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Research Article | Open Access

Some properties of overpartitions into nonmultiples of two integers

Abdulaziz M. Alanazi1( ), Augustine O. Munagi2, Manjil P. Saikia3
Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
The John Knopfmacher Centre for Applicable Analysis and Number Theory University of the Witwatersrand, Johannesburg, South Africa
Mathematical and Physical Sciences division, School of Arts and Sciences, Ahmedabad University, Ahmedabad 380009, Gujarat, India
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Abstract

We consider properties of overpartitions that are simultaneously ℓ-regular and μ-regular, where ℓ and μ 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.

Keywords

overpartitiontheta functioncongruencemodular formRadu's algorithm
CLC number: 05A17, 11P81, 11P83

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AIMS Mathematics
Volume 11 Issue 4,
April 2026
Pages 9876-9891
DOI: 10.3934/math.2026408

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Cite this article:
Alanazi AM, Munagi AO, Saikia MP. Some properties of overpartitions into nonmultiples of two integers. AIMS Mathematics, 2026, 11(4): 9876-9891. https://doi.org/10.3934/math.2026408

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Received: 26 January 2026
Revised: 23 March 2026
Accepted: 25 March 2026
Published: 13 April 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)