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JP Journal of Algebra, Number Theory and Applications

JP Journal of Algebra, Number Theory and Applications
Volume 64, Issue 5 , Pages 531 - 545 (September 2025)
http://dx.doi.org/10.17654/0972555525027

SOME INFINITE FAMILIES OF CONGRUENCES FOR OVERPARTITIONS WITH RESTRICTED ODD DIFFERENCES

Gouri Shankar Guru and Yudhisthira Jamudulia

Abstract:

Recently, Hanson and Smith [7] proved Ramanujan type congruences modulo 3 for where represents the number of overpartitions of n with restricted odd differences. They also derived congruences modulo 5 for In this paper, we prove several infinite families of congruences modulo powers of 2 for by employing q-series identities and iterative computations.

Keywords and phrases:

overpartitions, congruences, restricted odd differences

Received: January 30, 2025; Revised: May 22, 2025; Accepted: July 14, 2025; Published: July 31, 2025

How to cite this article: Gouri Shankar Guru and Yudhisthira Jamudulia, Some infinite families of congruences for overpartitions with restricted odd differences, JP Journal of Algebra, Number Theory and Applications 64(5) (2025), 531-545. https://doi.org/10.17654/0972555525027

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

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[9]M. D. Hirschhorn and J. A. Sellers, A congruence modulo 3 for partitions into distinct non-multiples of four, J. Integer Seq. 17(9) (2014), Article 14.9.6.

[10]M. D. Hirschhorn, An identity of Ramanujan and applications, q-series from a contemporary perspective, Contemporary Mathematics, 254, Amer. Math. Soc. Providence, 2000, pp. 229-234.

[11]M. D. Hirschhorn, The Power of q, Springer International Publishing, Switzerland, 2017.

[12]M. D. Hirschhorn and J. A. Sellers, Congruences for overpartitions with restricted odd differences, Ramanujan J. 53 (2020), 167-180.

[13]B. L. Lin, J. Liu, A. Y. Wang and J. Xiao, Infinite families of congruences for overpartitions with restricted odd differences, Bull. Austral. Math. Soc. 102(1) (2020), 59-66.

[14]M. S. Mahadeva Naika and D. S. Gireesh, Congruences for overpartitions with restricted odd differences, Afr. Mat. 30 (2019), 1-21.

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