Extendable shelling, simplicial and toric h-vector of some polytopes

Abstract

We show that the stellar subdivisions of a simplex are extendably shellable. These polytopes appear as the facets of the dual of a hypersim- plex. Using this fact, we calculate the simplicial and toric h-vector of the dual of a hypersimplex. Finally, we calculate the contribution of each shelling component to the toric h-vector.