{
  "id": "1603.00754",
  "version": "v1",
  "published": "2016-03-02T15:37:01.000Z",
  "updated": "2016-03-02T15:37:01.000Z",
  "title": "Matrix Characterization of Multidimensional Subshifts of Finite Type",
  "authors": [
    "Puneet Sharma",
    "Dileep Kumar"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $X\\subset A^{Z^d}$ be a $2$-dimensional subshift of finite type. We prove that any $2$-dimensional multidimensional subshift of finite type can be characterized by a square matrix of infinite dimension. We extend our result to a general $d$-dimensional case. We prove that the multidimensional shift space is non-empty if and only if the matrix obtained is of positive dimension. In the process, we give an alternative view of the necessary and sufficient conditions obtained for the non-emptiness of the multidimensional shift space. We also give sufficient conditions for the shift space $X$ to exhibit periodic points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-02T15:37:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "37B20",
      "37B50"
    ],
    "keywords": [
      "finite type",
      "matrix characterization",
      "multidimensional shift space",
      "sufficient conditions",
      "dimensional multidimensional subshift"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160300754S"
    }
  }
}