{
  "id": "1407.3516",
  "version": "v1",
  "published": "2014-07-14T00:14:39.000Z",
  "updated": "2014-07-14T00:14:39.000Z",
  "title": "Chebyshev Polynomials and Statistics on a New Collection of Words in the Catalan Family",
  "authors": [
    "Toufik Mansour",
    "Mark Shattuck"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Recently, a new class of words, denoted by L_n, was shown to be in bijection with a subset of the Dyck paths of length 2n having cardinality given by the (n-1)-st Catalan number. Here, we consider statistics on L_n recording the number of occurrences of a letter i. In the cases i = 0 and i = 1, we are able to determine explicit expressions for the number of members of L_n containing a given number of zeros or ones, which generalizes the prior result. To do so, we make use of recurrences to derive a functional equation satisfied by the generating function, which we solve by a new method employing Chebyshev polynomials. Recurrences and generating function formulas are also provided in the case of general i.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-14T00:14:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A05",
      "11B37"
    ],
    "keywords": [
      "catalan family",
      "statistics",
      "collection",
      "determine explicit expressions",
      "method employing chebyshev polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.3516M"
    }
  }
}