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

  • Sergey 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.

Author Biography

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

PhD (physics and mathematics); head of the laboratory of IT security

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Published
2022-04-15
Keywords: binomial coefficient, de Moivre – Laplace theorem, Walsh – Hadamard spectrum, bent function, sum of squares representation
How to Cite
Agievich, S. V. (2022). An upper bound on binomial coefficients in the de Moivre – Laplace form. Journal of the Belarusian State University. Mathematics and Informatics, 1, 66-74. https://doi.org/10.33581/2520-6508-2022-1-66-74
Section
Discrete Mathematics and Mathematical Cybernetics