{
  "id": "1809.08128",
  "version": "v1",
  "published": "2018-09-21T13:58:56.000Z",
  "updated": "2018-09-21T13:58:56.000Z",
  "title": "The partition algebra and the plethysm coefficients",
  "authors": [
    "Chris Bowman",
    "Rowena Paget"
  ],
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We propose a new approach to study plethysm coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. This allows us to explain the stability properties of plethysm and Kronecker coefficients in a simple and uniform fashion for the first time. We prove the strengthened Foulkes' conjecture for stable plethysm coefficients in an elementary fashion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-21T13:58:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "partition algebra",
      "study plethysm coefficients",
      "first time",
      "elementary fashion",
      "schur-weyl duality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}