Complementary sets of finite sets
type: Item
instance of: scholarly article
title: Complementary sets of finite sets
zbMATH Open document ID: 1026.11018
published in: Monatshefte für Mathematik
publication date: 2003-12-12T00:00:00Z
review text: Given an additive group \(G\) and \({\mathcal A}\subset G\), a set \({\mathcal S}\subset G\) is called complementary to \(\mathcal A\) in \(G\) if \({\mathcal A}+{\mathcal S}=\{a+s:a\in{\mathcal A}, s\in{\mathcal S}\}=G\). In the paper the groups \(\mathbb Z\), \({\mathbb Z}/(m{\mathbb Z})\), \(\mathbb R\), and \({\mathbb R}/{\mathbb Z}\) are considered, and some sufficient conditions for the existence of a complementary set \(\mathcal S\) with ``density'' not much larger than \(1/|{\mathcal A}|\) are given, where \(\mathcal A\) is finite. Some structural descriptions of complementary sets of small density which depend on approximation properties of elements of \(\mathcal A\) are also given.
reviewed by: Štefan Porubský
Mathematics Subject Classification ID: 11B05
Mathematics Subject Classification ID: 11B13
zbMATH DE Number: 1942706
zbMATH Keywords: complementary sets
zbMATH Keywords: density of subsets of \(\mathbb{Z}\)
zbMATH Keywords: tiling sets
MaRDI profile type: Publication
full work available at URL: s006050300001
OpenAlex ID: W2079342482
DOI: 10.1007/S006050300001
author: Wolfgang M. Schmidt
description: scientific article; zbMATH DE number 1942706