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Arithmetic properties of partitions into $k$ parts congruent to $\pm l$ modulo $m$

Volume 159 / 2020

Robson da Silva, Kelvin Souza de Oliveira, Almir Cunha da Graça Neto Colloquium Mathematicum 159 (2020), 47-59 MSC: Primary 11P83; Secondary 05A17. DOI: 10.4064/cm7742-2-2019 Published online: 7 October 2019

Abstract

Ramanujan-type congruences satisfied by functions that enumerate partitions whose parts belong to a finite set are well-known and have been studied by many authors. In this paper, we let the parts belong to the infinite set of integers congruent to $\pm l$ modulo $m$ and we obtain infinitely many Ramanujan-type congruences for the corresponding number of partitions into exactly $k$ parts, $p_{\pm l}^{m}(n, k)$. We also consider two other restricted partition functions.

Authors

  • Robson da SilvaUniversidade Federal de São Paulo
    Av. Cesare M. G. Lattes, 1201
    São José dos Campos, SP, 12247-014, Brazil
    e-mail
  • Kelvin Souza de OliveiraUniversidade Federal do Amazonas
    Manaus, AM, 69103-128, Brazil
    e-mail
  • Almir Cunha da Graça NetoUniversidade do Estado do Amazonas
    Manaus, AM, 69055-038, Brazil
    e-mail

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