ARITHMETIC FUNCTIONS VERIFYING A RECURRENCE RELATION, COMPOSITIONS AND BELL POLYNOMIALS

Bibliographic Details
Main Author: Alegri, Mateus
Publication Date: 2024
Other Authors: Bulnes, Juan, Kim, Taekyun, Bonilla, José Luís
Format: Article
Language: eng
Source: Revista Sergipana de Matemática e Educação Matemática
Download full: https://periodicos.ufs.br/ReviSe/article/view/21793
Summary: In the work we apply the Z-transform to the recurrence of Cauchy convolution type, satisfied by several arithmetic functions, to obtain its solution in terms of the complete Bell polynomials. One of the most important arithmetic function used here is sigma1(n), the function that sum all positive divisors of n. Our main result can be applied to find a closed formula for the number of k-colored partitions, sum of triangular numbers and more.
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spelling ARITHMETIC FUNCTIONS VERIFYING A RECURRENCE RELATION, COMPOSITIONS AND BELL POLYNOMIALSARITHMETIC FUNCTIONS VERIFYING A RECURRENCE RELATION, COMPOSITIONS AND BELL POLYNOMIALSIn the work we apply the Z-transform to the recurrence of Cauchy convolution type, satisfied by several arithmetic functions, to obtain its solution in terms of the complete Bell polynomials. One of the most important arithmetic function used here is sigma1(n), the function that sum all positive divisors of n. Our main result can be applied to find a closed formula for the number of k-colored partitions, sum of triangular numbers and more.In the work we apply the Z-transform to the recurrence of Cauchy convolution type, satisfied by several arithmetic functions, to obtain its solution in terms of the complete Bell polynomials. One of the most important arithmetic function used here is sigma1(n), the function that sum all positive divisors of n. Our main result can be applied to find a closed formula for the number of k-colored partitions, sum of triangular numbers and more.In the work we apply the Z-transform to the recurrence of Cauchy convolution type, satisfied by several arithmetic functions, to obtain its solution in terms of the complete Bell polynomials. One of the most important arithmetic function used here is sigma1(n), the function that sum all positive divisors of n. Our main result can be applied to find a closed formula for the number of k-colored partitions, sum of triangular numbers and more.In the work we apply the Z-transform to the recurrence of Cauchy convolution type, satisfied by several arithmetic functions, to obtain its solution in terms of the complete Bell polynomials. One of the most important arithmetic function used here is sigma1(n), the function that sum all positive divisors of n. Our main result can be applied to find a closed formula for the number of k-colored partitions, sum of triangular numbers and more.Universidade Federal de Sergipe2024-10-14info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://periodicos.ufs.br/ReviSe/article/view/2179310.34179/revisem.v9i3.21793Revista Sergipana de Matemática e Educação Matemática; v. 9 n. 3 (2024): Revista Sergipana de Matemática e Educação Matemática; 25-34Revista Sergipana de Matemática e Educação Matemática; Vol. 9 No. 3 (2024): Revista Sergipana de Matemática e Educação Matemática; 25-34Revista Sergipana de Matemática e Educação Matemática; Vol. 9 Núm. 3 (2024): Revista Sergipana de Matemática e Educação Matemática; 25-34Revista Sergipana de Matemática e Educação Matemática; Vol. 9 No 3 (2024): Revista Sergipana de Matemática e Educação Matemática; 25-342525-5444reponame:Revista Sergipana de Matemática e Educação Matemáticainstname:Universidade Federal de Sergipe (UFS)instacron:UFSenghttps://periodicos.ufs.br/ReviSe/article/view/21793/16321Copyright (c) 2024 Mateus Alegrihttps://creativecommons.org/licenses/by-nc/4.0info:eu-repo/semantics/openAccessAlegri, MateusBulnes, JuanKim, TaekyunBonilla, José Luís2024-10-14T15:18:13Zoai:ojs.ufs.emnuvens.com.br:article/21793Revistahttps://periodicos.ufs.br/ReviSePUBhttps://periodicos.ufs.br/ReviSe/oairevisem.ojs@gmail.com || arlucioviana@ufs.br2525-54442525-5444opendoar:2024-10-14T15:18:13Revista Sergipana de Matemática e Educação Matemática - Universidade Federal de Sergipe (UFS)false
dc.title.none.fl_str_mv ARITHMETIC FUNCTIONS VERIFYING A RECURRENCE RELATION, COMPOSITIONS AND BELL POLYNOMIALS
ARITHMETIC FUNCTIONS VERIFYING A RECURRENCE RELATION, COMPOSITIONS AND BELL POLYNOMIALS
In the work we apply the Z-transform to the recurrence of Cauchy convolution type, satisfied by several arithmetic functions, to obtain its solution in terms of the complete Bell polynomials. One of the most important arithmetic function used here is sigma1(n), the function that sum all positive divisors of n. Our main result can be applied to find a closed formula for the number of k-colored partitions, sum of triangular numbers and more.
