Séminaire Lotharingien de Combinatoire, 93B.111 (2025), 12 pp.
Yuhan Jiang
The Ehrhart h*-Polynomials of Positroid Polytopes
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, which is a rational function with the numerator called the h*-polynomial.
We compute the h*-polynomial of an arbitrary positroid polytope and an arbitrary half-open positroid polytope.
Our result generalizes that of Katzman, Early, Kim, and Li for hypersimplices.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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