Document Type

Conference Proceeding

Publication Date

3-12-2012

Publication Title

Proceedings of the Conference on Partitions, q-Series, and Modular Forms

DOI

10.1007/978-1-4614-0028-8_6

ISBN

978-1-4614-0027-1

Abstract

We use generalized lecture hall partitions to discover a new pair of q-series identities. These identities are unusual in that they involve partitions into parts from asymmetric residue classes, much like the little Göllnitz partition theorems. We derive a two-parameter generalization of our identities that, surprisingly, gives new analytic counterparts of the little Göllnitz theorems. Finally, we show that the little Göllnitz theorems also involve “lecture hall sequences,” that is, sequences constrained by the ratio of consecutive parts.

Comments

This is a preprint of the final published article available at Developments in Mathematics.

Included in

Mathematics Commons

Share

COinS