# 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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Conference papers

https://hal.inria.fr/hal-01229724
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• HAL Id : hal-01229724, version 1

### Citation

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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