Ehrhart h^*-vectors of hypersimplices

2011/04/28 by Nan Li, Li, Nan
Mathematics · #05A05 #05A15 #05C38 #06F99 #52B22 #52C07 #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1104.5292

openalex publication_date 2011/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 numbers. 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.

Related

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• Unimodality of the h^*-vector for unimodular triangulations whose boundary is an induced subcomplex
• Unimodality Problems in Ehrhart Theory