2 citations · 4 across the 7 of their papers we have counts for
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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…
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…
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…
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.…
Every latin hypercube of order 5 has transversals
A. L. Perezhogin, V. N. Potapov, S. Yu. Vladimirov
We prove that for all n>1 every latin n-dimensional cube of order 5 has transversals. We find all 123 paratopy classes of layer-latin cubes of order 5 with no transversals. For eac…