{
  "id": "2011.01577",
  "version": "v1",
  "published": "2020-11-03T09:05:39.000Z",
  "updated": "2020-11-03T09:05:39.000Z",
  "title": "Some identities involving derangement polynomials and numbers",
  "authors": [
    "Taekyun Kim",
    "Dae San Kim",
    "Lee-Chae Jang",
    "Hyunseok Lee"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "The problem of counting derangements was initiated by Pierre Remonde de Motmort in 1708. A derangement is a permutation that has no fixed points and the derangement number Dn is the number of fixed point free permutations on an n element set. Furthermore, the derangement polynomials are natural extensions of the derangement numbers. In this paper, we study the derangement polynomials and numbers, their connections with cosine-derangement polynomials and sine-derangement polynomials and their applications to moments of some variants of gamma random variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-03T09:05:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B73",
      "11B83",
      "65C50"
    ],
    "keywords": [
      "identities",
      "gamma random variables",
      "fixed point free permutations",
      "derangement number dn",
      "natural extensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}