{
  "id": "1010.4847",
  "version": "v1",
  "published": "2010-10-23T05:58:36.000Z",
  "updated": "2010-10-23T05:58:36.000Z",
  "title": "Some simple bijections involving lattice walks and ballot sequences",
  "authors": [
    "Marc A. A. Van Leeuwen"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this note we observe that a bijection related to Littelmann's root operators (for type $A_1$) transparently explains the well known enumeration by length of walks on $\\N$ (left factors of Dyck paths), as well as some other enumerative coincidences. We indicate a relation with bijective solutions of Bertrand's ballot problem: those can be mechanically transformed into bijective proofs of the mentioned enumeration formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-23T05:58:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ballot sequences",
      "lattice walks",
      "simple bijections",
      "littelmanns root operators",
      "bertrands ballot problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.4847V"
    }
  }
}