Partitions, q-Series, and Modular Forms
Georgia Southern University faculty member Andrew Sills co-authored “Lecture Hall Sequences, q-series, and Asymmetric Partition Identities” in the publication Proceedings of the Conference on Partitions, q-Series, and Modular Forms, University of Florida, March 12-16, 2008, Partitions, q-series, and Modular Forms in Developments in Mathematics.
Chapter Summary: 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.