A combinatorial proof of the Rogers-Ramanujan and Schur identities

2004/11/03 by Cilanne Boulet, Boulet, Cilanne, Igor Pak +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.math/0411072

12 pages, 5 figures; incorporated referee suggestions, simplified definition of (k,m)-rank, to appear in JCT(A)

openalex publication_date 2004/11/03 · arxiv created 2005/09/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a combinatorial proof of the first Rogers-Ramanujan identity by using two symmetries of a new generalization of Dyson's rank. These symmetries are established by direct bijections.

Related

• Dyson's new symmetry and generalized Rogers-Ramanujan identities
• Refinements of the Rogers-Ramanujan identities
• Simple proofs of Bressoud's and Schur's polynomial versions of the Rogers-Ramanujan identities
• A New Series for Rogers-Ramanujan-Gordon Identities when k = 3
• The Rogers-Ramanujan Identities and Cauchy's Identity