## Figures from this paper

## 9 Citations

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

- MathematicsDiscret. Math.
- 2011

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

- MathematicsSIAM 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.

On extensions of partial n-quasigroups of order 4

- Mathematics
- 2012

We prove that every collection of pairwise compatible (nowhere coinciding) n-ary quasigroups of order 4 can be extended to an (n + 1)-ary quasigroup. In other words, every Latin 4×…×4 ×…

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…

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…

On connection between the switching separability of a graph and its subgraphs

- Mathematics
- 2011

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 reducibility of n-ary quasigroups, II

- Mathematics
- 2008

An n-ary operation Q : Σ → Σ is called an n-ary quasigroup of order |Σ| if in the equation x0 = Q(x1, . . . , xn) knowledge of any n elements of x0, . . . , xn uniquely specifies the remaining one. Q…

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