Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
Title: Andrews and Bressoud Style Identities for Partitions and Overpartitions
Speaker: Kağan Kurşungöz, Faculty of Engineering and Natural Sciences, Sabanci University
Date: Thursday, November 19, 2015 5:00pm
Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ
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.