New congruences modulo powers of 2 for k-regular overpartition pairs

Riyajur Rahman and Nipen Saikia
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 4, Pages 691–703
DOI: 10.7546/nntdm.2024.30.4.691-703
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Authors and affiliations

Riyajur Rahman
Department of Mathematics, Rajiv Gandhi University
Rono Hills, Doimukh, Arunachal Pradesh, India

Nipen Saikia
Department of Mathematics, Rajiv Gandhi University
Rono Hills, Doimukh, Arunachal Pradesh, India

Abstract

Let \overline{B}_{k}(n) denote the number of k regular overpartition pairs where a k-regular overpartition pair of n is a pair of k-regular overpartitions (a,b) in which the sum of all the parts is n. Naika and Shivasankar (2017) proved infinite families of congruences for \overline{B}_3(n) and \overline{B}_4(n). In this paper, we prove infinite families of congruences modulo powers of 2 for \overline{B}_{3\gamma}(n), \overline{B}_{4\gamma}(n) and \overline{B}_{6\gamma}(n).

Keywords

  • Overpartition pair
  • k-regular partition
  • Congruences
  • Theta function

2020 Mathematics Subject Classification

  • 11P83
  • 05A17

References

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Manuscript history

  • Received: 7 November 2023
  • Revised: 29 October 2024
  • Accepted: 4 November 2024
  • Online First: 6 November 2024

Copyright information

Ⓒ 2024 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Cite this paper

Rahman, R., & Saikia, N. (2024). New congruences modulo powers of 2 for k-regular overpartition pairs. Notes on Number Theory and Discrete Mathematics, 30(4), 691-703, DOI: 10.7546/nntdm.2024.30.4.691-703.

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