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n-Ary quasigroups of order 4

Denis Krotov·Vladimir Potapov
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Abstract

We characterize the set of all N-ary quasigroups of order 4: every N-ary quasigroup of order 4 is permutably reducible or semilinear. Permutable reducibility means that an N-ary quasigroup can be represented as a composition of K-ary and (N-K+1)-ary quasigroups for some K from 2 to N-1, where the order of arguments in the representation can differ from the original order. The set of semilinear N-ary quasigroups has a characterization in terms of Boolean functions. Keywords: Latin hypercube, n-ary quasigroup, reducibility

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Denis Krotov, Vladimir Potapov. 2008-10-26. n-Ary quasigroups of order 4. https://doi.org/10.1137/070697331

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