D. Krotov

A vertex 2-coloring of a graph is said to be perfect with parameters $(a_{ij})_{i, j = 1}^{k}$ if for every $i, j \in {1, ..., k}$ every vertex of color $i$ is adjacent with exactly $a_{ij…

math.CO2008★ 1 cited

On mobile sets in the binary hypercube

Yuriy Vasil'ev, Sergey Avgustinovich, Denis Krotov

If two distance-3 codes have the same neighborhood, then each of them is called a mobile set. In the (4k+3)-dimensional binary hypercube, there exists a mobile set of cardinality 2…

math.CO2008★ 5 cited

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

Denis Krotov, Vladimir Potapov

An $n$ -ary operation $Q : S^{n} \to S$ is called an $n$ -ary quasigroup of order $∣ S ∣$ if in the equation $x_{0} = Q (x_{1}, ..., x_{n})$ knowledge of any $n$ elements of $x_{0}, ..., x_{n}$ uniquely spe…

Perfect colorings of Z2: Nine colors

Embedding in a perfect code

On perfect colorings of the halved 24-cube

On mobile sets in the binary hypercube

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

Perfect colorings of $Z^{2}$ : Nine colors