4 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…
Partitioning the hypercube into smaller hypercubes
Noga Alon, Jozsef Balogh, Vladimir N. Potapov
Denote by Q_d the d-dimensional hypercube. Addressing a recent question we estimate the number of ways the vertex set of Q_d can be partitioned into vertex disjoint smaller cubes.…
On the number of relevant variables for discrete functions
V. N. Potapov
We consider various definitions of degrees of discrete functions and establish relations between the number of relevant (essential) variables and degrees of two- and three-valued f…
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…