{
  "id": "1212.1266",
  "version": "v3",
  "published": "2012-12-06T09:24:28.000Z",
  "updated": "2013-01-21T00:18:31.000Z",
  "title": "Barycentric subdivisions and derangement polynomials for the even-signed permutation groups",
  "authors": [
    "Christina Savvidou"
  ],
  "comment": "This paper has been withdrawn by the author due to an error in the proof of the main theorem that cancels the theorem. It will be replaced by a new article with similar content",
  "categories": [
    "math.CO"
  ],
  "abstract": "The derangement polynomial for the symmetric group enumerates derangements by the number of excedances. It can be interpreted as the local $h$-polynomial, in the sense of Stanley, of the barycentric subdivision of the simplex. Motivated by this interpretation, we define a derangement polynomial for the even-signed permutation group. The coefficients of this polynomial are nonnegative, symmetric and unimodal. We show that they enumerate derangements in the even-signed permutation group according to a notion of excedance, which is analogous to the one introduced by Brenti for signed permutations. We also give an explicit formula for the corresponding exponential generating function.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-01-21T00:18:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45",
      "05A05",
      "05A19"
    ],
    "keywords": [
      "even-signed permutation group",
      "derangement polynomial",
      "barycentric subdivision",
      "symmetric group enumerates derangements",
      "enumerate derangements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.1266S"
    }
  }
}