Partitions of \(n\) into \(t\sqrt n\) parts
type: Item
instance of: scholarly article
title: Partitions of \(n\) into \(t\sqrt n\) parts
zbMATH Open document ID: 1066.05020
author: Dan Romik
published in: European Journal of Combinatorics
publication date: 2005-01-11T00:00:00Z
review text: \textit{G. Szekeres} [Q. J. Math., Oxf. II. Ser. 4, 96--111 (1953; Zbl 0050.04101)] used complex analysis to prove an asymptotic formula for \(P(n, k)\), the number of unordered partitions of \(n\) into at most \(k\) parts. \textit{E. R. Canfield} [Electron. J. Comb. 4, Research paper R6, 16p. (1997); printed version J. Comb. 4, 51--66 (1997; Zbl 0885.05015)] simplified the formula and avoided the use of complex analysis. Here the author proves this result again when \(k\) is at least a constant times \(\sqrt{n}\) using a central limit theorem of \textit{B. Fristedt} [Trans. Am. Math. Soc. 337, 703--735 (1993; Zbl 0795.05009)]. Using a probabilitistic approach he goes on to derive asympototics for the number of minimal difference \(d\) partitions with a given number of parts.
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 2126327
reviewed by: Gerald L. Alexanderson
MaRDI profile type: Publication
full work available at URL: j.ejc.2004.02.005
OpenAlex ID: W2028631706
cites work: Q4146776
cites work: From recursions to asymptotics: On Szekeres' formula for the number of partitions
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DOI: 10.1016/J.EJC.2004.02.005
description: scientific article; zbMATH DE number 2126327