Generalized Rogers-Ramanujan bijections
type: Item
instance of: scholarly article
title: Generalized Rogers-Ramanujan bijections
zbMATH Open document ID: 0685.05003
DOI: 10.1016/0001-8708(89)90028-5
author: Doron Zeilberger
author: David M. Bressoud
published in: Advances in Mathematics
publication date: 1989-01-01T00:00:00Z
review text: In an earlier paper [Discrete Math. 38, 313--315 (1982; Zbl 0476.05010)] the authors presented a short combinatorial proof of the first Rogers-Ramanujan identity, which states that the partitions of \(n\) into parts differing by at least two are equinumerous with the partitions of \(n\) with all parts \(\equiv\pm 1\pmod 5\). In the present paper they explain how the relevant bijection was obtained, and further give a much more general bijection closely related to results of \textit{D. M. Bressoud} [J. Number Theory 16, 235--241 (1983; Zbl 0516.10008)]. Among consequences of these results is the following: for given \(n,k\), the partitions of \(n\) with no part \(\equiv 0\) or \(\pm k\pmod{2k+1}\) are equinumerious with the partitions of \(n\) with no parts below the \((k-1)\)th Durfee square.
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 11P84
zbMATH DE Number: 4122000
zbMATH Keywords: Rogers-Ramanujan identity
zbMATH Keywords: partitions
MaRDI profile type: Publication
full work available at URL: 0001-8708(89)90028-5
OpenAlex ID: W2003158325
cites work: Q4146776
cites work: Partitions and Durfee Dissection
cites work: AN ANALYTIC GENERALIZATION OF THE ROGERS-RAMANUJAN IDENTITIES WITH INTERPRETATION
cites work: An easy proof of the Rogers-Ramanujan identities
cites work: A short Rogers-Ramanujan bijection
cites work: Method for constructing bijections for classical partition identities
cites work: Two Enumerative Proofs of an Identity of Jacobi
cites work: An Enumerative Proof of An Identity of Jacobi
cites work: A direct combinatorial proof of the Jacobi identity
description: scientific article; zbMATH DE number 4122000