{
  "id": "1712.09507",
  "version": "v1",
  "published": "2017-12-27T06:30:12.000Z",
  "updated": "2017-12-27T06:30:12.000Z",
  "title": "Protected Vertices in Motzkin trees",
  "authors": [
    "Anthony Van Duzer"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we find recurrence relations for the asymptotic probability a vertex is $k$ protected in all Motzkin trees. We use a similar technique to calculate the probabilities for balanced vertices of rank $k$. From this we calculate upper and lower bounds for the probability a vertex is balanced and upper and lower bounds for the expected rank of balanced vertices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-27T06:30:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "motzkin trees",
      "protected vertices",
      "lower bounds",
      "balanced vertices",
      "asymptotic probability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}