Bressoud Style Identities for Regular Partitions and Overpartitions

2014/09/18 by Kağan Kurşungöz, Kurşungöz, Kağan
Mathematics · #05A15 #05A17 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Primary 11P84 #Secondary 05A19

paper · doi:10.48550/arxiv.1409.5221

openalex publication_date 2014/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a family of partition identities which contain the following identities: Rogers-Ramanujan-Gordon identities, Bressoud's even moduli generalization of them, and their counterparts for overpartitions due to Lovejoy et al. and Chen et al. We obtain unusual companion identities to known theorems as well as to the new ones in the process. The proof is, against tradition, constructive and open to automation.

Related

• Overpartitions and Bressoud's conjecture, I
• An overpartition analogue of Bressoud conjecture for even moduli
• Modulo d extension of parity results in Rogers-Ramanujan-Gordon type overpartition identities
• Overpartitions, lattice paths and Rogers-Ramanujan identities
• Partition identities associated to Rogers-Ramanujan type identities