{
  "id": "1011.1001",
  "version": "v1",
  "published": "2010-11-03T20:18:42.000Z",
  "updated": "2010-11-03T20:18:42.000Z",
  "title": "Colourings of lattices and coincidence site lattices",
  "authors": [
    "Manuel Joseph C. Loquias",
    "Peter Zeiner"
  ],
  "comment": "9 pages, 6 figures",
  "journal": "Phil. Mag. 91 (2011) 19-21, 2680-2689",
  "doi": "10.1080/14786435.2010.524900",
  "categories": [
    "math.MG"
  ],
  "abstract": "The relationship between the coincidence indices of a lattice $\\Gamma_1$ and a sublattice $\\Gamma_2$ of $\\Gamma_1$ is examined via the colouring of $\\Gamma_1$ that is obtained by assigning a unique colour to each coset of $\\Gamma_2$. In addition, the idea of colour symmetry, originally defined for symmetries of lattices, is extended to coincidence isometries of lattices. An example involving the Ammann-Beenker tiling is provided to illustrate the results in the quasicrystal setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-03T20:18:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C07",
      "52C23",
      "11H06",
      "20G45",
      "20H15"
    ],
    "keywords": [
      "coincidence site lattices",
      "colour symmetry",
      "unique colour",
      "coincidence indices",
      "coincidence isometries"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Philosophical Magazine",
      "year": 2011,
      "month": "Jul",
      "volume": 91,
      "number": "19-21",
      "pages": 2680
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PMag...91.2680L"
    }
  }
}