The cardinality of restricted sumsets.
type: Item
instance of: scholarly article
title: The cardinality of restricted sumsets.
zbMATH Open document ID: 1043.11010
author: Tomasz Schoen
published in: Journal of Number Theory
publication date: 2003-03-23T00:00:00Z
review text: Estimates for the restricted sumset \(A \widehat + B\) (only distinct summands allowed) are notoriously more difficult to obtain than for the ordinary sumset. The author shows that this difference vanishes if only asymptotic results are sought. The main result asserts that, for arbitrary sets \(A, B\) of integers or residues modulo any integer we have \[ | A \widehat + B | \geq | A+B| (1- c ( \log | A+B| )^{-1/9}) \] with an absolute constant \(c\). The proof is based on a result of the reviewer asserting that a set free of 3-term arithmetic progressions must have a large sumset [Period. Math. Hung. 25, 105--111 (1992; Zbl 0761.11005)].
Mathematics Subject Classification ID: 11B05
Mathematics Subject Classification ID: 11B13
Mathematics Subject Classification ID: 11B25
zbMATH DE Number: 1886707
zbMATH Keywords: sumsets
zbMATH Keywords: restricted sums
zbMATH Keywords: arithmetic progressions
reviewed by: Imre Z. Ruzsa
MaRDI profile type: Publication
full work available at URL: jnth.2001.2772
OpenAlex ID: W1974361801
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DOI: 10.1006/JNTH.2001.2772
description: scientific article; zbMATH DE number 1886707