n-Ary quasigroups of order 4 Full article
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SIAM Journal on Discrete Mathematics
ISSN: 0895-4801 , E-ISSN: 1095-7146 |
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| Output data | Year: 2009, Volume: 23, Number: 2, Pages: 561-570 Pages count : 10 DOI: 10.1137/070697331 | ||
| Tags | Latin hypercube, n-ary quasigroup, reducibility | ||
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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.
Cite:
Krotov D.S.
, Potapov V.N.
n-Ary quasigroups of order 4
SIAM Journal on Discrete Mathematics. 2009. V.23. N2. P.561-570. DOI: 10.1137/070697331 WOS Scopus РИНЦ OpenAlex
n-Ary quasigroups of order 4
SIAM Journal on Discrete Mathematics. 2009. V.23. N2. P.561-570. DOI: 10.1137/070697331 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jul 16, 2007 |
| Accepted: | Oct 6, 2008 |
| Published print: | Feb 6, 2009 |
Identifiers:
| Web of science: | WOS:000267744700001 |
| Scopus: | 2-s2.0-73349093672 |
| Elibrary: | 15299459 |
| OpenAlex: | W3105130485 |