Lecture Hall Sequences, q -Series, and Asymmetric Partition Identities

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 Gollnitz partition theorems. We derive a two-parameter generalization of our identities that, surprisingly, gives new analytic counterparts of the little Gollnitz theorems. Finally, we show that the little Gollnitz theorems also involve “lecture hall sequences,” that is, sequences constrained by the ratio of consecutive parts.