{
  "id": "1906.01125",
  "version": "v1",
  "published": "2019-06-03T23:42:38.000Z",
  "updated": "2019-06-03T23:42:38.000Z",
  "title": "A combinatorial model for the decomposition of multivariate polynomials rings as an $S_n$-module",
  "authors": [
    "Rosa Orellana",
    "Mike Zabrocki"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider the symmetric group $S_n$ module of the polynomial ring with $m$ sets of $n$ commuting variables and $m'$ sets of $n$ anti-commuting variables and calculate that the multiplicity of an irreducible indexed by the partition $\\lambda$ (a partition of $n$) is the number of multiset tableaux of shape $\\lambda$ satisfying certain column and row strict conditions. We also present a finite generating set for the ring of $S_n$ invariant polynomials of this ring.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-03T23:42:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "05E10",
      "20C30"
    ],
    "keywords": [
      "multivariate polynomials rings",
      "combinatorial model",
      "decomposition",
      "row strict conditions",
      "symmetric group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}