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arXiv · 1911.10146

Hypersimplices are Ehrhart Positive

Luis Ferroni
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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.

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Luis Ferroni. 2020-11-12. Hypersimplices are Ehrhart Positive. https://doi.org/10.1016/j.jcta.2020.105365

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