2022/03/07 by Thomas Y. He, He, Thomas Y., Alice X. H. Zhao +1
Mathematics · #05A17 #11P81 #11P84 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2203.03257
openalex publication_date 2022/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Göllnitz-Gordon identities were found by Göllnitz and Gordon independently. In 1967, Andrews obtained a combinatorial generalization of the Göllnitz-Gordon identities, called the Andrews-Göllnitz-Gordon theorem. In 1980, Bressoud extended the Andrews-Göllnitz-Gordon theorem to even moduli, called the Bressoud-Göllnitz-Gordon theorem. Furthermore, Bressoud gave the generating functions for the generalizations of the Göllnitz-Gordon identities. In this article, we will give new companions to the generalizations of the Göllnitz-Gordon identities.