2004/04/23 by Margaret M. Bayer, Bayer, Margaret M.
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #Mathematics and Applications #math.CO #msc:52B12 #msc:52B22
paper · pdf · doi:10.48550/arxiv.math/0404430
27 pages
arxiv created 2004/04/23 · arxiv updated 2009/12/01
Ordinary polytopes were introduced by Bisztriczky as a (nonsimplicial) generalization of cyclic polytopes. We show that the colex order of facets of the ordinary polytope is a shelling order. This shelling shares many nice properties with the shellings of simplicial polytopes. We also give a shallow triangulation of the ordinary polytope, and show how the shelling and the triangulation are used to compute the toric h-vector of the ordinary polytope. As one consequence, we get that the contribution from each shelling component to the h-vector is nonnegative. Another consequence is a combinatorial proof that the entries of the h-vector of any ordinary polytope are simple sums of binomial coefficients.