An upper bound on binomial coefficients in the de Moivre – Laplace form
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 f...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | Belarusian |
| Published: |
Belarusian State University
2022-04-01
|
| Series: | Журнал Белорусского государственного университета: Математика, информатика |
| Subjects: | |
| Online Access: | https://journals.bsu.by/index.php/mathematics/article/view/4525 |
| _version_ | 1811229185157365760 |
|---|---|
| author | Sergey V. Agievich |
| author_facet | Sergey V. Agievich |
| author_sort | Sergey V. Agievich |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T10:09:48Z |
| format | Article |
| id | doaj.art-42a4fdd404e94ab685abecfd677a863c |
| institution | Directory Open Access Journal |
| issn | 2520-6508 2617-3956 |
| language | Belarusian |
| last_indexed | 2024-04-12T10:09:48Z |
| publishDate | 2022-04-01 |
| publisher | Belarusian State University |
| record_format | Article |
| series | Журнал Белорусского государственного университета: Математика, информатика |
| spelling | doaj.art-42a4fdd404e94ab685abecfd677a863c2022-12-22T03:37:20ZbelBelarusian State UniversityЖурнал Белорусского государственного университета: Математика, информатика2520-65082617-39562022-04-011667410.33581/2520-6508-2022-1-66-744525An upper bound on binomial coefficients in the de Moivre – Laplace formSergey V. Agievich0Research Institute for Applied Problems of Mathematics and Informatics, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, BelarusWe 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.https://journals.bsu.by/index.php/mathematics/article/view/4525binomial coefficientde moivre – laplace theoremwalsh – hadamard spectrumbent functionsum of squares representation |
| spellingShingle | Sergey V. Agievich An upper bound on binomial coefficients in the de Moivre – Laplace form Журнал Белорусского государственного университета: Математика, информатика binomial coefficient de moivre – laplace theorem walsh – hadamard spectrum bent function sum of squares representation |
| title | An upper bound on binomial coefficients in the de Moivre – Laplace form |
| title_full | An upper bound on binomial coefficients in the de Moivre – Laplace form |
| title_fullStr | An upper bound on binomial coefficients in the de Moivre – Laplace form |
| title_full_unstemmed | An upper bound on binomial coefficients in the de Moivre – Laplace form |
| title_short | An upper bound on binomial coefficients in the de Moivre – Laplace form |
| title_sort | upper bound on binomial coefficients in the de moivre laplace form |
| topic | binomial coefficient de moivre – laplace theorem walsh – hadamard spectrum bent function sum of squares representation |
| url | https://journals.bsu.by/index.php/mathematics/article/view/4525 |
| work_keys_str_mv | AT sergeyvagievich anupperboundonbinomialcoefficientsinthedemoivrelaplaceform AT sergeyvagievich upperboundonbinomialcoefficientsinthedemoivrelaplaceform |