{
  "id": "2401.08481",
  "version": "v1",
  "published": "2024-01-16T16:35:00.000Z",
  "updated": "2024-01-16T16:35:00.000Z",
  "title": "Determinant evaluations inspired by Di Francesco's determinant for twenty-vertex configurations",
  "authors": [
    "Christoph Koutschan",
    "Christian Krattenthaler",
    "Michael Schlosser"
  ],
  "comment": "AmS-LaTeX, 37 pages",
  "journal": "J. Symbol. Comput. 127 (2025), 102352",
  "categories": [
    "math.CO",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In his work on the twenty vertex model, Di Francesco [Electron. J. Combin. 28(4) (2021), Paper No. 4.38] found a determinant formula for the number of configurations in a specific such model, and he conjectured a closed form product formula for the evaluation of this determinant. We prove this conjecture here. Moreover, we actually generalize this determinant evaluation to a one-parameter family of determinant evaluations, and we present many more determinant evaluations of similar type - some proved, some left open as conjectures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-16T16:35:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A15",
      "05A15",
      "05A19",
      "05B45",
      "82B20"
    ],
    "keywords": [
      "determinant evaluation",
      "di francescos determinant",
      "twenty-vertex configurations",
      "closed form product formula",
      "vertex model"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}