Thomas Y. He, Alice X. H. Zhao
Published 2022-03-07Version 1
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.
Euler's partition theorem for all moduli and new companions to Rogers-Ramanujan-Andrews-Gordon identities
Andrews-Gordon Type Series for Capparelli's and Göllnitz-Gordon Identities
A combinatorial generalization of the Boson-Fermion correspondence
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