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Ehrhart -vectors of hypersimplices
We consider the Ehrhart -vector for the hypersimplex. It is well-known
that the sum of the is the normalized volume which equals an Eulerian
numbers. The main result is a proof of a conjecture by R. Stanley which gives
an interpretation of the coefficients in terms of descents and
excedances. Our proof is geometric using a careful book-keeping of a shelling
of a unimodular triangulation. We generalize this result to other closely
related polytopes
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