The Rogers-Ramanujan identities without Jacobi's triple product
type: Item
instance of: scholarly article
title: The Rogers-Ramanujan identities without Jacobi's triple product
zbMATH Open document ID: 0653.05009
DOI: 10.1216/RMJ-1987-17-4-659
author: George E. Andrews
published in: Rocky Mountain Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The first bijective proof of the Rogers-Ramanujan identities was given in 1981 by \textit{A. M. Garsia} and \textit{S. C. Milne} [J. Comb. Theory, Ser. A 31, 289--339 (1981; Zbl 0477.05009)]. Subsequently another bijective proof was given by \textit{D. M. Bressoud} and \textit{D. Zeilberger} [Discrete Math. 38, 313--315 (1982; Zbl 0476.05010)]. Both of these proofs use an involution principle and Jacobi's triple product identity. The author here presents a proof which avoids the use of the Jacobi identity, instead making use of a finite rational function identity which converges to Jacobi's triple product in the limit.
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 11P84
zbMATH DE Number: 4064995
zbMATH Keywords: partitions
zbMATH Keywords: Rogers-Ramanujan identities
zbMATH Keywords: finite rational function identity
MaRDI profile type: Publication
full work available at URL: rmj-1987-17-4-659
OpenAlex ID: W1992879577
description: scientific article; zbMATH DE number 4064995