On the lower estimation of non-averaging sets
type: Item
instance of: scholarly article
title: On the lower estimation of non-averaging sets
zbMATH Open document ID: 0682.10049
DOI: 10.1007/BF02170066
published in: Acta Mathematica Hungarica
publication date: 1989-01-01T00:00:00Z
review text: A set S of positive integers is non-averaging if the arithmetic mean of two or more members of S never belongs to S. Straus showed that the cardinality f(n) of the largest non-averaging subset of \(\{\) 1,2,...,n\(\}\) satisfies \(f(n)>\exp (c_ 1 \sqrt{\log n}).\) In the other direction, Erdős and Straus proved that \(f(n)<c_ 2 n^{2/3}.\) It is shown that for all sufficiently large n, \(f(n)>c_ 3 n^{1/4}\) for some \(c_ 3>0\). This improves the exponent of 1/5 obtained by \textit{H. L. Abbott} [Acta Math. Hung. 47, 117-119 (1986; Zbl 0607.10039)].
Mathematics Subject Classification ID: 11B83
Mathematics Subject Classification ID: 11B13
zbMATH DE Number: 4116651
zbMATH Keywords: lower estimation
zbMATH Keywords: non-averaging sets
zbMATH Keywords: arithmetic mean
zbMATH Keywords: cardinality
author: Á. P. Bosznay
reviewed by: M. M. Dodson
MaRDI profile type: Publication
cites work: On the Erdős-Straus non-averaging set problem
description: scientific article; zbMATH DE number 4116651