{
  "id": "1004.4571",
  "version": "v1",
  "published": "2010-04-26T16:47:55.000Z",
  "updated": "2010-04-26T16:47:55.000Z",
  "title": "Jucys-Murphy Elements and a Combinatorial Proof of an Identity of S. Kerov",
  "authors": [
    "Jennifer R. Galovich"
  ],
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "Consider the elements of the group algebra CS_{n} given by R_{j}=Sigma_{i=1}^{j-1}(ij), for 2<=j<=n. Jucys [3 - 5] and Murphy[7] showed that these elements act diagonally on elements of S_{n} and gave explicit formulas for the diagonal entries. As requested by the late S. Kerov, we give a combinatorial proof of this work in case j=n and present several similar results which arise from these combinatorial methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-26T16:47:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "combinatorial proof",
      "jucys-murphy elements",
      "gave explicit formulas",
      "group algebra",
      "similar results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.4571G"
    }
  }
}