{
  "id": "1208.1367",
  "version": "v2",
  "published": "2012-08-07T08:52:03.000Z",
  "updated": "2012-08-13T09:29:19.000Z",
  "title": "The Distribution of Heights of Discrete Excursions",
  "authors": [
    "Uwe Schwerdtfeger"
  ],
  "comment": "This paper has been withdrawn by the author due to an error in section 2.3. Unless a=1, more than the said k+1 tableaux have to be taken into account. As it stands the subsequent derivation is only valid for a=1, i.e. excursions with precisely one positive step 1 and an arbitrary finite set of non-positive steps",
  "categories": [
    "math.CO"
  ],
  "abstract": "We compute the limiting distribution of height of a random discrete excursion with step sets consisting of one positive step 1 and arbitrary finite set of non-positive integers. The limit law is the supremum of a Brownian excursion. This is well-known for Dyck and Motzkin paths. We apply a representation of the length and height generating function in terms of certain Schur polynomials put forward in a 2008 paper by Bousquet-Melout which leads to a form of the moment generating functions amenable to a Mellin transform analysis.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-08-13T09:29:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "82B41"
    ],
    "keywords": [
      "distribution",
      "mellin transform analysis",
      "random discrete excursion",
      "arbitrary finite set",
      "step sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1367S"
    }
  }
}