Combinatorial interpretation for an identity involving overpartitions into parts = l (mod i)

Authors

DOI:

https://doi.org/10.35819/remat2020v6i1id3856

Keywords:

Integer Partitions, Integer Overpartitions, Generating Functions, Matrices, Combinatorial Interpretations

Abstract

In the present paper we provide a combinatorial interpretation for an identity involving hypergeometric q-series in terms of matrices. This makes an identity that can be interpreted as a generating function for the number of overpartitions of an integer n whose parts are congruent to l module i. We will use the well-known Santos method, described in Santos, Mondek and Ribeiro (2011), that interprets coefficients of q-series as the number of certain matrices, in which their entries respect some neighborhood rules.

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Author Biography

Mateus Alegri, Universidade Federal de Sergipe (UFS), Departamento de Matemática (DMAI), Itabaiana, SE, Brasil

Possui graduação em bacharelado em matemática pela Universidade Estadual Paulista Júlio de Mesquita Filho (2003), mestrado em Matemática Aplicada pela Universidade Estadual de Campinas (2006) e doutorado em Matemática Aplicada pela Universidade Estadual de Campinas (2010). Atualmente é professor efetivo, associado II, da Universidade Federal de Sergipe. Tem experiência na área de Matemática, atuando principalmente nos seguintes temas: combinatória, teoria aditiva dos números, ensino e aprendizagem, funções geradoras e funções especiais.

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Published

2020-06-29

How to Cite

ALEGRI, M. Combinatorial interpretation for an identity involving overpartitions into parts = l (mod i). REMAT: Revista Eletrônica da Matemática, Bento Gonçalves, RS, v. 6, n. 1, p. 1–11, 2020. DOI: 10.35819/remat2020v6i1id3856. Disponível em: https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/3856. Acesso em: 3 jul. 2024.

Issue

Vol. 6 No. 1 (2020)

Section

Matemática Pura e/ou Aplicada

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