On the Erdos-Szekeres convex polygon problem

@article{Suk2016OnTE,
  title={On the Erdos-Szekeres convex polygon problem},
  author={Andrew Suk},
  journal={ArXiv},
  year={2016},
  volume={abs/1604.08657}
}
  • Andrew Suk
  • Published 2016
  • Mathematics, Computer Science
  • ArXiv
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, Erdos 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 Erdos-Szekeres conjecture by showing that $ES(n) =2^{n +o(n)}$. 

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