This article is cited in 1 paper

Discrete mathematics and Mathematical cybernetics

An upper bound on binomial coefficients in the de Moivre – Laplace form

S. V. Agievich

Research Institute for Applied Problems of Mathematics and Informatics, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

Abstract: We provide an upper bound on binomial coefficients that holds over the entire parameter range an whose form repeats the form of the de Moivre – Laplace approximation of the symmetric binomial distribution. Using the bound, we estimate the number of continuations of a given Boolean function to bent functions, investigate dependencies into the Walsh – Hadamard spectra, obtain restrictions on the number of representations as sums of squares of integers bounded in magnitude.

Keywords: binomial coefficient; de Moivre – Laplace theorem; Walsh – Hadamard spectrum; bent function; sum of squares representation.

UDC: 519.118

Received: 20.01.2022
Revised: 18.02.2022
Accepted: 21.02.2022

DOI: 10.33581/2520-6508-2022-1-66-74

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