Dot product rearrangements
type: Item
instance of: scholarly article
title: Dot product rearrangements
zbMATH Open document ID: 0539.40001
DOI: 10.1155/S0161171283000368
author: Gary Weiss
author: P. Erdős
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1983-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/45376
review text: Let \(a=(a_n)\) and \(x=(x_n)\) be sequences of non-negative integers. Let \(a.x=\sum a_nx_n.\) Letting \(x_{\pi}\) denote a permutation of the sequence \(x\), this paper investigates which subsets of \({\mathbb{R}}\) can be realised as \(a.x_{\pi}\). The main result is that if \(a_n\) increases unboundedly and \(x_n\) is positive and decreases to zero, then the set of numbers in question is the interval \([a.x,\infty]\) if and only if \(a_{n+1}/a_n\) is uniformly bounded.
reviewed by: K.E.Hirst
Mathematics Subject Classification ID: 40A05
zbMATH DE Number: 3857638
zbMATH Keywords: dot product, series rearrangements
zbMATH Keywords: conditional convergence
MaRDI profile type: Publication
OpenAlex ID: W1986327397
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description: scientific article; zbMATH DE number 3857638