Truncated theta series and a problem of Guo and Zeng
type: Item
instance of: scholarly article
title: Truncated theta series and a problem of Guo and Zeng
zbMATH Open document ID: 1454.05015
author: George E. Andrews
author: Mircea Merca
published in: Journal of Combinatorial Theory. Series A
publication date: 2017-11-09T00:00:00Z
review text: \textit{V. J. W. Guo} and \textit{J. Zeng} [J. Comb. Theory, Ser. A 120, No. 3, 700--707 (2013; Zbl 1259.05020)] proved truncated versions of two classical theta identities of Gauss. These results have inequality-consequences concerning \(\overline{p}(n)\), the number of overpartitions of \(n\), resp. \(\mathrm{pod}(n)\), the number of partitions of \(n\) in which odd parts are not repeated. In the paper under review, the authors give partition-theoretic interpretations of these inequalities by the number of overpartitions of \(n\) in which the first part larger than \(k\) appears at least \(k+1\) times, resp. by the number of partitions of \(n\) in which the first part larger than \(2k-1\) is odd and appears exactly \(k\) times, all other odd parts appear at most once. The authors also prove that the truncated versions in question, together with their previous truncation of Euler's pentagonal number theorem, are essentially corollaries of the Rogers-Fine identity.
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 11P84
zbMATH DE Number: 6804252
zbMATH Keywords: partitions
zbMATH Keywords: Euler's pentagonal number theorem
zbMATH Keywords: theta series
reviewed by: Mihály Szalay
MaRDI profile type: Publication
full work available at URL: j.jcta.2017.10.003
OpenAlex ID: W2767326970
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DOI: 10.1016/J.JCTA.2017.10.003
description: scientific article; zbMATH DE number 6804252