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September 23, 2025Open Access

Overpartitions with parts separated by parity

Key Points

Various identities related to overpartitions are established, enhancing the understanding of generating functions.
The study examines 16 different overpartition families, detailing their generating functions based on parity separation.
Proven identities link to significant areas in mathematics, including modular forms and q-hypergeometric series.
Identities developed may lead to deeper insights into the properties of mock modular forms.

Abstract

In this paper, we generalize Andrews' partitions separated by parity to overpartitions in two ways. We investigate the generating functions for 16 overpartition families whose parts are separated by parity, and we prove various q-series identities for these functions. These identities include relations to modular forms, q-hypergeometric series, and mock modular forms.

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Cite This Study

Bringmann et al. (Tue,) studied this question.

synapsesocial.com/papers/68d4759931b076d99fa6daa7 https://doi.org/https://doi.org/10.48550/arxiv.2507.16769

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