{
  "id": "math/0606169",
  "version": "v2",
  "published": "2006-06-07T21:04:49.000Z",
  "updated": "2007-09-27T07:02:48.000Z",
  "title": "Polynomials, meanders, and paths in the lattice of noncrossing partitions",
  "authors": [
    "David Savitt"
  ],
  "comment": "24 pages, 7 figures. To appear, Transactions of the A.M.S. Revised based on referee report; final section added",
  "categories": [
    "math.CO"
  ],
  "abstract": "For every polynomial f of degree n with no double roots, there is an associated family C(f) of harmonic algebraic curves, fibred over the circle, with at most n-1 singular fibres. We study the combinatorial topology of C(f) in the generic case when there are exactly n-1 singular fibres. In this case, the topology of C(f) is determined by the data of an n-tuple of noncrossing matchings on the set {0,1,...,2n-1} with certain extra properties. We prove that there are 2(2n)^{n-2} such n-tuples, and that all of them arise from the topology of C(f) for some polynomial f.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-09-27T07:02:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C99",
      "05A18"
    ],
    "keywords": [
      "noncrossing partitions",
      "polynomial",
      "singular fibres",
      "harmonic algebraic curves",
      "extra properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6169S"
    }
  }
}