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

TL;DR

This paper introduces new partition inequalities involving $q$-products with multiple parameters, generalizing previous results and suggesting potential links to lecture hall partitions.

Contribution

It presents a novel injection method to prove a broad class of partition inequalities involving two to four finitization parameters, extending prior work by Andrews, Berkovich, and Grizzell.

Findings

Proved new partition inequalities using an injection method.

Generalized previous inequalities to include more parameters.

Discussed potential connections to lecture hall partitions.

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.