A proof of the G\"ollnitz-Gordon-Andrews identities via commutative algebra

Abstract

The G\"ollnitz-Gordon-Andrews identities generalize the partition identities discovered independently by H. G\"ollnitz and B. Gordon. In this article, we present a commutative algebra proof of the G\"ollnitz-Gordon-Andrews identities. More generally, we establish a family of identities, the special cases of which are the G\"ollnitz-Gordon-Andrews identities. In the proof, we relate the generating functions associated with these identities to the Hilbert-Poincar\'e series of suitably constructed graded algebras.