{
  "id": "math/0101009",
  "version": "v2",
  "published": "2001-01-01T18:00:57.000Z",
  "updated": "2001-07-13T18:13:54.000Z",
  "title": "A (conjectural) 1/3-phenomenon for the number of rhombus tilings of a hexagon which contain a fixed rhombus",
  "authors": [
    "Christian Krattenthaler"
  ],
  "comment": "16 pages, AmS-LaTeX, uses TeXDraw; a few typos corrected",
  "journal": "in: Number Theory and Discrete Mathematics, A. K. Agarwal et al., eds., Hindustan Book Agency, New Delhi, 2002, pp. 13-30.",
  "categories": [
    "math.CO"
  ],
  "abstract": "We state, discuss, provide evidence for, and prove in special cases the conjecture that the probability that a random tiling by rhombi of a hexagon with side lengths $2n+a,2n+b,2n+c,2n+a,2n+b,2n+c$ contains the (horizontal) rhombus with coordinates $(2n+x,2n+y)$ is equal to ${1/3} + g_{a,b,c,x,y}(n) {\\binom {2n}{n}}^3 / \\binom {6n}{3n}$, where $g_{a,b,c,x,y}(n)$ is a rational function in $n$. Several specific instances of this \"1/3-phenomenon\" are made explicit.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-07-13T18:13:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A19",
      "05B45",
      "33C20",
      "33C45",
      "52C20"
    ],
    "keywords": [
      "rhombus tilings",
      "fixed rhombus",
      "conjectural",
      "special cases",
      "side lengths"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......1009K"
    }
  }
}