Asymptotic analogs of the Rogers-Ramanujan identities
type: Item
instance of: scholarly article
title: Asymptotic analogs of the Rogers-Ramanujan identities
zbMATH Open document ID: 0622.10008
DOI: 10.1016/0097-3165(86)90069-5
author: Charles H. Brenner
published in: Journal of Combinatorial Theory. Series A
publication date: 1986-01-01T00:00:00Z
review text: Let p(n,S) be the number of partitions of n with parts belonging to the set S; let q(n,S) be the number of partitions of n with parts distinct and belonging to the set S; let \(q_ d(n)\) be the number of partitions of n with parts differing by at least d. Asymptotic formulas for p(n,S), q(n,S), and \(q_ d(n)\) are derived. Using these formulas necessary and/or sufficient conditions are obtained on sets S and S' for the various asymptotic relations p(n,S)\(\sim q(n,S')\), q(n,S)\(\sim q(n,S')\), and \(q_ d(n)\sim q(n,S)\). The last case leads to a nonexistence theorem analogous to those of Lehmer for equality. The other comparisons lead to infinite families of cases of asymptotic equality without strict equality. These new formulas can be interpreted as asymptotic analogs of classical Rogers-Ramanujan identities.
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 4008476
zbMATH Keywords: restricted partition functions
zbMATH Keywords: Asymptotic formulas
zbMATH Keywords: Rogers-Ramanujan identities
MaRDI profile type: Publication
full work available at URL: 0097-3165(86)90069-5
OpenAlex ID: W1964723848
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description: scientific article; zbMATH DE number 4008476