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.
Done