A motivated proof of Gordon's identities

TL;DR

This paper extends Andrews and Baxter's motivated proof technique from Rogers-Ramanujan identities to Gordon's identities, offering new insights into vertex-algebraic structures.

Contribution

It introduces a motivated proof of Gordon's identities, enhancing understanding of their vertex-algebraic framework.

Findings

Provides a new motivated proof of Gordon's identities

Links Gordon's identities to vertex-algebraic structures

Enhances conceptual understanding of partition identities

Abstract

We generalize the "motivated proof" of the Rogers-Ramanujan identities given by Andrews and Baxter to provide an analogous "motivated proof" of Gordon's generalization of the Rogers-Ramanujan identities. Our main purpose is to provide insight into certain vertex-algebraic structure being developed.