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 ErdAs-Szekeres theorem in the context of convex bodies.
Keywords: Order type ; Convex bodies ; Ovals ; Independent convex sets ; Oriented matroid ; Erdos Szekeres ; Geometric ramsey theory ; Convex position ; Geometric transversal ; Erdos-Szekeres Theorem ; Sets
Record created on 2011-12-16, modified on 2016-08-09