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Ehrhart $h^*$-vectors of hypersimplices

Abstract : We consider the Ehrhart $h^*$-vector for the hypersimplex. It is well-known that the sum of the $h_i^*$ is the normalized volume which equals an Eulerian number. The main result is a proof of a conjecture by R. Stanley which gives an interpretation of the $h^*_i$ 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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https://hal.inria.fr/hal-01229724
Contributor : Alain Monteil <>
Submitted on : Tuesday, November 17, 2015 - 10:20:36 AM
Last modification on : Wednesday, June 26, 2019 - 2:48:03 PM
Long-term archiving on: : Friday, April 28, 2017 - 3:51:45 PM

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Nan Li. Ehrhart $h^*$-vectors of hypersimplices. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.121-132. ⟨hal-01229724⟩

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