Optimally small sumsets in finite abelian groups.
type: Item
instance of: scholarly article
title: Optimally small sumsets in finite abelian groups.
zbMATH Open document ID: 1043.11021
DOI: 10.1016/S0022-314X(03)00060-X
author: Shalom Eliahou
author: Alain Plagne
author: Michel Kervaire
published in: Journal of Number Theory
publication date: 2003-08-07T00:00:00Z
review text: Let \(G\) be a finite Abelian group of order \(g\) and for the sum set \[ A+B:= \{a+b\mid a\in A,\,b\in B\}\;(A,B\subset G) \] denote \[ \mu_G(r,s):= \min\{| A+B|\mid | A|= r,\,| B|= s\}. \] In the introduction the authors recall earlier results on \(\mu_G(r,s)\). The purpose of this paper is the following theorem: For all \(r,s\in \{1,\dots, g\}\) one has \[ \mu_G(r,s)= \min_{d| g}\,\Biggl\{\Biggl(\Biggl\lceil{r\over d}\Biggr\rceil+ \Biggl\lceil{s\over d}\Biggr\rceil- 1\Biggr) d\Biggr\}. \]
reviewed by: Erich Härtter
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 20K01
Mathematics Subject Classification ID: 11P70
zbMATH DE Number: 1961839
zbMATH Keywords: Sumset
zbMATH Keywords: Cauchy-Davenport theorem
zbMATH Keywords: Kneser theorem
zbMATH Keywords: Initial segment
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1961839