A partition inequality involving products of two $q$-Pochhammer symbols

Abstract

We use an injection method to prove a new class of partition inequalities involving certain $q$-products with two to four finitization parameters. Our new theorems are a substantial generalization of work by Andrews and of previous work by Berkovich and Grizzell. We also briefly discuss how our products might relate to lecture hall partitions.

arXiv comment14 pages, 5 tables