{
  "id": "1807.07458",
  "version": "v1",
  "published": "2018-07-19T14:18:40.000Z",
  "updated": "2018-07-19T14:18:40.000Z",
  "title": "On the Sweep Map for Fuss Rational Dyck Paths",
  "authors": [
    "Adriano M. Garsia",
    "Guoce Xin"
  ],
  "comment": "24 pages, 7 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Our main contribution here is the discovery of a new family of standard Young tableaux $ {\\cal T}^k_n$ which are in bijection with the family ${\\cal D}_{m,n}$ of Rational Dyck paths for $m=k\\times n\\pm 1$ (the so called \"Fuss\" case). Using this family we give a new proof of the invertibility of the sweep map in the Fuss case by means of a very simple explicit algorithm. This new algorithm has running time $O(m+n)$. It is independent of the Thomas-William algorithm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-19T14:18:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19",
      "05E40"
    ],
    "keywords": [
      "fuss rational dyck paths",
      "sweep map",
      "simple explicit algorithm",
      "standard young tableaux",
      "fuss case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}