Some properties of overpartitions into nonmultiples of two integers

Abdulaziz M. Alanazi; Augustine O. Munagi; Manjil P. Saikia; Abdulaziz M. Alanazi; Augustine O. Munagi; Manjil P. Saikia

doi:10.3934/math.2026408

AIMS Mathematics

2026, Volume 11, Issue 4: 9876-9891. doi: 10.3934/math.2026408

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Some properties of overpartitions into nonmultiples of two integers

1.
Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
2.
The John Knopfmacher Centre for Applicable Analysis and Number Theory University of the Witwatersrand, Johannesburg, South Africa
3.
Mathematical and Physical Sciences division, School of Arts and Sciences, Ahmedabad University, Ahmedabad 380009, Gujarat, India

Received: 26 January 2026 Revised: 23 March 2026 Accepted: 25 March 2026 Published: 13 April 2026
MSC : 05A17, 11P81, 11P83

We consider properties of overpartitions that are simultaneously $ \ell $-regular and $ \mu $-regular, where $ \ell $ and $ \mu $ are positive relatively prime integers. We prove a seven-way combinatorial identity related to these overpartitions. We also prove several congruence properties satisfied by this class of partitions (and a further related class) using both generating functions and modular forms with Radu's algorithm.
- overpartition,
- theta function,
- congruence,
- modular form,
- Radu's algorithm
Citation: Abdulaziz M. Alanazi, Augustine O. Munagi, Manjil P. Saikia. Some properties of overpartitions into nonmultiples of two integers[J]. AIMS Mathematics, 2026, 11(4): 9876-9891. doi: 10.3934/math.2026408

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Abstract

We consider properties of overpartitions that are simultaneously $ \ell $-regular and $ \mu $-regular, where $ \ell $ and $ \mu $ are positive relatively prime integers. We prove a seven-way combinatorial identity related to these overpartitions. We also prove several congruence properties satisfied by this class of partitions (and a further related class) using both generating functions and modular forms with Radu's algorithm.

References

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