{
  "id": "1302.3012",
  "version": "v1",
  "published": "2013-02-13T08:28:46.000Z",
  "updated": "2013-02-13T08:28:46.000Z",
  "title": "Standard Young Tableaux and Colored Motzkin Paths",
  "authors": [
    "Sen-Peng Eu",
    "Tung-Shan Fu",
    "Justin T. Hou",
    "Te-Wei Hsu"
  ],
  "comment": "21 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we propose a notion of colored Motzkin paths and establish a bijection between the $n$-cell standard Young tableaux (SYT) of bounded height and the colored Motzkin paths of length $n$. This result not only gives a lattice path interpretation of the standard Young tableaux but also reveals an unexpected intrinsic relation between the set of SYTs with at most $2d+1$ rows and the set of SYTs with at most 2d rows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-13T08:28:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19",
      "05A15"
    ],
    "keywords": [
      "colored motzkin paths",
      "cell standard young tableaux",
      "lattice path interpretation",
      "2d rows",
      "unexpected intrinsic relation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.3012E"
    }
  }
}