  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.

Combinatorics