{
  "id": "1602.09132",
  "version": "v1",
  "published": "2016-02-29T20:45:48.000Z",
  "updated": "2016-02-29T20:45:48.000Z",
  "title": "Continuous Analogues for the Binomial Coefficients and the Catalan Numbers",
  "authors": [
    "Leonardo Cano",
    "Rafael Diaz"
  ],
  "categories": [
    "math.CO",
    "math-ph",
    "math.DG",
    "math.MP",
    "math.PR"
  ],
  "abstract": "Using techniques from the theories of convex polytopes, lattice paths, and indirect influences on directed manifolds, we construct continuous analogues for the binomial coefficients and the Catalan numbers. Our approach for constructing these analogues can be applied to a wide variety of combinatorial sequences. As an application we develop a continuous analogue for the binomial distribution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-29T20:45:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "catalan numbers",
      "binomial coefficients",
      "convex polytopes",
      "construct continuous analogues",
      "wide variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160209132C"
    }
  }
}