English

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 qq-series identities for these functions. These identities include relations to modular forms, qq-hypergeometric series, and mock modular forms.

Keywords

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}
}
R2 v1 2026-07-01T04:13:46.482Z