title ARITHMETIC FUNCTIONS VERIFYING A RECURRENCE RELATION, COMPOSITIONS AND BELL POLYNOMIALS
spellingShingle ARITHMETIC FUNCTIONS VERIFYING A RECURRENCE RELATION, COMPOSITIONS AND BELL POLYNOMIALS
Alegri, Mateus
title_short ARITHMETIC FUNCTIONS VERIFYING A RECURRENCE RELATION, COMPOSITIONS AND BELL POLYNOMIALS
title_full ARITHMETIC FUNCTIONS VERIFYING A RECURRENCE RELATION, COMPOSITIONS AND BELL POLYNOMIALS
title_fullStr ARITHMETIC FUNCTIONS VERIFYING A RECURRENCE RELATION, COMPOSITIONS AND BELL POLYNOMIALS
title_full_unstemmed ARITHMETIC FUNCTIONS VERIFYING A RECURRENCE RELATION, COMPOSITIONS AND BELL POLYNOMIALS
title_sort ARITHMETIC FUNCTIONS VERIFYING A RECURRENCE RELATION, COMPOSITIONS AND BELL POLYNOMIALS
author Alegri, Mateus
author_facet Alegri, Mateus
Bulnes, Juan
Kim, Taekyun
Bonilla, José Luís
author_role author
author2 Bulnes, Juan
Kim, Taekyun
Bonilla, José Luís
author2_role author
author
author
dc.contributor.author.fl_str_mv Alegri, Mateus
Bulnes, Juan
Kim, Taekyun
Bonilla, José Luís
description In the work we apply the Z-transform to the recurrence of Cauchy convolution type, satisfied by several arithmetic functions, to obtain its solution in terms of the complete Bell polynomials. One of the most important arithmetic function used here is sigma1(n), the function that sum all positive divisors of n. Our main result can be applied to find a closed formula for the number of k-colored partitions, sum of triangular numbers and more.
publishDate 2024
dc.date.none.fl_str_mv 2024-10-14
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://periodicos.ufs.br/ReviSe/article/view/21793
10.34179/revisem.v9i3.21793
url https://periodicos.ufs.br/ReviSe/article/view/21793
identifier_str_mv 10.34179/revisem.v9i3.21793
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://periodicos.ufs.br/ReviSe/article/view/21793/16321
dc.rights.driver.fl_str_mv Copyright (c) 2024 Mateus Alegri
https://creativecommons.org/licenses/by-nc/4.0
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2024 Mateus Alegri
https://creativecommons.org/licenses/by-nc/4.0
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidade Federal de Sergipe
publisher.none.fl_str_mv Universidade Federal de Sergipe
dc.source.none.fl_str_mv Revista Sergipana de Matemática e Educação Matemática; v. 9 n. 3 (2024): Revista Sergipana de Matemática e Educação Matemática; 25-34
Revista Sergipana de Matemática e Educação Matemática; Vol. 9 No. 3 (2024): Revista Sergipana de Matemática e Educação Matemática; 25-34
Revista Sergipana de Matemática e Educação Matemática; Vol. 9 Núm. 3 (2024): Revista Sergipana de Matemática e Educação Matemática; 25-34
Revista Sergipana de Matemática e Educação Matemática; Vol. 9 No 3 (2024): Revista Sergipana de Matemática e Educação Matemática; 25-34
2525-5444
reponame:Revista Sergipana de Matemática e Educação Matemática
instname:Universidade Federal de Sergipe (UFS)
instacron:UFS
instname_str Universidade Federal de Sergipe (UFS)
instacron_str UFS
institution UFS
reponame_str Revista Sergipana de Matemática e Educação Matemática
collection Revista Sergipana de Matemática e Educação Matemática
repository.name.fl_str_mv Revista Sergipana de Matemática e Educação Matemática - Universidade Federal de Sergipe (UFS)
repository.mail.fl_str_mv revisem.ojs@gmail.com || arlucioviana@ufs.br
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