The Ehrhart -polynomials of positroid polytopes
arXiv:2410.01743
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 -polynomial. We give explicit formulas for the -polynomials of an arbitrary positroid polytope regarding permutation descents. Our result generalizes that of Early, Kim, and Li for hypersimplices.
arXiv admin note: text overlap with arXiv:2404.03026 by other authors