New companions to the generations of the G\"ollnitz-Gordon identities

TL;DR

This paper introduces new mathematical companions to the existing generalizations of the G"ollnitz-Gordon identities, expanding the combinatorial and generating function frameworks established by prior researchers.

Contribution

It provides novel companions to the known generalizations of the G"ollnitz-Gordon identities, enriching the combinatorial and generating function perspectives.

Findings

New companions to the G"ollnitz-Gordon identities are established.

The work extends the combinatorial framework of previous identities.

Additional generating functions for these generalizations are derived.

Abstract

The G\"ollnitz-Gordon identities were found by G\"ollnitz and Gordon independently. In 1967, Andrews obtained a combinatorial generalization of the G\"ollnitz-Gordon identities, called the Andrews-G\"ollnitz-Gordon theorem. In 1980, Bressoud extended the Andrews-G\"ollnitz-Gordon theorem to even moduli, called the Bressoud-G\"ollnitz-Gordon theorem. Furthermore, Bressoud gave the generating functions for the generalizations of the G\"ollnitz-Gordon identities. In this article, we will give new companions to the generalizations of the G\"ollnitz-Gordon identities.