{
  "id": "1408.5708",
  "version": "v1",
  "published": "2014-08-25T09:52:00.000Z",
  "updated": "2014-08-25T09:52:00.000Z",
  "title": "Plethysm and lattice point counting",
  "authors": [
    "Thomas Kahle",
    "Mateusz Michalek"
  ],
  "comment": "23 pages including appendix, 1 figure, computational results and code available at http://thomas-kahle.de/plethysm.html",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "It is shown that the multiplicities in the plethysm of GL(n) are given by the answer to a lattice point counting problem. This problem is attacked with the help of computer algebra. An explicit answer is obtained for $S^\\mu(S^k)$, when $\\mu$ is any partition of 4 or 5. In the general case, asymptotics of the solution are studied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-25T09:52:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "11P21",
      "11H06",
      "05A16",
      "52B20",
      "52B55",
      "20C15"
    ],
    "keywords": [
      "lattice point counting problem",
      "explicit answer",
      "computer algebra",
      "general case",
      "multiplicities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.5708K"
    }
  }
}