{
  "id": "1704.01095",
  "version": "v1",
  "published": "2017-04-04T16:35:25.000Z",
  "updated": "2017-04-04T16:35:25.000Z",
  "title": "Fringe Analysis of Plane Trees Related to Cutting and Pruning",
  "authors": [
    "Benjamin Hackl",
    "Clemens Heuberger",
    "Sara Kropf",
    "Helmut Prodinger"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Rooted plane trees are reduced by four different operations on the fringe. The number of surviving nodes after reducing the tree repeatedly for a fixed number of times is asymptotically analyzed. The four different operations include cutting all or only the leftmost leaves or maximal paths. This generalizes the concept of pruning a tree. The results include exact expressions and asymptotic expansions for the expected value and the variance as well as central limit theorems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-04T16:35:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16",
      "05C05",
      "05A15",
      "05A19",
      "60C05"
    ],
    "keywords": [
      "fringe analysis",
      "central limit theorems",
      "operations",
      "maximal paths",
      "asymptotic expansions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}