{
  "id": "1511.02804",
  "version": "v1",
  "published": "2015-11-09T19:11:14.000Z",
  "updated": "2015-11-09T19:11:14.000Z",
  "title": "Difference operators for partitions under the Littlewood decomposition",
  "authors": [
    "Paul-Olivier Dehaye",
    "Guo-Niu Han",
    "Huan Xiong"
  ],
  "comment": "24 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The concept of $t$-difference operator for functions of partitions is introduced to prove a generalization of Stanley's theorem on polynomiality of Plancherel averages of symmetric functions related to contents and hook lengths. Our extension uses a generalization of the notion of Plancherel measure, based on walks in the Young lattice with steps given by the addition of $t$-hooks. It is well-known that the hook lengths of multiples of $t$ can be characterized by the Littlewood decomposition. Our study gives some further information on the contents and hook lengths of other congruence classes modulo $t$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-09T19:11:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A17",
      "05A19",
      "05E05",
      "05E10",
      "11P81"
    ],
    "keywords": [
      "littlewood decomposition",
      "difference operator",
      "hook lengths",
      "partitions",
      "congruence classes modulo"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151102804D"
    }
  }
}