{
  "id": "2305.01774",
  "version": "v1",
  "published": "2023-05-02T20:32:15.000Z",
  "updated": "2023-05-02T20:32:15.000Z",
  "title": "Domino tilings of generalized Aztec triangles",
  "authors": [
    "Sylvie Corteel",
    "Frederick Huang",
    "Christian Krattenthaker"
  ],
  "comment": "39 pages; 17 figures",
  "categories": [
    "math.CO",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Di Francesco introduced Aztec triangles as combinatorial objects for which their domino tilings are equinumerous with certain sets of configurations of the twenty-vertex model that are the main focus of his article. We generalize Di Francesco's construction of Aztec triangles. While we do not know whether there is again a correspondence with configurations in the twenty-vertex model, we prove closed-form product formulas for the number of domino tilings of our generalized Aztec triangles. As a special case, we obtain a proof of Di Francesco's conjectured formula for the number of domino tilings of his Aztec triangles, and thus for the number of the corresponding configurations in the twenty-vertex model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-02T20:32:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A19",
      "82B23"
    ],
    "keywords": [
      "generalized aztec triangles",
      "domino tilings",
      "twenty-vertex model",
      "di francescos conjectured formula",
      "configurations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}