{
  "id": "2011.11885",
  "version": "v1",
  "published": "2020-11-24T04:13:29.000Z",
  "updated": "2020-11-24T04:13:29.000Z",
  "title": "Dihedral Sieving on Cluster Complexes",
  "authors": [
    "Zachary Stier",
    "Julian Wellman",
    "Zixuan Xu"
  ],
  "comment": "27 pages, 16 figures",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "The cyclic sieving phenomenon of Reiner, Stanton, and White characterizes the stabilizers of cyclic group actions on finite sets using q-analogue polynomials. Eu and Fu demonstrated a cyclic sieving phenomenon on generalized cluster complexes of every type using the q-Catalan numbers. In this paper, we exhibit the dihedral sieving phenomenon, introduced for odd n by Rao and Suk, on clusters of every type, and on generalized clusters of type A. In the type A case, we show that the Raney numbers count both reflection-symmetric k-angulations of an n-gon and a particular evaluation of the (q,t)-Fuss--Catalan numbers. We also introduce a sieving phenomenon for the symmetric group, and discuss possibilities for dihedral sieving for even n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-24T04:13:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cyclic sieving phenomenon",
      "cyclic group actions",
      "raney numbers count",
      "finite sets",
      "q-analogue polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}