22 citations · 51 across the 7 of their papers we have counts for
7 papers
On the Fourier Entropy-Influence Conjecture for Boolean Plateaued Functions
Vladimir N. Potapov
We prove the following inequality for Boolean functions: . Using this inequality, we establish the Fourier Entropy-Influence (FEI)…
Perfect Combinatorial Structures in Coding Theory and Cryptography
Vladimir N. Potapov
This book develops algebraic and combinatorial methods for studying discrete structures. It brings together graph theory, Boolean functions, Fourier analysis on finite groups, codi…
On the reconstruction of -quasigroups of order and upper bounds on their number
Denis S. Krotov, Vladimir N. Potapov
(This is a reprint of the thesis published in the Transactions of the Conference Devoted to the 90th Anniversary Of Alexei A. Lyapunov, Novosibirsk, October 8-12, 2001, pages 323-3…
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 the number of n-ary quasigroups of finite order
Denis Krotov, Vladimir Potapov
Let be the number of -ary quasigroups of order . We derive a recurrent formula for Q(n,4). We prove that for all and the following inequalities h…
On reconstructing reducible n-ary quasigroups and switching subquasigroups
Denis Krotov, Vladimir Potapov, Polina Sokolova
(1) We prove that, provided n>=4, a permutably reducible n-ary quasigroup is uniquely specified by its values on the n-ples containing zero. (2) We observe that for each n,k>=2 and…