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New Trends in Intuitive GeometryErdős–Szekeres Theorems for Families of Convex Sets

New Trends in Intuitive Geometry: Erdős–Szekeres Theorems for Families of Convex Sets [The well-known Erdős–Szekeres theorem states that every sufficiently large set of points in the plane containing no three points on a line, has a large subset in convex position. This classical result has been generalized in several directions. In this article we review recent progress related to one such direction, initiated by Bisztriczky and Fejes Tóth, in which the points are replaced by convex sets.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

New Trends in Intuitive GeometryErdős–Szekeres Theorems for Families of Convex Sets

Part of the Bolyai Society Mathematical Studies Book Series (volume 27)
Editors: Ambrus, Gergely; Bárány, Imre; Böröczky, Károly J.; Fejes Tóth, Gábor ; Pach, János
Holmsen, Andreas F.
New Trends in Intuitive Geometry — Nov 3, 2018
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17 pages

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Publisher
Springer Berlin Heidelberg
Copyright
© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018. Corrected Publication 2018
ISBN
978-3-662-57412-6
Pages
201 –218
DOI
10.1007/978-3-662-57413-3_9
Publisher site
See Chapter on Publisher Site

Abstract

[The well-known Erdős–Szekeres theorem states that every sufficiently large set of points in the plane containing no three points on a line, has a large subset in convex position. This classical result has been generalized in several directions. In this article we review recent progress related to one such direction, initiated by Bisztriczky and Fejes Tóth, in which the points are replaced by convex sets.]

Published: Nov 3, 2018

Keywords: Convex Position; Bisztriczky; Convex Bodies; Monotone Path; Ramsey Numbers

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