On distinct distances among points in general position and other related problems
type: Item
instance of: scholarly article
title: On distinct distances among points in general position and other related problems
zbMATH Open document ID: 1199.52031
author: Adrian Dumitrescu
published in: Periodica Mathematica Hungarica
publication date: 2009-12-29T00:00:00Z
review text: The author studies some variants of Erdős classical and famous problem asking for the minimum number of distinct distances determined by \(n\) points in the plane. For instance, it is shown that there exist \(n\)-element point sets in strong general position and which do not contain the vertices of a parallelogram that determine only \(O(n^2/\sqrt{\log n})\) distinct distances. For more information on distance problems, we refer to \textit{P. Brass, W. Moser} and \textit{J. Pach} [Research problems in discrete geometry, New York, Springer (2005; Zbl 1086.52001)].
reviewed by: Martin Henk
Mathematics Subject Classification ID: 52C10
zbMATH DE Number: 5651906
zbMATH Keywords: distinct distances
zbMATH Keywords: distinct vectors
zbMATH Keywords: general position
zbMATH Keywords: Sidon sequence
MaRDI profile type: Publication
full work available at URL: s10998-008-8165-4
OpenAlex ID: W2165434229
cites work: Sidon Sets
cites work: Distinct distances determined by subsets of a point set in space
cites work: The probabilistic method. With an appendix on the life and work of Paul Erdős.
cites work: On the lattice property of the plane and some problems of Dirac, Motzkin and Erdős in combinatorial geometry
cites work: On Sets of Integers Which Contain No Three Terms in Arithmetical Progression
cites work: The number of different distances determined by n points in the plane
cites work: The number of different distances determined by a set of points in the Euclidean plane
cites work: Combinatorial complexity bounds for arrangements of curves and spheres
cites work: On distinct distances and \(\lambda \)-free point sets
cites work: On Sets of Distances of n Points
cites work: Some Remarks on Set Theory
cites work: On some metric and combinatorial geometric problems
cites work: Q4871153
cites work: The grid revisited
cites work: Distinct distances between lattice points
cites work: A Problem of Leo Moser About Repeated Distances on the Sphere
cites work: Q4871765
cites work: On a Problem of Sidon in Additive Number Theory, and on some Related Problems
cites work: Unsolved problems in number theory
cites work: Q3856819
cites work: Q4657584
cites work: A Lower Bound for Heilbronn'S Problem
cites work: Linear problems in combinatorial number theory
cites work: Point sets with distinct distances
cites work: An inequality for B2-sequences
cites work: On the Different Distances Determined by n Points
cites work: Q4455112
cites work: Isosceles triangles determined by a planar point set
cites work: Q4871768
cites work: A Theorem in Finite Projective Geometry and Some Applications to Number Theory
cites work: Distinct distances in the plane
cites work: Crossing Numbers and Hard Erdős Problems in Discrete Geometry
cites work: On distinct sums and distinct distances.
cites work: The no-four-on-circle problem
DOI: 10.1007/S10998-008-8165-4
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description: scientific article; zbMATH DE number 5651906