{
  "id": "math/0401217",
  "version": "v1",
  "published": "2004-01-18T07:00:06.000Z",
  "updated": "2004-01-18T07:00:06.000Z",
  "title": "Involutions Restricted by 3412, Continued Fractions, and Chebyshev Polynomials",
  "authors": [
    "Eric Egge",
    "Toufik Mansour"
  ],
  "comment": "30 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study generating functions for the number of involutions, even involutions, and odd involutions in $S_n$ subject to two restrictions. One restriction is that the involution avoid 3412 or contain 3412 exactly once. The other restriction is that the involution avoid another pattern $\\tau$ or contain $\\tau$ exactly once. In many cases we express these generating functions in terms of Chebyshev polynomials of the second kind.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-01-18T07:00:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15",
      "30B70",
      "42C05"
    ],
    "keywords": [
      "chebyshev polynomials",
      "continued fractions",
      "involutions",
      "involution avoid",
      "restriction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......1217E"
    }
  }
}