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pro vyhledávání: '"Potapov, P N"'
A multidimensional nonnegative matrix is called polystochastic if the sum of its entries over each line is equal to $1$. The permanent of a multidimensional matrix is the sum of products of entries over all diagonals. We prove that if $d$ is even, th
Externí odkaz:
http://arxiv.org/abs/2410.09546
A multidimensional nonnegative matrix is called polystochastic if the sum of entries in each line is equal to $1$. The set of all polystochastic matrices of order $n$ and dimension $d$ is a convex polytope $\Omega_n^d$. In the present paper, we compa
Externí odkaz:
http://arxiv.org/abs/2406.14160
Autor:
Potapov, V. N., Avgustinovich, S. V.
Publikováno v:
Siberian Mathematical Journal, 2020, Vol. 61, No. 5, P. 867-877
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--Hoffman bound; 2) each transversal in a uniform regular hypergraph is an ind
Externí odkaz:
http://arxiv.org/abs/2403.02904
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. Among other results, we prove that the asymptotic order of this functi
Externí odkaz:
http://arxiv.org/abs/2401.00299
Autor:
Potapov, Vladimir N.
It is disproved the Tokareva's conjecture that any balanced boolean function of appropriate degree is a derivative of some bent function. This result is based on new upper bounds for the numbers of bent and plateaued functions.
Comment: 3 pages
Comment: 3 pages
Externí odkaz:
http://arxiv.org/abs/2309.04244
Autor:
Potapov, Vladimir N.
The logarithm of the number of binary n-variable bent functions is asymptotically less than $11(2^n)/32$ as n tends to infinity. Keywords: boolean function, Walsh--Hadamard transform, plateaued function, bent function, upper bound
Comment: 9 pag
Comment: 9 pag
Externí odkaz:
http://arxiv.org/abs/2303.16547
Autor:
Krotov, Denis S., Potapov, Vladimir N.
Publikováno v:
Discrete Math. 347(1) 2024, 113657(1-9)
A frequency $n$-cube $F^n(q;l_0,...,l_{m-1})$ is an $n$-dimensional $q$-by-...-by-$q$ array, where $q = l_0+...+l_{m-1}$, filled by numbers $0,...,m-1$ with the property that each line contains exactly $l_i$ cells with symbol $i$, $i = 0,...,m-1$ (a
Externí odkaz:
http://arxiv.org/abs/2212.03694
Autor:
Potapov, Vladimir N.
A coloring of vertices of a graph is called perfect if, for every vertex, the collection of colors of its neighbors depends only on its own color. The correspondent color partition of vertices is called equitable. We note that a number of bounds (Hof
Externí odkaz:
http://arxiv.org/abs/2204.03308
Autor:
Potapov, Vladimir N.
Publikováno v:
Journal of Combinatorial Designs. 2022. V. 30 (9). P. 626--633
An embedding of a code is a mapping that preserves distances between codewords. We prove that any code with code distance $\rho$ and length $d$ can be embedded into an MDS code with the same code distance and length but under a larger alphabet. As a
Externí odkaz:
http://arxiv.org/abs/2109.14962
A Boolean function $f$ on $n$ variables is said to be a bent function if the absolute value of all its Walsh coefficients is $2^{n/2}$. Our main result is a new asymptotic lower bound on the number of Boolean bent functions. It is based on a modifica
Externí odkaz:
http://arxiv.org/abs/2108.00232