Affiliation:
1. Faculty of Engineering and Natural Sciences, Sabancı University, Tuzla, Istanbul 34956, Turkey
Abstract
Sang, Shi and Yee, in 2020, found overpartition analogs of Andrews’ results involving parity in Rogers–Ramanujan–Gordon identities. Their result partially answered an open question of Andrews’. The open question was to involve parity in overpartition identities. We extend Sang, Shi and Yee’s work to arbitrary moduli, and also provide a missing case in their identities. We also unify proofs of Rogers–Ramanujan–Gordon identities for overpartitions due to Lovejoy and Chen et al.; Sang, Shi and Yee’s results; and ours. Although verification type proofs are given for brevity, a construction of series as solutions of functional equations between partition generating functions is sketched.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Algebra and Number Theory