Variations on the theme of repeated distances

DOI10.1007/BF02122780zbMath0722.52009OpenAlexW2033259203MaRDI QIDQ756139

János Pach, Paul Erdős

Publication date: 1990

Published in: Combinatorica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02122780

zbMATH Keywords

convex setspoints in \({\mathbb{R}}^d\)repeated distances

Mathematics Subject Classification ID

Erd?s problems and related topics of discrete geometry (52C10) Convex sets in (2) dimensions (including convex curves) (52A10) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (11)

Multiplicities of interpoint distances in finite planar sets ⋮ A product inequality for extreme distances ⋮ Favourite distances in \(3\)-space ⋮ Ball polytopes and the Vázsonyi problem ⋮ Large simplices determined by finite point sets ⋮ Repeated angles in the plane and related problems ⋮ Antipodality properties of finite sets in Euclidean space ⋮ Unnamed Item ⋮ Computational geometric aspects of rhythm, melody, and voice-leading ⋮ Unit distances and diameters in Euclidean spaces ⋮ Popular distances in 3-space

Cites Work

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• Digraph extremal problems, hypergraph extremal problems, and the densities of graph structures
• Combinatorial complexity bounds for arrangements of curves and spheres
• On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
• Repeated distances in space
• A Problem of Leo Moser About Repeated Distances on the Sphere
• On Some Applications of Graph Theory to Geometry
• On a problem of K. Zarankiewicz
• On Sets of Distances of n Points
• On the structure of linear graphs

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