{
  "id": "0803.0848",
  "version": "v1",
  "published": "2008-03-06T12:35:36.000Z",
  "updated": "2008-03-06T12:35:36.000Z",
  "title": "Asymptotic analysis of $k$-noncrossing matchings",
  "authors": [
    "Emma Y. Jin",
    "Christian M. Reidys",
    "Rita R. Wang"
  ],
  "comment": "19 pages and 1 figure",
  "categories": [
    "math.CO",
    "math.GM"
  ],
  "abstract": "In this paper we study $k$-noncrossing matchings. A $k$-noncrossing matching is a labeled graph with vertex set $\\{1,...,2n\\}$ arranged in increasing order in a horizontal line and vertex-degree 1. The $n$ arcs are drawn in the upper halfplane subject to the condition that there exist no $k$ arcs that mutually intersect. We derive: (a) for arbitrary $k$, an asymptotic approximation of the exponential generating function of $k$-noncrossing matchings $F_k(z)$. (b) the asymptotic formula for the number of $k$-noncrossing matchings $f_{k}(n) \\sim c_k n^{-((k-1)^2+(k-1)/2)} (2(k-1))^{2n}$ for some $c_k>0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-06T12:35:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16"
    ],
    "keywords": [
      "noncrossing matching",
      "asymptotic analysis",
      "upper halfplane subject",
      "asymptotic formula",
      "vertex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.0848J"
    }
  }
}