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arXiv · 2507.16769

Overpartitions with parts separated by parity

Kathrin Bringmann·Catherine Cossaboom·William Craig
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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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Kathrin Bringmann, Catherine Cossaboom, William Craig. 2025-07-22. Overpartitions with parts separated by parity. https://doi.org/10.4153/s0008439525101616

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