The Erdős-Szekeres Problem

Walter Morris () and Valeriu Soltan ()
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Walter Morris: George Mason University
Valeriu Soltan: George Mason University

A chapter in Open Problems in Mathematics, 2016, pp 351-375 from Springer

Abstract: Abstract Erdős and Szekeres proved in their 1935 paper that for every integer n ≥ 3 there exists a smallest positive integer N(n) such that any set of at least N(n) points in general position in the plane contains n points which are the vertices of a convex n-gon. They also posed the problem to determine the value of N(n) and conjectured that $$N(n) = 2^{n-2} + 1$$ for all n ≥ 3. Despite the efforts of many mathematicians, the Erdős-Szekeres problem is still far from being solved. This chapter describes recent achievements towards the solution of this problem and some of its close relatives.

Keywords: Convex Hull; Convex Body; General Position; Small Positive Integer; Oriented Matroids (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-32162-2_10

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DOI: 10.1007/978-3-319-32162-2_10

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