{
  "id": "2410.01743",
  "version": "v2",
  "published": "2024-10-02T16:54:01.000Z",
  "updated": "2024-11-24T12:25:28.000Z",
  "title": "The Ehrhart $h^*$-polynomials of positroid polytopes",
  "authors": [
    "Yuhan Jiang"
  ],
  "comment": "20 pages, 10 figures. arXiv admin note: text overlap with arXiv:2404.03026 by other authors",
  "categories": [
    "math.CO"
  ],
  "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. We also compute the $h^*$-polynomial of any positroid polytope with some facets removed and relate it to the descents of permutations. Our result generalizes that of Early, Kim, and Li for hypersimplices.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-11-24T12:25:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ehrhart polynomial",
      "arbitrary positroid polytope regarding permutation",
      "positroid polytope regarding permutation descents",
      "lattice polytope counts",
      "result generalizes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}