{
  "id": "1407.2015",
  "version": "v1",
  "published": "2014-07-08T09:49:40.000Z",
  "updated": "2014-07-08T09:49:40.000Z",
  "title": "Symmetric polyomino tilings, tribones, ideals, and Groebner bases",
  "authors": [
    "Manuela Muzika Dizdarevic",
    "Rade T. Zivaljevic"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We apply the theory of Groebner bases to the study of signed, symmetric polyomino tilings of planar domains. Complementing the results of Conway and Lagarias we show that the triangular regions T_N=T_{3k-1} and T_N=T_{3k} in a hexagonal lattice admit a signed tiling by three-in-line polyominoes (tribones) symmetric with respect to the 120 degrees rotation of the triangle if and only if either N=27r-1 or N=27r for some integer r.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-08T09:49:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B45"
    ],
    "keywords": [
      "symmetric polyomino tilings",
      "groebner bases",
      "hexagonal lattice admit",
      "degrees rotation",
      "triangular regions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.2015M"
    }
  }
}