{
  "id": "1301.7714",
  "version": "v1",
  "published": "2013-01-31T18:29:15.000Z",
  "updated": "2013-01-31T18:29:15.000Z",
  "title": "Even and Odd Pairs of Lattice Paths with Multiple Intersections",
  "authors": [
    "Ira M. Gessel",
    "Walter Shur"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let M(n,k,r,s) be the number of ordered paths in the plane, with unit steps E or N, that intersect k times in which the first path ends at the point (r,n-r) and the second path ends at the point (s,n-s). Our main object of study in this paper is the sum of the numbers M(n,k,r,s) over r and s where r+s is fixed. We consider even and odd values of r+s separately, and we derive a simpler formula for M(n,k,r,s) than previously appeared in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-31T18:29:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15"
    ],
    "keywords": [
      "lattice paths",
      "multiple intersections",
      "odd pairs",
      "first path ends",
      "second path ends"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.7714G"
    }
  }
}