On reconstructing reducible n-ary quasigroups and switching subquasigroups

Krotov Denis; Potapov Vladimir; Sokolova Polina

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KROTOV, 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

On reconstructing reducible n-ary quasigroups and switching subquasigroups

Pag. 55-67

Krotov Denis, Potapov Vladimir, Sokolova Polina

Disponibil în IBN: 16 decembrie 2013

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Rezumat

(1) We prove that, provided n > 4, a permutably reducible n-ary quasigroup is uniquely specied 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.

Cuvinte-cheie
irreducible quasigroups, n-ary quasigroups, reducibility, subquasigroup,

latin hypercubes

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<dc:creator>Krotov, D.S.</dc:creator>
<dc:creator>Potapov, V.N.</dc:creator>
<dc:creator>Sokolova, P.V.</dc:creator>
<dc:date>2008-01-01</dc:date>
<dc:description xml:lang='en'>(1) We prove that, provided n > 4, a permutably reducible n-ary quasigroup
is uniquely specied 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.
</dc:description>
<dc:source>Quasigroups and Related Systems 19 (1) 55-67</dc:source>
<dc:subject>irreducible quasigroups</dc:subject>
<dc:subject>latin hypercubes</dc:subject>
<dc:subject>n-ary quasigroups</dc:subject>
<dc:subject>reducibility</dc:subject>
<dc:subject>subquasigroup</dc:subject>
<dc:title>On reconstructing reducible n-ary quasigroups and switching subquasigroups
</dc:title>
<dc:type>info:eu-repo/semantics/article</dc:type>
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