New companions to the Andrews--Gordon identities motivated by commutative algebra

TL;DR

This paper proves a recent combinatorial conjecture rooted in commutative algebra, leading to new identities related to Andrews-Gordon, using algebraic and combinatorial tools like graded rings and q-series.

Contribution

It introduces new companions to Andrews-Gordon identities motivated by commutative algebra, providing a novel proof of a recent conjecture.

Findings

Proof of a recent combinatorial conjecture

Introduction of new identities related to Andrews-Gordon

Application of algebraic and combinatorial tools

Abstract

We give a proof of a recent combinatorial conjecture due to the first author, which was discovered in the framework of commutative algebra. This result gives rise to new companions to the famous Andrews-Gordon identities. Our tools involve graded quotient rings, Durfee squares and rectangles for integer partitions, and $q$-series identities.