{
  "id": "1403.7506",
  "version": "v1",
  "published": "2014-03-28T19:31:42.000Z",
  "updated": "2014-03-28T19:31:42.000Z",
  "title": "Involution Statistics in Finite Coxeter Groups",
  "authors": [
    "Sarah B. Hart",
    "Peter J. Rowley"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $W$ be a finite Coxeter group and $X$ a subset of $W$. The length polynomial $L_{W,X}(t)$ is defined by $L_{W,X}(t) = \\sum_{x \\in X} t^{\\ell(x)}$, where $\\ell$ is the length function on $W$. In this article we derive expressions for the length polynomial where $X$ is any conjugacy class of involutions, or the set of all involutions, in any finite Coxeter group $W$. In particular, these results correct errors in the paper \"Permutation statistics on involutions\", W.M.B. Dukes., European J. Combin. 28 (2007), 186--198. for the involution length polynomials of Coxeter groups of type $B_n$ and $D_n$. Moreover, we give a counterexample to a unimodality conjecture of Dukes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-28T19:31:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite coxeter group",
      "involution statistics",
      "results correct errors",
      "involution length polynomials",
      "conjugacy class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.7506H"
    }
  }
}