Erdős–Szekeres Without Induction

Sergey Norin; Yelena Yuditsky

doi:10.1007/s00454-016-9778-2

Erdős–Szekeres Without Induction

Sergey Norin, Yelena Yuditsky

Research output: Contribution to journal › Article › peer-review

6 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 language	English
Pages (from-to)	963-971
Number of pages	9
Journal	Discrete and Computational Geometry
Volume	55
Issue number	4
DOIs	https://doi.org/10.1007/s00454-016-9778-2
State	Published - 1 Jun 2016
Externally published	Yes

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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10.1007/s00454-016-9778-2

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title = "Erd{\H o}s–Szekeres Without Induction",

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 Erd{\H o}s 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 Erd{\H o}s and Szekeres, 2015). We improve this to (Formula presented.).",

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T1 - Erdős–Szekeres Without Induction

AU - Norin, Sergey

AU - Yuditsky, Yelena

PY - 2016/6/1

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N2 - 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.).

AB - 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.).

KW - Convex sets in the plane

KW - Erdős–Szekeres problem

KW - Ramsey theory

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JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 4

ER -

Erdős–Szekeres Without Induction

Abstract

Keywords

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