Some Properties of Overpartitions into Nonmultiples of Two Integers
Number Theory
2024-12-30 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.2412.18938,
title = {Some Properties of Overpartitions into Nonmultiples of Two Integers},
author = {Abdulaziz M. Alanazi and Augustine O. Munagi and Manjil P. Saikia},
journal= {arXiv preprint arXiv:2412.18938},
year = {2024}
}