| dc.contributor.author | Mojarrad, Hossein Nassajian | |
| dc.contributor.author | Vlachos, Georgios | |
| dc.date.accessioned | 2017-06-23T16:05:16Z | |
| dc.date.available | 2017-06-23T16:05:16Z | |
| dc.date.issued | 2016-05 | |
| dc.date.submitted | 2016-04 | |
| dc.identifier.issn | 0179-5376 | |
| dc.identifier.issn | 1432-0444 | |
| dc.identifier.uri | http://hdl.handle.net/1721.1/110213 | |
| dc.description.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). | en_US |
| dc.description.sponsorship | Swiss National Science Foundation (Grant 200020-144531) | en_US |
| dc.description.sponsorship | Swiss National Science Foundation (Grant 200021-137574) | en_US |
| dc.description.sponsorship | Swiss National Science Foundation (Grant 200020-162884) | en_US |
| dc.publisher | Springer US | en_US |
| dc.relation.isversionof | http://dx.doi.org/10.1007/s00454-016-9791-5 | en_US |
| dc.rights | 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. | en_US |
| dc.source | Springer US | en_US |
| dc.title | An Improved Upper Bound for the Erdős–Szekeres Conjecture | en_US |
| dc.type | Article | en_US |
| dc.identifier.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. | en_US |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science | en_US |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
| dc.contributor.mitauthor | Vlachos, Georgios | |
| dc.relation.journal | Discrete & Computational Geometry | en_US |
| dc.eprint.version | Author's final manuscript | en_US |
| dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
| eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
| dc.date.updated | 2016-06-30T12:07:29Z | |
| dc.language.rfc3066 | en | |
| dc.rights.holder | Springer Science+Business Media New York | |
| dspace.orderedauthors | Mojarrad, Hossein Nassajian; Vlachos, Georgios | en_US |
| dspace.embargo.terms | N | en |
| mit.license | PUBLISHER_POLICY | en_US |
