{
  "id": "1210.7353",
  "version": "v1",
  "published": "2012-10-27T18:08:58.000Z",
  "updated": "2012-10-27T18:08:58.000Z",
  "title": "Cyclic sieving phenomenon on annular noncrossing permutations",
  "authors": [
    "Jang Soo Kim"
  ],
  "comment": "12 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show an instance of the cyclic sieving phenomenon on annular noncrossing permutations with given cycle types. We define annular $q$-Kreweras numbers, annular $q$-Narayana numbers, and annular $q$-Catalan number, all of which are polynomials in $q$. We then show that these polynomials exhibit the cyclic sieving phenomenon on annular noncrossing permutations. We also show that a sum of annular $q$-Kreweras numbers becomes an annular $q$-Narayana number and a sum of $q$-Narayana numbers becomes an annular $q$-Catalan number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-27T18:08:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cyclic sieving phenomenon",
      "annular noncrossing permutations",
      "narayana number",
      "kreweras numbers",
      "catalan number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.7353K"
    }
  }
}