Bressoud Style Identities for Regular Partitions and Overpartitions

TL;DR

This paper develops a unified framework for partition identities, including Rogers-Ramanujan-Gordon, Bressoud's generalizations, and overpartition identities, with constructive proofs that facilitate automation.

Contribution

It introduces a new family of partition identities encompassing several classical and recent results, with constructive proofs that are suitable for automation.

Findings

Unified framework for multiple partition identities

Construction of companion identities

Automatable proof methods

Abstract

We construct a family of partition identities which contain the following identities: Rogers-Ramanujan-Gordon identities, Bressoud's even moduli generalization of them, and their counterparts for overpartitions due to Lovejoy et al. and Chen et al. We obtain unusual companion identities to known theorems as well as to the new ones in the process. The proof is, against tradition, constructive and open to automation.