{
  "id": "2005.11312",
  "version": "v1",
  "published": "2020-05-22T17:57:07.000Z",
  "updated": "2020-05-22T17:57:07.000Z",
  "title": "A simple bijective proof of a familiar derangement recurrence",
  "authors": [
    "Sergi Elizalde"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "It is well known that the derangement numbers $d_n$, which count permutations of length $n$ with no fixed points, satisfy the recurrence $d_n=nd_{n-1}+(-1)^n$ for $n\\ge1$. Combinatorial proofs of this formula have been given by Remmel, Wilf, D\\'esarm\\'enien and Benjamin--Ornstein. Here we present yet another, arguably simpler, bijective proof.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-22T17:57:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A19"
    ],
    "keywords": [
      "familiar derangement recurrence",
      "simple bijective proof",
      "derangement numbers",
      "combinatorial proofs",
      "count permutations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}