Order Types of convex bodies
Combinatorics
2010-10-25 v1
Abstract
We give new bounds on the Erdos-Szekeres theorems for convex bodies of Bisztriczky and Fejes Toth and of Pach and Toth. We derive them from a combinatorial characterization of convex position of a family of planar convex bodies. This characterization confirms that the concept of Order Type for points can be extended to noncrossing families of convex bodies in a geometrically meaningful way.
Cite
@article{arxiv.1010.4613,
title = {Order Types of convex bodies},
author = {Alfredo Hubard and Luis Montejano and Emiliano Mora and Andrew Suk},
journal= {arXiv preprint arXiv:1010.4613},
year = {2010}
}