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 SM ISO690:2012KROTOV, Denis, POTAPOV, Vladimir, SOKOLOVA, Polina. On reconstructing reducible n-ary quasigroups and switching subquasigroups
. In: Quasigroups and Related Systems, 2008, vol. 16, nr. 1(19), pp. 55-67. ISSN 1561-2848. |
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| Quasigroups and Related Systems | ||||||
| Volumul 16, Numărul 1(19) / 2008 / ISSN 1561-2848 | ||||||
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| Pag. 55-67 | ||||||
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(1) We prove that, provided n > 4, a permutably reducible n-ary quasigroup
is uniquely speci ed by its values on the n-ples containing zero. (2) We
observe that for each n, k > 2 and r 6 k/2 there exists a reducible n-
ary quasigroup of order k with an n-ary subquasigroup of order r. As
corollaries, we have the following: (3) For each k > 4 and n > 3 we can
construct a permutably irreducible n-ary quasigroup of order k. (4) The
number of n-ary quasigroups of order k > 3 has double-exponential growth
as n → ∞; it is greater than exp exp(n ln k/3 ) if k > 6, and exp exp( ln 3 n−
3
0.44) if k = 5.
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| Cuvinte-cheie irreducible quasigroups, n-ary quasigroups, reducibility, subquasigroup, latin hypercubes |
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