{
  "id": "1903.12108",
  "version": "v1",
  "published": "2019-03-28T16:47:29.000Z",
  "updated": "2019-03-28T16:47:29.000Z",
  "title": "Pak-Stanley labeling of the $m$-Catalan hyperplane arrangement",
  "authors": [
    "Rui Duarte",
    "António Guedes de Oliveira"
  ],
  "comment": "14 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We characterize in simple terms the Pak-Stanley labels $\\lambda(R)$ of the regions $R$ of the $m$-Catalan arrangement. We also propose a simple algorithm that returns $R$ from $\\lambda(R)$. Finally, we characterize in close terms the labels of the relatively bounded regions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-28T16:47:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19"
    ],
    "keywords": [
      "catalan hyperplane arrangement",
      "pak-stanley labeling",
      "simple terms",
      "pak-stanley labels",
      "catalan arrangement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}