{
  "id": "0810.1422",
  "version": "v2",
  "published": "2008-10-08T12:49:16.000Z",
  "updated": "2009-03-11T11:29:19.000Z",
  "title": "A bijection between noncrossing and nonnesting partitions of types A and B",
  "authors": [
    "Ricardo Mamede"
  ],
  "comment": "11 pages, 11 figures. Inverse map described. Minor changes to correct typos and clarify content",
  "journal": "Contributions to Discrete Mathematics , Vol 6, No 2 (2011), 70-90",
  "categories": [
    "math.CO"
  ],
  "abstract": "The total number of noncrossing partitions of type $\\Psi$ is the $n$th Catalan number $\\frac{1}{n+1}\\binom{2n}{n}$ when $\\Psi=A_{n-1}$, and the binomial $\\binom{2n}{n}$ when $\\Psi=B_n$, and these numbers coincide with the correspondent number of nonnesting partitions. For type A, there are several bijective proofs of this equality, being the intuitive map that locally converts each crossing to a nesting one of them. In this paper we present a bijection between nonnesting and noncrossing partitions of types A and B that generalizes the type A bijection that locally converts each crossing to a nesting.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-03-11T11:29:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonnesting partitions",
      "noncrossing partitions",
      "locally converts",
      "th catalan number",
      "correspondent number"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.1422M"
    }
  }
}