Reconstructing integer sets from their representation functions
type: Item
instance of: scholarly article
title: Reconstructing integer sets from their representation functions
zbMATH Open document ID: 1068.11006
author: Vsevolod F. Lev
published in: The Electronic Journal of Combinatorics
publication date: 2005-04-25T00:00:00Z
full work available at URL: https://eudml.org/doc/124929
full work available at URL: v11i1r78.html
review text: First proofs of two theorems of \textit{G. Dombi} [Acta Arith. 103, No. 2, 137--146 (2002; Zbl 1014.11009)] and \textit{Y.-G. Chen} and \textit{B. Wang} [Acta Arith. 110, No. 3, 299--303 (2003; Zbl 1032.11008)] are given. Then the parallel problem for differences is investigated. A set \(A\subseteq\mathbb{Z}\) is a perfect difference set if any integer \(\neq 0\) has a unique representation as a difference of two elements of \(A\). Then the following theorem is proved: There is a partition \(\mathbb{N}=\bigcup^\infty_{k=1} A_k\) such that each \(A_k\) is a perfect difference set and \(|A_i\cap(A_j+ z)|\leq 2\) for any \(i,j,z\in\mathbb{N}\).
reviewed by: Erich Härtter
Mathematics Subject Classification ID: 11B34
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 11B13
zbMATH DE Number: 2161285
zbMATH Keywords: representation functions
zbMATH Keywords: additive bases
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2161285