2024/10/13 by Shishuo Fu, Haijun Li, Fu, Shishuo +1 · 1 citation
Mathematics · #05A15 #05A19 #11P84 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2410.09777
openalex publication_date 2024/10/13 · openalex created_date 2024/10/20 · openalex updated_date 2026/07/28
Strict partitions are enumerated with respect to the weight, the number of parts, and the number of sequences of odd length. We write this trivariate generating function as a double sum q-series. Equipped with such a combinatorial set-up, we investigate a handful of double sum identities appeared in recent works of Cao-Wang, Wang-Wang, Wei-Yu-Ruan, Andrews-Uncu, Chern, and Wang, finding partition theoretical interpretations to all of these identities, and in most cases supplying Franklin-type involutive proofs. This approach dates back more than a century to P. A. MacMahon's interpretations of the celebrated Rogers-Ramanujan identities, and has been further developed by Kurşungöz in the last decade.