{
  "id": "1511.08133",
  "version": "v1",
  "published": "2015-11-25T17:47:20.000Z",
  "updated": "2015-11-25T17:47:20.000Z",
  "title": "How rigid the finite ultrametric spaces can be?",
  "authors": [
    "O. Dovgoshey",
    "E. Petrov",
    "H. -M. Teichert"
  ],
  "comment": "19 pages, 4 figures",
  "categories": [
    "math.MG"
  ],
  "abstract": "A metric space $X$ is rigid if the isometry group of $X$ is trivial. The finite ultrametric spaces $X$ with $|X| \\geq 2$ are not rigid since for every such $X$ there is a self-isometry having exactly $|X|-2$ fixed points. Using the representing trees we characterize the finite ultrametric spaces $X$ for which every self-isometry has at least $|X|-2$ fixed points. Some other extremal properties of such spaces and related graph theoretical characterizations are also obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-25T17:47:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54E35"
    ],
    "keywords": [
      "finite ultrametric spaces",
      "fixed points",
      "self-isometry",
      "related graph theoretical characterizations",
      "isometry group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}