Overpartitions with parts separated by parity
Kathrin Bringmann, Catherine H. Cossaboom, William Craig · Canadian Mathematical Bulletin · 2026
Abstract In this article, we generalize Andrews’ partitions separated by parity to overpartitions in two ways. We investigate the generating functions for 16 $16$ 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.