Finding systems of functional equations for Andrews-Gordon type series

TL;DR

This paper introduces a search algorithm for discovering systems of $q$-difference equations related to Andrews-Gordon series, combining it with Euler's algorithm to identify infinite product representations, and provides proofs and interpretations within partition frameworks.

Contribution

The paper presents a novel algorithmic approach to find $q$-difference systems for Andrews-Gordon series, enhancing understanding of their structure and connections to partitions.

Findings

Identified new systems of $q$-difference equations for Andrews-Gordon series

Connected double series to partition and move frameworks

Provided proofs for the discovered systems

Abstract

We develop a search algorithm for systems of $q$-difference equations satisfied by Andrews-Gordon type double series. We then couple the search algorithm with Euler's algorithm for finding infinite products to narrow the search space. We exemplify some findings of the algorithm, along with their proofs. We also explain some of the double series in a base partition and moves framework.