10 citations · 42 across the 14 of their papers we have counts for
16 papers
Combinatorial designs, difference sets and bent functions as perfect colorings of graphs and multigraphs
V. N. Potapov, S. V. Avgustinovich
It is proved that 1) the indicator function of some onefold or multifold independent set in a regular graph is a perfect coloring if and only if the set attain the Delsarte--Hoffma…
Singleton mesh patterns in multidimensional permutations
Sergey Avgustinovich, Sergey Kitaev, Jeffrey Liese +2
This paper introduces the notion of mesh patterns in multidimensional permutations and initiates a systematic study of singleton mesh patterns (SMPs), which are multidimensional me…
On five types of crucial permutations with respect to monotone patterns
Sergey Avgustinovich, Sergey Kitaev, Anna Taranenko
A crucial permutation is a permutation that avoids a given set of prohibitions, but any of its extensions, in an allowable way, results in a prohibition being introduced. In this p…
On perfect colorings of infinite multipath graphs
M. A. Lisitsyna, S. V. Avgustinovich, O. G. Parshina
A coloring of vertices of a given graph is called perfect if the color structure of each ball of radius in the graph depends only on the color of the ball center. Let be a…
Completely regular codes in the infinite hexagonal grid
Sergey V. Avgustinovich, Denis S. Krotov, Anastasia Yu. Vasil'eva
A set of vertices of a simple graph is called a completely regular code if for each , , , \ldots and , , , all vertices at distance from hav…
Canonical Representatives of Morphic Permutations
Sergey Avgustinovich, Anna Frid, Svetlana Puzynina
An infinite permutation can be defined as a linear ordering of the set of natural numbers. In particular, an infinite permutation can be constructed with an aperiodic infinite word…