. Mileva

"Ss Cyril and Methodius" University, Faculty of Sciences, Institute of Informatics, Skopje, Rep. of Macedonia

Abstract: We use the isotopy classes of quasigroups for computing the numbers of finite $n$-quasigroups $(n= 1,2,3,\dots)$. 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.

Keywords and phrases: $n$-quasigroup, isotopism, $n$-Latin square.

MSC: 20N05, 20N15, 05B15

Received: 18.09.2006

Language: English

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