An Improved Upper Bound for the Erdős–Szekeres Conjecture
Name
454_2016_9791_ReferencePDF.pdf
Size
333.79 KB
Format
Adobe PDF
Checksum (MD5)
48969a9016ba0974bced562bee89f457
Author(s)
Mojarrad, Hossein Nassajian
Vlachos, Georgios
Date Issued
May 2016
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
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).
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00454-016-9791-5
