{
  "id": "2102.09982",
  "version": "v1",
  "published": "2021-02-19T15:25:23.000Z",
  "updated": "2021-02-19T15:25:23.000Z",
  "title": "Macdonald polynomial and cyclic sieving",
  "authors": [
    "Jaeseong Oh"
  ],
  "comment": "11 pages, comments welcome!",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Garsia--Haiman module is a bigraded $\\mathfrak{S}_n$-module whose Frobenius image is a Macdonald polynomial. The method of orbit harmonics promotes the $\\mathfrak{S}_n$-set $X$ to a graded polynomial ring. The orbit harmonics can be applied to prove cyclic sieving phenomena which is a notion that encapsulates the fixed-point structure of finite cyclic group action on a finite set. By applying this idea to the Garsia--Haiman module, we provide cyclic sieving results regarding the enumeration of matrices that are invariant under certain cyclic row and column rotation and translation of entries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-19T15:25:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E18",
      "05E10",
      "05E05"
    ],
    "keywords": [
      "macdonald polynomial",
      "garsia-haiman module",
      "finite cyclic group action",
      "orbit harmonics promotes",
      "fixed-point structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}