{
  "id": "1610.06624",
  "version": "v1",
  "published": "2016-10-20T23:07:20.000Z",
  "updated": "2016-10-20T23:07:20.000Z",
  "title": "W-Operators and Permutation Groups",
  "authors": [
    "Hao Sun"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "W-operators are differential operators on the polynomial ring. A special example of W-operators is the cut-and-join operator. We study the relation between W-operators and permutation groups. We find the W-operator $W([d])$ can be written as the sum of $d!$ summations. Each summation can be determined by a unique permutation in the permutation group $S_d$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-20T23:07:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "permutation group",
      "w-operator",
      "cut-and-join operator",
      "special example"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}