On the ordinary and signed G\"ollnitz--Gordon partitions

Abstract

Dedicated to George E. Andrews on the occasion of his 70th birthday. Submitted to a special issue for this occasion. We use Andrews' notion of a `signed partition' (i.e. partition where some parts are allowed to be negative) to interpret the G\"ollnitz--Gordon sum, and then provide a bijective map between these signed partitions and the usual G\"ollnitz--Gordon partitions (partitions with difference at least two between parts, and no consecutive even parts).