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. © Springer Science+Business Media, LLC 2012.
CITATION STYLE
Corteel, S., Savage, C. D., & Sills, A. V. (2012). Lecture hall sequences, q-series, and asymmetric partition identities. Developments in Mathematics, 23, 53–68. https://doi.org/10.1007/978-1-4614-0028-8_6
Mendeley helps you to discover research relevant for your work.