Shelling and triangulating the (extra)ordinary polytope

Details Shelling and triangulating the (extra)ordinary polytope Shelling and triangulating the (extra)ordinary polytope

2004-04-23

arxiv.org/abs/math/0404430v1

Mathematics

Combinatorics

27 pages

Scientific paper

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.

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