A motivated proof of the G\"ollnitz-Gordon-Andrews identities

TL;DR

This paper provides a new motivated proof of the G"ollnitz-Gordon-Andrews identities, aiming to shed light on their structure and connections to vertex-algebraic constructions, building on prior proofs of related identities.

Contribution

It introduces a novel motivated proof of the G"ollnitz-Gordon-Andrews identities, extending the approach used for Rogers-Ramanujan and Gordon's identities to this set.

Findings

The proof offers insights into twisted vertex-algebraic constructions.

It generalizes previous motivated proofs to a new class of identities.

The approach may facilitate further algebraic and combinatorial understanding.

Abstract

We present what we call a "motivated proof" of the G\"{o}llnitz-Gordon-Andrews identities. A similar motivated proof of the Rogers-Ramanujan identities was previously given by G. E. Andrews and R. J. Baxter, and was subsequently generalized to Gordon's identities by J. Lepowsky and M. Zhu. We anticipate that the present proof of the G\"{o}llnitz-Gordon-Andrews identities will illuminate certain twisted vertex-algebraic constructions.