Hypersimplices are Ehrhart Positive
arXiv:1911.10146 · doi:10.1016/j.jcta.2020.105365
Abstract
We consider the Ehrhart polynomial of hypersimplices. It is proved that these polynomials have positive coefficients and we give a combinatorial formula for each of them. This settles a problem posed by Stanley and also proves that uniform matroids are Ehrhart positive, an important and yet unsolved particular case of a conjecture posed by De Loera et al. To this end, we introduce a new family of numbers that we call weighted Lah numbers and study some of their properties.
arXiv comment10 pages, 2 tables
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Cited by in corpus (8)
- Matroids are not Ehrhart positive
- On the Ehrhart Polynomial of Minimal Matroids
- Valuative invariants for large classes of matroids
- Ehrhart polynomials of rank two matroids
- Integer point enumeration on independence polytopes and half-open hypersimplices
- Lattice points in slices of prisms
- Schubert matroids, Delannoy paths, and Speyer's invariant
- Equivariant Ehrhart Theory of Hypersimplices