A correspondence between partitions related to generalizations of the Rogers-Ramanujan identities
type: Item
instance of: scholarly article
title: A correspondence between partitions related to generalizations of the Rogers-Ramanujan identities
zbMATH Open document ID: 0451.10009
DOI: 10.1016/0012-365X(81)90017-0
author: William H. Burge
published in: Discrete Mathematics
publication date: 1981-01-01T00:00:00Z
review text: A \(1-1\) correspondence is given between partitions \(p_1+p_2+\ldots+p_n\) of a positive integer \(n\) where \(p_j - p_{j+k-1} \ge 2\) and at most \(i -1\) of the parts equal 1, and the partitions of \(n\) whose hook differences \(d_i\) satisfy \(-i +2\le d_j \le 2k - i - 1\). From Andrews' work these are equinumerous with the number of partitions of \(n\) into parts \(\not\equiv 0, \pm 1\pmod{2k+1}\). The same correspondence is applied to the case of even moduli. Compare \textit{D. M. Bressoud}, J. Number Theory 12, 87--100 (1980; Zbl 0425.10014)].
reviewed by: Graham Lord
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 11P84
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 3704669
zbMATH Keywords: restricted partitions
zbMATH Keywords: Rogers-Ramanujan identities
zbMATH Keywords: hook differences
MaRDI profile type: Publication
cites work: Q5635503
cites work: Sieves in the Theory of Partitions
cites work: Partially ordered sets and the Rogers-Ramanujan identities
cites work: Q4146776
cites work: A generalization of the Rogers-Ramanujan identities for all moduli
cites work: A Combinatorial Generalization of the Rogers-Ramanujan Identities
description: scientific article; zbMATH DE number 3704669