New companions to the generations of the G\"ollnitz-Gordon identities
Thomas Y. He, Alice X.H. Zhao

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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · Advanced Algebra and Geometry
