{
  "id": "0810.3388",
  "version": "v1",
  "published": "2008-10-19T11:47:06.000Z",
  "updated": "2008-10-19T11:47:06.000Z",
  "title": "Labeled Partitions with Colored Permutations",
  "authors": [
    "William Y. C. Chen",
    "Henry Y. Gao",
    "Jia He"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we extend the notion of labeled partitions with ordinary permutations to colored permutations in the sense that the colors are endowed with a cyclic structure. We use labeled partitions with colored permutations to derive the generating function of the $\\mathrm{fmaj}_k$ indices of colored permutations. The second result is a combinatorial treatment of a relation on the q-derangement numbers with respect to colored permutations which leads to the formula of Chow for signed permutations and the formula of Faliharimalala and Zeng [10] on colored permutations. The third result is an involution on permutations that implies the generating function formula for the signed q-counting of the major indices due to Gessel and Simon. This involution can be extended to signed permutations. In this way, we obtain a combinatorial interpretation of a formula of Adin, Gessel and Roichman.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-19T11:47:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "colored permutations",
      "labeled partitions",
      "signed permutations",
      "second result",
      "combinatorial treatment"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.3388C"
    }
  }
}