{
  "id": "1409.2841",
  "version": "v1",
  "published": "2014-09-09T18:44:14.000Z",
  "updated": "2014-09-09T18:44:14.000Z",
  "title": "Increasing tableaux and Narayana numbers",
  "authors": [
    "Timothy Pressey",
    "Anna Stokke",
    "Terry Visentin"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a counting formula for the set of rectangular increasing tableaux in terms of generalized Narayana numbers. We define small $m$-Schr\\\"oder paths and give a bijection between the set of increasing rectangular tableaux and small $m$-Schr\\\"oder paths, generalizing a result of Pechenik [3]. Using $K$-jeu de taquin promotion, which was defined by Thomas and Yong [10], we give a cyclic sieving phenomenon for the set of increasing hook tableaux.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-09T18:44:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E99"
    ],
    "keywords": [
      "cyclic sieving phenomenon",
      "rectangular increasing tableaux",
      "taquin promotion",
      "generalized narayana numbers",
      "define small"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.2841P"
    }
  }
}