In this paper, we highlight two q-series identities arising from the "five guidelines" approach to enumerating lecture hall partitions and give direct, q-series proofs. This requires two new finite corollaries of a q-analog of Gauss's second theorem. In fact, the method reveals stronger results about lecture hall partitions and anti-lecture hall compositions that are only partially explained combinatorially.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory