{
  "id": "1911.00977",
  "version": "v1",
  "published": "2019-11-03T21:39:59.000Z",
  "updated": "2019-11-03T21:39:59.000Z",
  "title": "Partitions for semi-magic squares of size three",
  "authors": [
    "Robert W. Donley"
  ],
  "comment": "18 pages, 16 figures",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "In the theory of Clebsch-Gordan coefficients, one may recognize the domain space as the set of weakly semi-magic squares of size three. Two partitions on this set are considered: a triangle-hexagon model based on top lines, and one based on the orbits under a finite group action. In addition to giving another proof of McMahon's formula, we give a generating function that counts the so-called trivial zeros of Clebsch-Gordan coefficients and its associated quasi-polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-03T21:39:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05E10",
      "15B36",
      "22E70",
      "81R05"
    ],
    "keywords": [
      "partitions",
      "clebsch-gordan coefficients",
      "finite group action",
      "domain space",
      "weakly semi-magic squares"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}