{
  "id": "2104.08454",
  "version": "v1",
  "published": "2021-04-17T05:22:45.000Z",
  "updated": "2021-04-17T05:22:45.000Z",
  "title": "The Convex Hull of Parking Functions of Length $n$",
  "authors": [
    "Aruzhan Amanbayeva",
    "Danielle Wang"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\mathcal{P}_n$ be the convex hull in $\\mathbb{R}^n$ of all parking functions of length $n$. Stanley found the number of vertices and the number of facets of $\\mathcal{P}_n$. Building upon these results, we determine the number of faces of arbitrary dimension, the volume, and the number of integer points of $\\mathcal{P}_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-17T05:22:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "52B05"
    ],
    "keywords": [
      "convex hull",
      "parking functions",
      "arbitrary dimension",
      "integer points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}