Andrews-Gordon Type Series for Capparelli's and Göllnitz-Gordon Identities

2018/07/30 by Kağan Kurşungöz, Kurşungöz, Kağan
Mathematics · #05A15 #05A17 #11P84 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.11189

openalex publication_date 2018/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct Andrews-Gordon type evidently positive series as generating functions for the partitions satisfying the difference conditions imposed by Capparelli's identities and Göllnitz-Gordon identities. The construction involves building base partitions, and move parts around subject to certain rules. Some missing cases are also considered, but no new identities are given.

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