Order Types of Convex Bodies

We prove a Hadwiger transversal type result, characterizing convex position on a family of non-crossing convex bodies in the plane. This theorem suggests a definition for the order type of a family of convex bodies, generalizing the usual definition of order type for point sets. This order type turns out to be an oriented matroid. We also give new upper bounds on the Erd˝os-Szekeres theorem in the context of convex bodies.

• Type: Journal
• Year: 2011
• Where: ORDER
• Authors: Alfredo Hubard, Luis Montejano, Emiliano Mora, Andrew Suk
• Keywords: Convex Bodies, Non-crossing Convex Bodies, Operations Research, ORDER 2011, Order Type