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

## TL;DR

This paper explores the G"ollnitz--Gordon partitions by employing Andrews' concept of signed partitions, establishing a bijection that deepens understanding of their combinatorial structure.

## Contribution

It introduces a novel bijective correspondence between signed G"ollnitz--Gordon partitions and the classical form, enhancing combinatorial interpretations.

## Key findings

- Established a bijection between signed and usual G"ollnitz--Gordon partitions
- Provided new combinatorial insights into the structure of these partitions
- Connected signed partitions to classical partition identities

## 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).