The Method of Combinatorial Telescoping

2010/01/02 by William Y. C. Chen, Chen, William Y. C., Qing-Hu Hou +3
Mathematics · #05A17 #11P83 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:05A17 #msc:11P83

paper · pdf · doi:10.48550/arxiv.1001.0312

11 pages, 5 figures; to appear in J. Combin. Theory Ser. A

openalex publication_date 2010/01/02 · arxiv created 2010/09/05 · arxiv updated 2010/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a method for proving q-series identities by combinatorial telescoping, in the sense that one can transform a bijection or a classification of combinatorial objects into a telescoping relation. We shall illustrate this method by giving a combinatorial proof of Watson's identity which implies the Rogers-Ramanujan identities.

Related

• Combinatorial Telescoping for an Identity of Andrews on Parity in Partitions
• The Method of Multiple Combinatorial Telescoping
• Tiling proofs of Jacobi triple product and Rogers-Ramanujan identities
• "Overpartitionized" Rogers--Ramanujan type identities
• Combinatorial approach to Andrews-Gordon and Bressoud type identities