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

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.