{
  "id": "math/0310461",
  "version": "v1",
  "published": "2003-10-29T15:16:37.000Z",
  "updated": "2003-10-29T15:16:37.000Z",
  "title": "A uniformly distributed parameter on a class of lattice paths",
  "authors": [
    "David Callan"
  ],
  "comment": "LateX 8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let G_n denote the set of lattice paths from (0,0) to (n,n) with steps of the form (i,j) where i and j are nonnegative integers, not both 0. Let D_n denote the set of paths in G_n with steps restricted to (1,0), (0,1), (1,1), so-called Delannoy paths. Stanley has shown that | G_n | = 2^(n-1) | D_n | and Sulanke has given a bijective proof. Here we give a simple parameter on G_n that is uniformly distributed over the 2^(n-1) subsets of [n-1] = {1,2,...,n-1} and takes the value [n-1] precisely on the Delannoy paths.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-10-29T15:16:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15"
    ],
    "keywords": [
      "lattice paths",
      "uniformly distributed parameter",
      "delannoy paths",
      "simple parameter",
      "nonnegative integers"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10461C"
    }
  }
}