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arXiv · 2410.01743

The Ehrhart $h^*$-polynomials of positroid polytopes

Yuhan Jiang
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Abstract

A positroid is a matroid realized by a matrix such that all maximal minors are non-negative. Positroid polytopes are matroid polytopes of positroids. In particular, they are lattice polytopes. The Ehrhart polynomial of a lattice polytope counts the number of integer points in the dilation of that polytope. The Ehrhart series is the generating function of the Ehrhart polynomial, a rational function with a numerator called the $h^*$-polynomial. We give explicit formulas for the $h^*$-polynomials of an arbitrary positroid polytope regarding permutation descents. Our result generalizes that of Early, Kim, and Li for hypersimplices.

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Yuhan Jiang. 2024-10-02. The Ehrhart $h^*$-polynomials of positroid polytopes. https://arxiv.org/abs/2410.01743

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