{
  "id": "1304.6105",
  "version": "v1",
  "published": "2013-04-22T20:48:29.000Z",
  "updated": "2013-04-22T20:48:29.000Z",
  "title": "$k$-protected vertices in binary search trees",
  "authors": [
    "Miklos Bona"
  ],
  "comment": "12 pages 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that for every $k$, the probability that a randomly selected vertex of a random binary search tree on $n$ nodes is at distance $k-1$ from the closest leaf converges to a rational constant $c_k$ as $n$ goes to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-22T20:48:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A16"
    ],
    "keywords": [
      "protected vertices",
      "random binary search tree",
      "closest leaf converges",
      "rational constant",
      "randomly selected vertex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.6105B"
    }
  }
}