{
  "id": "math/9808017",
  "version": "v4",
  "published": "1998-08-04T19:17:13.000Z",
  "updated": "2004-10-29T21:54:56.000Z",
  "title": "Plane partitions I: a generalization of MacMahon's formula",
  "authors": [
    "Mihai Ciucu"
  ],
  "comment": "35 pages, 34 figures. New to this version: a few typos were corrected, and the journal information is included. Memoirs of Amer. Math. Soc., accepted, to appear",
  "categories": [
    "math.CO"
  ],
  "abstract": "The number of plane partitions contained in a given box was shown by MacMahon to be given by a simple product formula. By a simple bijection, this formula also enumerates lozenge tilings of hexagons of side-lengths $a,b,c,a,b,c$ (in cyclic order) and angles of 120 degrees. We present a generalization in the case $b=c$ by giving simple product formulas enumerating lozenge tilings of regions obtained from a hexagon of side-lengths $a,b+k,b,a+k,b,b+k$ (where $k$ is an arbitrary non-negative integer) and angles of 120 degrees by removing certain triangular regions along its symmetry axis.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2004-10-29T21:54:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05B45"
    ],
    "keywords": [
      "plane partitions",
      "macmahons formula",
      "generalization",
      "product formulas enumerating lozenge tilings",
      "simple product formulas enumerating lozenge"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......8017C"
    }
  }
}