Alladi Ramakrishnan Hall

Partitions with non-repeating odd parts: $q$-hypergeometric and combinatorial identities

Krishnaswami Alladi

University of Florida

By representing partitions with non-repeating

odd parts in terms of $2$-modular graphs, and by considering the Durfee
square classification, we first

derive a new Lebesgue type identity in two free

parameters. Specializations include classical identities of Gauss and
Sylvester. By combinatorially studying the

two parameter identity we obtain modular identities for the Gollnitz-Gordon
functions and a new proof of a famous shifted partition identity mod $32$ of
Andrews.

Some new partial theta identities will also be derived.