{
  "id": "1006.5706",
  "version": "v1",
  "published": "2010-06-29T19:20:11.000Z",
  "updated": "2010-06-29T19:20:11.000Z",
  "title": "Partitions, pairs of trees and Catalan numbers",
  "authors": [
    "Eliana Zoque"
  ],
  "comment": "13 pages. This paper follows the work done in arXiv0912.4983",
  "categories": [
    "math.CO"
  ],
  "abstract": "In \"Square partitions and Catalan numbers\" (arXiv0912.4983), Bennett et al. presented a recursive algorithm to create a family of partitions from one or several partitions. They were mainly interested in the cases when we begin with a single square partition or with several partitions with only one part. The cardinalities of those families of partitions are the Catalan and ballot numbers, respectively. In this paper we present a closed description for those families. We also present bijections between those sets of partitions and sets of trees and forests enumerated by the Catalan an ballot numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-29T19:20:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "05A19"
    ],
    "keywords": [
      "catalan numbers",
      "ballot numbers",
      "single square partition",
      "recursive algorithm",
      "cardinalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.5706Z"
    }
  }
}