{
  "id": "1908.00701",
  "version": "v1",
  "published": "2019-08-02T04:27:46.000Z",
  "updated": "2019-08-02T04:27:46.000Z",
  "title": "A new refinement of Euler numbers on counting alternating permutations",
  "authors": [
    "Masato Kobayashi"
  ],
  "comment": "11 pages, 4 tables",
  "categories": [
    "math.CO"
  ],
  "abstract": "In mathematics, we often encounter surprising interactions with two topics from seemingly different areas. At a crossroads of calculus and combinatorics, the generating function of secant and tangent numbers (Euler numbers) provides enumeration of alternating permutations. In this article, we present a new refinement of Euler numbers to answer the combinatorial question on some particular relation of Euler numbers proved by Heneghan-Petersen, Power series for up-down min-max permutations, College Math. Journal, Vol. 45, No. 2 (2014), 83-91.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-02T04:27:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "11B68"
    ],
    "keywords": [
      "euler numbers",
      "counting alternating permutations",
      "refinement",
      "up-down min-max permutations",
      "college math"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}