Neighborly partitions, hypergraphs and Gordon's identities

TL;DR

This paper introduces a new family of partition identities, inspired by hypergraph-partition correspondences, and proves their duality to Andrews-Gordon identities using combinatorial algebra techniques.

Contribution

It presents a novel family of partition identities and establishes their duality to known identities through combinatorial algebra methods.

Findings

Proved a new family of partition identities.

Established duality with Andrews-Gordon identities.

Used combinatorial commutative algebra in proofs.

Abstract

We prove a family of partition identities which is "dual" to the family of Andrews-Gordon's identities. These identities are inspired by a correspondence between a special type of partitions and "hypergraphs" and their proof uses combinatorial commutative algebra.