{
  "id": "1404.1708",
  "version": "v2",
  "published": "2014-04-07T09:39:52.000Z",
  "updated": "2014-05-23T15:21:25.000Z",
  "title": "On a new collection of words in the Catalan family",
  "authors": [
    "Christian Stump"
  ],
  "comment": "5 pages, v2: title changed + fixed typos; final version",
  "journal": "Journal of Integer Sequences, Vol. 17 (2014), Article 14.7.1",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this note, we provide a bijection between a new collection of words on nonnegative integers of length n and Dyck paths of length 2n-2, thus proving that this collection belongs to the Catalan family. The surprising key step in this bijection is the zeta map which is an important map in the study of q,t-Catalan numbers. Finally we discuss an alternative approach to this new collection of words using two statistics on planted trees that turn out to be closely related to the Tutte polynomial on the Catalan matroid.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-23T15:21:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19"
    ],
    "keywords": [
      "catalan family",
      "catalan matroid",
      "tutte polynomial",
      "t-catalan numbers",
      "important map"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.1708S"
    }
  }
}