Overpartitions with parts separated by parity
Number Theory
2026-01-14 v1 Combinatorics
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 -series identities for these functions. These identities include relations to modular forms, -hypergeometric series, and mock modular forms.
Cite
@article{arxiv.2507.16769,
title = {Overpartitions with parts separated by parity},
author = {Kathrin Bringmann and Catherine Cossaboom and William Craig},
journal= {arXiv preprint arXiv:2507.16769},
year = {2026}
}