{
  "id": "1509.07832",
  "version": "v1",
  "published": "2015-09-25T18:57:28.000Z",
  "updated": "2015-09-25T18:57:28.000Z",
  "title": "New Formulas for Dyck Paths in a Rectangle",
  "authors": [
    "Jose Eduardo Blazek"
  ],
  "journal": "Combinatorics on Words, Volume 9304 of the series Lecture Notes in Computer Science, pp 85-96, Date: 27 August 2015, Springer",
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider the problem of counting the set of $\\mathscr{D}_{a,b}$ of Dyck paths inscribed in a rectangle of size $a\\times b$. They are a natural generalization of the classical Dyck words enumerated by the Catalan numbers. By using Ferrers diagrams associated to Dyck paths, we derive formulas for the enumeration of $\\mathscr{D}_{a,b}$ with $a$ and $b$ non relatively prime, in terms of Catalan numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-25T18:57:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dyck paths",
      "catalan numbers",
      "non relatively prime",
      "natural generalization",
      "classical dyck words"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150907832B"
    }
  }
}