n-Ary quasigroups of order 4

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dc.creatorKrotov, Denis
dc.creatorPotapov, Vladimir
dc.date2007-01-18
dc.date2008-10-26
dc.date.accessioned2026-07-07T12:38:22Z
dc.date.available2026-07-07T12:38:22Z
dc.descriptionWe 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
dc.description10pp. V2: revised
dc.identifierhttps://arxiv.org/abs/math/0701519
dc.identifierhttp://arxiv.org/abs/math/0701519
dc.identifierSIAM J. Discrete Math. 23(2) 2009, 561-570
dc.identifierdoi:10.1137/070697331
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/218734
dc.subjectCombinatorics
dc.subjectGroup Theory
dc.subject05B15; 20N05; 20N15; 94B25
dc.titlen-Ary quasigroups of order 4
dc.typetext

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