Extendable Shelling, Simplicial and Toric h-vector of some Polytopes


Duško Jojić


We show that the stellar subdivisions of a simplex are extendably shellable. These polytopes appear as the facets of the dual of a hypersimplex. 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.