"Partitions with non-Repeating Odd Parts –
q-Hypergeometric and Combinatorial Identities"
(University of Florida)
By studying partitions with non-repeating odd parts using representations in terms of 2-modular graphs, we first derive a Lebesgue type q-series identity and use this to give a unified treatment of several fundamental identities in the theory of q-hypergeometric series. Next we study these partitions combinatorially and obtain new weighted partition identities. Consequences include a combinatorial proof of a modular relation for the Gollnitz-Gordon functions, and a new derivation of a shifted partition identity due to Andrews. Finally we discuss some new parity results and hint at a theory of basis partitions.
Date: Tuesday, August 19, 2014
Time: 15.40 – 16:30
Place: Mathematics Seminar Room, SA-141
Tea and cookies will be served after the seminar.