Geodesic
An upper bound on binomial coefficients in the de Moivre – Laplace form
Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2022), pp. 66-74

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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.
Mots-clés : binomial coefficient; de Moivre – Laplace theorem; Walsh – Hadamard spectrum; bent function; sum of squares representation. 
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     author = {S. V. Agievich},
     title = {An upper bound on binomial coefficients in the de {Moivre} {\textendash} {Laplace} form},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {66--74},
     publisher = {mathdoc},
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     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/BGUMI_2022_1_a6/}
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S. V. Agievich. An upper bound on binomial coefficients in the de Moivre – Laplace form. Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2022), pp. 66-74. http://geodesic.mathdoc.fr/item/BGUMI_2022_1_a6/