Erdős–Szekeres Without Induction

Sergey Norin, Yelena Yuditsky

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Let ES(n) be the minimal integer such that any set of ES(n) points in the plane in general position contains n points in convex position. The problem of estimating ES(n) was first formulated by Erdős and Szekeres (Compos Math 2: 463–470, 1935), who proved that ES(n)≤(2n-4n-2)+1. The current best upper bound, limsupn→∞ES(n)(2n-5n-2)≤2932, is due to Vlachos (On a conjecture of Erdős and Szekeres, 2015). We improve this to (Formula presented.).

Original languageEnglish
Pages (from-to)963-971
Number of pages9
JournalDiscrete and Computational Geometry
Volume55
Issue number4
DOIs
StatePublished - 1 Jun 2016
Externally publishedYes

Keywords

  • Convex sets in the plane
  • Erdős–Szekeres problem
  • Ramsey theory

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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