{
  "id": "2307.05850",
  "version": "v1",
  "published": "2023-07-11T23:49:22.000Z",
  "updated": "2023-07-11T23:49:22.000Z",
  "title": "Entropy for $k$-trees defined by $k$ transition matrices",
  "authors": [
    "Andressa Paola Cordeiro",
    "Alexandre Tavares Baraviera",
    "Alex Jenaro Becker"
  ],
  "comment": "16 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this work we consider Markov tree-shifts given by $k$ transition matrices, one for each of its $k$ directions. We analyse some topological properties introduced by arXiv:1509.01355 in order to answer some of the questions raised by those authors. Moreover, we provide a method to characterize the complexity function for Markov tree-shifts; this function is used to calculate the tree entropies defined by arXiv:1712.02251 and arXiv:1509.08325. We compare both entropies in order to determine some of its properties. Finally, the characterization of the complexity function is used to calculate the entropy of all binary Markov tree-shifts over the alphabet $\\{0,1\\}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-11T23:49:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "transition matrices",
      "complexity function",
      "binary markov tree-shifts",
      "tree entropies",
      "topological properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}