On small sumsets in \((\mathbb{Z}/2\mathbb{Z})^n\)
type: Item
instance of: scholarly article
title: On small sumsets in \((\mathbb{Z}/2\mathbb{Z})^n\)
zbMATH Open document ID: 1049.11108
author: Jean-Marc Deshouillers
author: François Hennecart
author: Alain Plagne
published in: Combinatorica
publication date: 2004-10-19T00:00:00Z
review text: For a subset \(\mathcal A\) of \((\mathbb Z/2\mathbb Z)^n\) for which \(| 2\mathcal A| \leq c| \mathcal A| \) obtains for some constant \(c<4\) it is shown that \(\mathcal A\) is contained in the coset of a subgroup of \((\mathbb Z/2\mathbb Z)^n\) which has order bounded by \(u(c)\). The function \(u(c)\) for small \(c\) is given by \(u(c)={-c^3+3c-1\over 2c-1}\). This yields structural results on such sets \(\mathcal A\) improving earlier results of \textit{I. Z. Ruzsa} [''Structure theory of set addition'', Asterisque, Deshouillers, Landreau, Yudin eds; 258, 323-326 (1999; Zbl 0946.11007)].
Mathematics Subject Classification ID: 11P70
Mathematics Subject Classification ID: 11B75
zbMATH DE Number: 2108688
zbMATH Keywords: inverse additive number theory
zbMATH Keywords: small doubling
MaRDI profile type: Publication
full work available at URL: s00493-004-0004-0
OpenAlex ID: W1967594375
Wikidata QID: Q103405092
DOI: 10.1007/S00493-004-0004-0
description: scientific article; zbMATH DE number 2108688