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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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On the Erdős-Szekeres convex polygon problem
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by Andrew Suk PDF
J. Amer. Math. Soc. 30 (2017), 1047-1053 Request permission

Abstract:

Let $ES(n)$ be the smallest integer such that any set of $ES(n)$ points in the plane in general position contains $n$ points in convex position. In their seminal 1935 paper, Erdős and Szekeres showed that $ES(n) \leq {2n - 4\choose n-2} + 1 = 4^{n -o(n)}$. In 1960, they showed that $ES(n) \geq 2^{n-2} + 1$ and conjectured this to be optimal. In this paper, we nearly settle the Erdős-Szekeres conjecture by showing that $ES(n) =2^{n +o(n)}$.
References
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Additional Information
  • Andrew Suk
  • Affiliation: University of Illinois, Chicago, Illinois 60607
  • Email: suk@uic.edu
  • Received by editor(s): May 3, 2016
  • Received by editor(s) in revised form: August 26, 2016
  • Published electronically: September 30, 2016
  • Additional Notes: The author is supported by NSF grant DMS-1500153.
  • © Copyright 2016 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 30 (2017), 1047-1053
  • MSC (2010): Primary 52C10; Secondary 05D10
  • DOI: https://doi.org/10.1090/jams/869
  • MathSciNet review: 3671936