Kağan Kurşungöz, Rutgers Experimental Mathematics Seminar, November 19, 2015
Abstract: We propose a method to construct a variety of partition identities at once. The main applications are all-moduli generalization of some of Andrews' results in [Andrews, Parity in partition identities. Ramanujan Journal 23:45-90 (2010)] and Bressoud's even moduli generalization of Rogers-Ramanujan-Gordon identities, and their counterparts for overpartitions due to Lovejoy et al. and Chen et al. We obtain unusual companion identities to known theorems as well as to the new ones in the process. The novelty is that the method constructs solutions to functional equations which are satisfied by the generating functions. In contrast, the conventional approach is to show that a variant of well-known series satisfies the system of functional equations, thus reconciling two separate lines of computations.