Nan Li - Ehrhart $h^*$-vectors of hypersimplices

dmtcs:12798 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.12798
Ehrhart $h^*$-vectors of hypersimplicesArticle

Authors: Nan Li ORCID1

  • 1 Department of Mathematics [MIT]

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.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: Hypersimplex,Ehrhart h^*-vector,Shellable triangulation,Eulerian statistics,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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