Point configurations in \(d\)-space without large subsets in convex position

DOI10.1007/s00454-003-0009-4zbMath1051.52012OpenAlexW2057647747MaRDI QIDQ1423586

Pavel Valtr, Gyula Károlyi

Publication date: 7 March 2004

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-003-0009-4

zbMATH Keywords

Erdős-Szekeres theorem\(d\)-Horton setslower bound for the Erdős-Szekeres numberpoints in convex position

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Erd?s problems and related topics of discrete geometry (52C10) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (max. 100)

On the Erdős-Szekeres convex polygon problem ⋮ Separating families of convex sets ⋮ Erdős-Szekeres theorem for \(k\)-flats ⋮ Erdős-Szekeres ``happy end-type theorems for separoïds ⋮ THE ERDŐS–SZEKERES PROBLEM AND AN INDUCED RAMSEY QUESTION ⋮ Erdős-Szekeres theorem for point sets with forbidden subconfigurations ⋮ Unnamed Item ⋮ Separation with restricted families of sets ⋮ A Ramsey-type result for geometric \(\ell\)-hypergraphs ⋮ Convex polygons in Cartesian products ⋮ The Erdős-Szekeres Problem ⋮ The logarithmic capacitary Minkowski problem for polytopes

Cites Work

• Sets in \(\mathbb{R}^ d\) with no large empty convex subsets
• Some Erdős-Szekeres type results about points in space
• On empty convex polytopes
• Note on the Erdős-Szekeres theorem
• Sets with No Empty Convex 7-Gons
• The Erdos-Szekeres problem on points in convex position – a survey
• Ramsey-remainder for convex sets and the Erdős-Szekeres theorem
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