{
  "id": "0810.2727",
  "version": "v1",
  "published": "2008-10-15T15:28:28.000Z",
  "updated": "2008-10-15T15:28:28.000Z",
  "title": "Derangements and Euler's difference table for $C_\\ell\\wr S_n$",
  "authors": [
    "Hilarion L. M. Faliharimalala",
    "Jiang Zeng"
  ],
  "comment": "22 pages",
  "journal": "The Electronic Journal of Combinatorics 15 (2008); #R65",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "Euler's difference table associated to the sequence $\\{n!\\}$ leads naturally to the counting formula for the derangements. In this paper we study Euler's difference table associated to the sequence $\\{\\ell^n n!\\}$ and the generalized derangement problem. For the coefficients appearing in the later table we will give the combinatorial interpretations in terms of two kinds of $k$-successions of the group $C_\\ell\\wr S_n$. In particular for $\\ell=1$ we recover the known results for the symmetric groups while for $\\ell=2$ we obtain the corresponding results for the hyperoctahedral groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-15T15:28:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperoctahedral groups",
      "combinatorial interpretations",
      "symmetric groups",
      "study eulers difference table",
      "generalized derangement problem",
      "derangements",
      "wreath product"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.2727F"
    }
  }
}