{
  "id": "0807.0383",
  "version": "v3",
  "published": "2008-07-02T15:57:41.000Z",
  "updated": "2009-04-10T16:38:00.000Z",
  "title": "Some Combinatorial Properties of Hook Lengths, Contents, and Parts of Partitions",
  "authors": [
    "Richard P. Stanley"
  ],
  "comment": "20 pages. Correction of some inaccuracies, and a new Theorem 4.4",
  "categories": [
    "math.CO"
  ],
  "abstract": "This paper proves a generalization of a conjecture of Guoniu Han, inspired originally by an identity of Nekrasov and Okounkov. The main result states that certain sums over partitions p of n, involving symmetric functions of the squares of the hook lengths of p, are polynomial functions of n. A similar result is obtained for symmetric functions of the contents and shifted parts of n.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-04-10T16:38:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05"
    ],
    "keywords": [
      "hook lengths",
      "combinatorial properties",
      "partitions",
      "symmetric functions",
      "main result states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.0383S"
    }
  }
}