{
  "id": "1505.01961",
  "version": "v1",
  "published": "2015-05-08T09:09:34.000Z",
  "updated": "2015-05-08T09:09:34.000Z",
  "title": "Some results on Dyck paths and Motzkin paths",
  "authors": [
    "Stefano Capparelli",
    "Alberto Del Fra"
  ],
  "comment": "22 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce an equivalence relation on the set of Dyck paths and some operations on them. We determine a formula for the cardinality of those equivalence classes and use this information to obtain a combinatorial formula for the number of Dyck and Motzkin paths of a fixed length.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-08T09:09:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A99"
    ],
    "keywords": [
      "motzkin paths",
      "dyck paths",
      "equivalence relation",
      "combinatorial formula",
      "equivalence classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}