{
  "id": "1104.4584",
  "version": "v3",
  "published": "2011-04-23T18:51:51.000Z",
  "updated": "2012-10-19T19:30:45.000Z",
  "title": "Enumeration formulas for generalized q-Euler numbers",
  "authors": [
    "Jang Soo Kim"
  ],
  "comment": "21 pages, 12 figures",
  "journal": "Advances in Applied Mathematics 49 (2012) 326-350",
  "categories": [
    "math.CO"
  ],
  "abstract": "We find an enumeration formula for a $(t,q)$-Euler number which is a generalization of the $q$-Euler number introduced by Han, Randrianarivony, and Zeng. We also give a combinatorial expression for the $(t,q)$-Euler number and find another formula when $t=\\pm q^r$ for any integer $r$. Special cases of our latter formula include the formula of the $q$-Euler number recently found by Josuat-Verg\\`es and Touchard-Riordan's formula.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-10-19T19:30:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19",
      "05A30",
      "05E35"
    ],
    "keywords": [
      "generalized q-euler numbers",
      "enumeration formula",
      "touchard-riordans formula",
      "special cases",
      "combinatorial expression"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.4584K"
    }
  }
}