{
  "id": "2002.02410",
  "version": "v1",
  "published": "2020-02-05T15:53:08.000Z",
  "updated": "2020-02-05T15:53:08.000Z",
  "title": "Generalized Schröder paths and Young tableaux with skew shapes",
  "authors": [
    "Xiaomei Chen"
  ],
  "comment": "20 pages, 7figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A generalized Schr\\\"{o}der path is a lattice path with steps (1,0), (1,1) and (0,1), and never goes above the diagonal line $y=x$. In this paper, we firstly give the distribution of the major index over generalized Schr\\\"{o}der paths. Then by providing a bijection between generalized Schr\\\"{o}der paths and row-increasing tableaux of skew shapes with two rows, we obtain the distribution of the major index and the amajor index over these tableaux. We also generalize a result of Pechenik, and give the distribution of the major index over increasing tableaux of skew shapes with two rows. Especially, a bijection from row-increasing tableaux with shape $(n,m)$ and maximal value $n+m-k$ to standard Young tableaux with a skew shape is obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-05T15:53:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05E05"
    ],
    "keywords": [
      "skew shape",
      "generalized schröder paths",
      "standard young tableaux",
      "distribution",
      "row-increasing tableaux"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}