{
  "id": "1606.00083",
  "version": "v1",
  "published": "2016-06-01T00:50:32.000Z",
  "updated": "2016-06-01T00:50:32.000Z",
  "title": "$k$-protected vertices in unlabeled rooted plane trees",
  "authors": [
    "Keith Copenhaver"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We find a simple, closed formula for the proportion of vertices which are $k$-protected in all unlabeled rooted plane trees on $n$ vertices. We also find that, as $n$ goes to infinity, the average rank of a random vertex in a tree of size $n$ approaches 0.727649, and the average rank of the root of a tree of size $n$ approaches 1.62297.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-01T00:50:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05C05",
      "05A16"
    ],
    "keywords": [
      "unlabeled rooted plane trees",
      "protected vertices",
      "average rank",
      "random vertex",
      "approaches"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}