Splits: Simple Subdivisions of Convex PolytopesAlgebra & Discrete Mathematics
|Sven Hermann, Technische Universität Darmstadt
|Mon, Oct 29 2007, 4:10PM
The aim of this talk is to develop the theory of splits of convex polytopes. Splits are the simplest possible (non-trivial) subdivisions of a polytope P. Since they are all regular we get in this way a bunch of facets for the secondary polytope of P. If P is the second hypersimplex our theory reduces to the split decomposition theory for finite metric spaces developed by Dress et al. Lots of their results can be generalized to arbitrary polytopes. The presented theory is very similar to work of Hirai who developed a split decomposition of polyhedral convex functions. We will illustrate this similarities here and also give an explicit algorithm to compute splits.