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The Erdős-Szekeres Problem

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Open Problems in Mathematics

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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.

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Authors and Affiliations

  1. George Mason University, 4400 University Drive, Fairfax, VA, 22030, USA

    Walter Morris & Valeriu Soltan

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  1. Walter Morris
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  2. Valeriu Soltan
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Correspondence to Walter Morris .

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Editors and Affiliations

  1. Department of Mathematics, Senior Research Mathematician, Princeton University, Princeton, New Jersey, USA

    John Forbes Nash, Jr.

  2. Department of Mathematics, Princeton University, Princeton, New Jersey, USA

    Michael Th. Rassias

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Morris, W., Soltan, V. (2016). The Erdős-Szekeres Problem. In: Nash, Jr., J., Rassias, M. (eds) Open Problems in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-32162-2_10

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