On some metric and combinatorial geometric problems

DOI10.1016/0012-365X(86)90009-9zbMath0595.52013OpenAlexW2006073641MaRDI QIDQ1077726

Paul Erdős

Publication date: 1986

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0012-365x(86)90009-9

zbMATH Keywords

surveydistancescombinatorial geometryfinite point sets in the plane

Mathematics Subject Classification ID

Problem books (00A07) Combinatorial inequalities (05A20) Other combinatorial number theory (11B75) Inequalities and extremum problems involving convexity in convex geometry (52A40) Enumerative combinatorics (05A99) Other problems of combinatorial convexity (52A37) Convex sets in (2) dimensions (including convex curves) (52A10) Combinatorial geometries and geometric closure systems (51D20)

Related Items (22)

Bisector energy and few distinct distances ⋮ General position subsets and independent hyperplanes in \(d\)-space ⋮ A construction for difference sets with local properties ⋮ Distinct angle problems and variants ⋮ Few distinct distances implies no heavy lines or circles ⋮ Finding Points in General Position ⋮ Sets in Almost General Position ⋮ Every large point set contains many collinear points or an empty pentagon ⋮ On Cartesian products which determine few distinct distances ⋮ On the number of points in general position in the plane ⋮ The grid revisited ⋮ A note on the number of different inner products generated by a finite set of vectors ⋮ More distinct distances under local conditions ⋮ Computational geometric aspects of rhythm, melody, and voice-leading ⋮ Unit distances and diameters in Euclidean spaces ⋮ A note on distinct distances in rectangular lattices ⋮ Lattice-point examples for a question of Erdős ⋮ A new lower bound on Hadwiger-Debrunner numbers in the plane ⋮ The maximum number of unit distances in a convex \(n\)-gon ⋮ Distinct distances in planar point sets with forbidden 4-point patterns ⋮ On distinct distances among points in general position and other related problems ⋮ Sets with few distinct distances do not have heavy lines

Cites Work

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• On the lattice property of the plane and some problems of Dirac, Motzkin and Erdős in combinatorial geometry
• The number of different distances determined by n points in the plane
• Sets with No Empty Convex 7-Gons
• Linear problems in combinatorial number theory
• Some Theorems on Convex Polygons
• Some Remarks on Set Theory
• On Sets of Integers Which Contain No Three Terms in Arithmetical Progression
• On Sets of Distances of n Points

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