**"****Partitions
with non-Repeating Odd Parts – **

**q-Hypergeometric and Combinatorial Identities****"**

By

**(University of Florida)**

__Abstract:__

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.