13 citations · 39 across the 18 of their papers we have counts for
23 papers
Multidimensional convolution matrices and perfect colorings of subspace hypergraphs applied for bent functions and related designs
Vladimir N. Potapov, Anna A. Taranenko
The main aim of the present paper is to introduce new methods for the study of combinatorial designs related to bent functions. They are based on interpretations of convolution on…
Multidimensional quadrangle condition and cuboctahedra in latin hypercubes
Anna A. Taranenko
The well-known quadrangle criterion states that a latin square is isotopic to the Cayley table of a group if and only if all quadrangles spanned by the same triple of symbols coinc…
Enumeration and constructions of vertices of the polytope of polystochastic matrices
Anna A. Taranenko
A multidimensional nonnegative matrix is called polystochastic if the sum of entries in each of its lines equals . The set of all polystochastic matrices of order and dimens…
Characterization of polystochastic matrices of order with zero permanent
A. L. Perezhogin, V. N. Potapov, A. A. Taranenko +1
A multidimensional nonnegative matrix is called polystochastic if the sum of its entries over each line is equal to . The permanent of a multidimensional matrix is the sum of pr…
Asymptotic bounds on the numbers of vertices of polytopes of polystochastic matrices
Vladimir N. Potapov, Anna A. Taranenko
A multidimensional nonnegative matrix is called polystochastic if the sum of entries in each line is equal to . The set of all polystochastic matrices of order and dimension…
Vertices of the polytope of polystochastic matrices and product constructions
Anna A. Taranenko
A multidimensional nonnegative matrix is called polystochastic if the sum of its entries at each line is equal to . The set of all polystochastic matrices of order and dimen…
Products of multidimensional matrices, stochastic matrices, and permanents
Anna A. Taranenko
In this paper we consider four basic multidimensional matrix operations (outer product, Kronecker product, contraction, and projection) and two derivative operations (dot and circl…
Multidimensional threshold matrices and extremal matrices of order
Anna A. Taranenko
The paper is devoted to multidimensional -matrices extremal with respect to containing a polydiagonal (a fractional generalization of a diagonal). Every extremal matrix is a…
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…
Perfect colorings of hypergraphs
Anna A. Taranenko
Perfect colorings (equitable partitions) of graphs are extensively studied, while the same concept for hypergraphs attracts much less attention. The aim of this paper is to develop…
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…
An asymptotic lower bound on the number of bent functions
V. N. Potapov, A. A. Taranenko, Yu. V. Tarannikov
A Boolean function on variables is said to be a bent function if the absolute value of all its Walsh coefficients is . Our main result is a new asymptotic lower bo…
On a metric property of perfect colorings
Anna A. Taranenko
Given a perfect coloring of a graph, we prove that the distance between two rows of the adjacency matrix of the graph is not less than the distance between the correspo…
Transversals, near transversals, and diagonals in iterated groups and quasigroups
Anna A. Taranenko
Given a binary quasigroup of order , a -iterated quasigroup is the -ary quasigroup equal to the -times composition of with itself. The Cayley table o…
Perfect 2-colorings of Hamming graphs
Evgeny A. Bespalov, Denis S. Krotov, Aleksandr A. Matiushev +2
We consider the problem of existence of perfect -colorings (equitable -partitions) of Hamming graphs with given parameters. We start with conditions on parameters of graphs a…
Regularity and counting lemmas for multidimensional matrices
Anna A. Taranenko
In the present paper we propose generalizations of the regularity and counting lemmas for multidimensional matrices under a finite alphabet. Firstly, we prove a variant of a multid…
Algebraic properties of perfect structures
Anna A. Taranenko
A perfect structure is a triple of matrices and of consistent sizes such that . Perfect structures comprise similar matrices, eigenvectors, perfect co…
On the König-Hall-Egerváry theorem for multidimensional matrices and multipartite hypergraphs
Anna A. Taranenko
One of possible interpretations of the well-known König--Hall--Egerváry theorem is a full characterization of all bipartite graphs extremal for fractional matchings of a given weig…
Positiveness of the permanent of 4-dimensional polystochastic matrices of order 4
Anna Taranenko
A nonnegative multidimensional matrix is called polystochastic if the sum of its entries over each line is equal to . In this paper we overview known results on positiveness of…
Transversals, plexes, and multiplexes in iterated quasigroups
Anna Taranenko
A -ary quasigroup of order is a -ary operation over a set of cardinality such that the Cayley table of the operation is a -dimensional latin hypercube of the same…
Transversals in completely reducible multiary quasigroups and in multiary quasigroups of order 4
Anna Taranenko
An -ary quasigroup of order is an -ary operation over a set of cardinality such that the Cayley table of the operation is an -dimensional latin hypercube of or…
On the numbers of 1-factors and 1-factorizations of hypergraphs
Anna Taranenko
A 1-factor of a hypergraph is a set of hyperedges such that every vertex of is incident to exactly one hyperedge from the set. A 1-factorization is a partition of all…
Upper bounds on the permanent of multidimensional (0,1)-matrices
A. A. Taranenko
The permanent of a multidimensional matrix is the sum of products of entries over all diagonals. By Minc's conjecture, there exists a reachable upper bound on the permanent of 2-di…