Hypersimplices are Ehrhart Positive
Combinatorics
2020-11-23 v2
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.
Cite
@article{arxiv.1911.10146,
title = {Hypersimplices are Ehrhart Positive},
author = {Luis Ferroni},
journal= {arXiv preprint arXiv:1911.10146},
year = {2020}
}
Comments
10 pages, 2 tables