# On connection between reducibility of an n-ary quasigroup and that of its retracts

```@article{Krotov2011OnCB,
title={On connection between reducibility of an n-ary quasigroup and that of its retracts},
author={Denis S. Krotov and Vladimir N. Potapov},
journal={Discret. Math.},
year={2011},
volume={311},
pages={58-66}
}```
• Published 1 January 2008
• Mathematics
• Discret. Math.
6 Citations
A ug 2 01 9 Constructions of transitive latin hypercubes
• Mathematics
• 2019
A function f : {0, ..., q−1}n → {0, ..., q−1} invertible in each argument is called a latin hypercube. A collection (π0, π1, ..., πn) of permutations of {0, ..., q − 1} is called an autotopism of a
On one test for the switching separability of graphs modulo q
• Mathematics
• 2016
We consider graphs whose edges are marked by numbers (weights) from 1 to q - 1 (with zero corresponding to the absence of an edge). A graph is additive if its vertices can be marked so that, for
Further results on the classification of MDS codes
• Computer Science
• 2016
The results are used here to complete the classification of all \$7-ary and \$8-ary MDS codes with \$d\geq 3\$ using a computer search.
On connection between the switching separability of a graph and its subgraphs
A graph of order n ≥ 4 is called switching separable if its modulo-2 sum with some complete bipartite graph on the same set of vertices is divided into two mutually independent subgraphs, each having
ON SWITCHING NONSEPARABLE GRAPHS WITH SWITCHING SEPARABLE SUBGRAPHS
• Mathematics
• 2014
A graph of order n ≥ 4 is called switching separable if its modulo-2 sum with some complete bipartite graph on the same set of vertices is divided into two mutually independent subgraphs, each having

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On reducibility of n-ary quasigroups
Solution of Belousov's problem
• Mathematics
• 2000
The authors prove that a local \$n\$-quasigroup defined by the equation x_{n+1} = F (x_1, ..., x_n) = [f_1 (x_1) + ... + f_n (x_n)]/[x_1 + ... + x_n], where f_i (x_i), i, j = 1, ..., n, are arbitrary
On reconstructing reducible n-ary quasigroups and switching subquasigroups
• Mathematics
• 2006
(1) We prove that, provided n>=4, a permutably reducible n-ary quasigroup is uniquely specified by its values on the n-ples containing zero. (2) We observe that for each n,k>=2 and r =4 and n>=3 we
n-Ary Quasigroups of Order 4
• Mathematics
SIAM J. Discret. Math.
• 2009
Every n-ary quasigroups of order 4 is permutably reducible or semilinear, which means that an \$n\$-aryQuasigroup can be represented as a composition of \$k-ary and \$(n-k+1)\$-aries for some \$k\$ from 2 to \$n-1\$, where the order of arguments in the representation can differ from the original order.
Varieties I:
Summary. For a complex polynomial, f: (C" + 1, 0)-.~ (C, 0), with a singular set of complex dimension s at the origin, we define a sequence of varieties -the L6 varieties, Af ), of f at 0. The
A Census of Small Latin Hypercubes
• Mathematics
SIAM J. Discret. Math.
• 2008
It is proved that no \$3-ary loop of order \$n\$ can have exactly \$n-1\$ identity elements (but no such result holds in dimensions other than 3).
Asymptotics for the number of n-quasigroups of order 4
• Mathematics
• 2006
AbstractThe asymptotic form of the number of n-quasigroups of order 4 is \$\$3^{n + 1} 2^{2^n + 1} (1 + o(1))\$\$ .
On connection between the switching separability of a graph and its subgraphs
A graph of order n ≥ 4 is called switching separable if its modulo-2 sum with some complete bipartite graph on the same set of vertices is divided into two mutually independent subgraphs, each having
АСИМПТОТИКА ЧИСЛА n – КВАЗИГРУПП ПОРЯДКА 4
Алгебраическая система, состоящая из множества мощности | | = k и n-арной операции f : n → , однозначно обратимой по каждой своей переменной, называется n-квазигруппой порядка k. Принято (см. [1])