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- W2239826551 abstract "Let ES(n) denote the minimum natural number such that every set of ES(n) points in general position in the plane contains n points in convex position. In 1935, Erdős and Szekeres proved that ES((n) le {2n-4 atopwithdelims ()n-2}+1). In 1961, they obtained the lower bound (2^{n-2}+1 le mathrm{ES}(n)), which they conjectured to be optimal. In this paper, we prove that $$begin{aligned} mathrm{ES}(n) le Big (begin{array}{c}{2n-5} {n-2}end{array}Big ) -Big (begin{array}{c}{2n-8} {n-3}+2end{array}Big ) approx frac{7}{16} Big (begin{array}{c}{2n-4} {n-2}end{array}Big ). end{aligned}$$" @default.
- W2239826551 created "2016-06-24" @default.
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- W2239826551 date "2016-05-25" @default.
- W2239826551 modified "2023-10-17" @default.
- W2239826551 title "An Improved Upper Bound for the Erdős–Szekeres Conjecture" @default.
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- W2239826551 doi "https://doi.org/10.1007/s00454-016-9791-5" @default.
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