{
  "id": "math/0511248",
  "version": "v1",
  "published": "2005-11-10T00:41:50.000Z",
  "updated": "2005-11-10T00:41:50.000Z",
  "title": "Harmonic algebraic curves and noncrossing partitions",
  "authors": [
    "Jeremy Martin",
    "David Savitt",
    "Ted Singer"
  ],
  "comment": "18 pages, 14 color figures; uses epsfig and psfrag",
  "journal": "Discrete Comput. Geom. 37, no. 2 (2007), 267-286",
  "categories": [
    "math.CO",
    "math.AG",
    "math.CV"
  ],
  "abstract": "Motivated by Gauss's first proof of the Fundamental Theorem of Algebra, we study the topology of harmonic algebraic curves. By the maximum principle, a harmonic curve has no bounded components; its topology is determined by the combinatorial data of a noncrossing matching. Similarly, every complex polynomial gives rise to a related combinatorial object that we call a basketball, consisting of a pair of noncrossing matchings satisfying one additional constraint. We prove that every noncrossing matching arises from some harmonic curve, and deduce from this that every basketball arises from some polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-11-10T00:41:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14P25",
      "26C10",
      "30C15",
      "05A18",
      "52C99"
    ],
    "keywords": [
      "harmonic algebraic curves",
      "noncrossing partitions",
      "harmonic curve",
      "gausss first proof",
      "noncrossing matching"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....11248M"
    }
  }
}