n-Ary quasigroups of order 4
Combinatorics
2009-02-06 v2 Group Theory
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
Cite
@article{arxiv.math/0701519,
title = {n-Ary quasigroups of order 4},
author = {Denis Krotov and Vladimir Potapov},
journal= {arXiv preprint arXiv:math/0701519},
year = {2009}
}
Comments
10pp. V2: revised