{
  "id": "1705.03138",
  "version": "v1",
  "published": "2017-05-09T01:23:51.000Z",
  "updated": "2017-05-09T01:23:51.000Z",
  "title": "Characterization for entropy of shifts of finite type on Cayley trees",
  "authors": [
    "Jung-Chao Ban",
    "Chih-Hung Chang"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "The notion of tree-shifts constitutes an intermediate class in between one-sided shift spaces and multidimensional ones. This paper proposes an algorithm for computing of the entropy of a tree-shift of finite type. Meanwhile, the entropy of a tree-shift of finite type is $\\dfrac{1}{p} \\ln \\lambda$ for some $p \\in \\mathbb{N}$, where $\\lambda$ is a Perron number. This extends Lind's work on one-dimensional shifts of finite type. As an application, the entropy minimality problem is investigated, and we obtain the necessary and sufficient condition for a tree-shift of finite type being entropy minimal with some additional conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-09T01:23:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E05",
      "11A63"
    ],
    "keywords": [
      "finite type",
      "cayley trees",
      "characterization",
      "entropy minimality problem",
      "extends linds work"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}