Distance sets of well-distributed planar point sets
type: Item
instance of: scholarly article
title: Distance sets of well-distributed planar point sets
zbMATH Open document ID: 1060.52008
author: Alex Iosevich
author: Izabella Łaba
published in: Discrete \& Computational Geometry
publication date: 2004-09-22T00:00:00Z
review text: For \(K\) a balanced convex compact set in \(\mathbb{R}^2\), the set \(S\subset \mathbb{R}^2\) is \(K\)-well distributed if any point of \(\mathbb{R}^2\) lies within a uniformly bounded \(K\)-distance from \(S\). The paper studies for such \(S\) the asymptotic behavior of \(\Delta_N(S)\), the number of distinct \(K\)-distances \(\leq N\) between pairs in \(S\). E.g. it is shown that if \(\Delta_N(S)=O(N^{1.5})\) then \(K\) is polygonal.
reviewed by: Frank Plastria
Mathematics Subject Classification ID: 52C10
zbMATH DE Number: 2101563
zbMATH Keywords: well-distributed sets
zbMATH Keywords: Erdös distance problem
MaRDI profile type: Publication
full work available at URL: s00454-003-2857-1
OpenAlex ID: W2069812454
DOI: 10.1007/S00454-003-2857-1
description: scientific article; zbMATH DE number 2101563