Year: 2024
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Jiang, Yuhan
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403852089