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arXiv · 1010.4613

Order Types of convex bodies

Alfredo Hubard·Luis Montejano·Emiliano Mora·Andrew Suk
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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.

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Alfredo Hubard, Luis Montejano, Emiliano Mora, Andrew Suk. 2010-10-22. Order Types of convex bodies. https://arxiv.org/abs/1010.4613

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