An Improved Upper Bound for the Erdős–Szekeres Conjecture

Author(s)
Mojarrad, Hossein Nassajian; Vlachos, Georgios
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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)≤(2n−4n−2)+1. In 1961, they obtained the lower bound 2n−2+1≤ES(n), which they conjectured to be optimal. In this paper, we prove that ES(n)≤(2n−5n−2)−(2n−8n−3+2)≈716(2n−4n−2).
Date issued
2016-05
URI
http://hdl.handle.net/1721.1/110213
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Department of Mathematics
Journal
Discrete & Computational Geometry
Publisher
Springer US
Citation
Mojarrad, Hossein Nassajian, and Georgios Vlachos. “An Improved Upper Bound for the Erdős–Szekeres Conjecture.” Discrete Comput Geom 56, no. 1 (May 25, 2016): 165–180.
Version: Author's final manuscript
ISSN
0179-5376
1432-0444
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