{
  "id": "1905.12387",
  "version": "v1",
  "published": "2019-05-29T12:52:14.000Z",
  "updated": "2019-05-29T12:52:14.000Z",
  "title": "Twenty-Vertex model with domain wall boundaries and domino tilings",
  "authors": [
    "Philippe Di Francesco",
    "Emmanuel Guitter"
  ],
  "comment": "63 pages, 22+16 figures",
  "categories": [
    "math.CO",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the triangular lattice ice model (20-Vertex model) with four types of domain-wall type boundary conditions. In types 1 and 2, the configurations are shown to be equinumerous to the quarter-turn symmetric domino tilings of an Aztec-like holey square, with a central cross-shaped hole. The proof of this statement makes extensive use of integrability and of a connection to the 6-Vertex model. The type 3 configurations are conjectured to be in same number as domino tilings of a particular triangle. The four enumeration problems are reformulated in terms of four types of Alternating Phase Matrices with entries 0 and sixth roots of unity, subject to suitable alternation conditions. Our result is a generalization of the ASM-DPP correspondence. Several refined versions of the above correspondences are also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-29T12:52:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "domain wall boundaries",
      "twenty-vertex model",
      "quarter-turn symmetric domino tilings",
      "domain-wall type boundary conditions",
      "triangular lattice ice model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 63,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}