{
  "id": "2011.09546",
  "version": "v1",
  "published": "2020-11-18T21:02:18.000Z",
  "updated": "2020-11-18T21:02:18.000Z",
  "title": "Combinatorial proof of the log-convexity for the derangements in the Coxeter groups",
  "authors": [
    "Hiranya Kishore Dey",
    "Subhajit Ghosh"
  ],
  "comment": "21 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We provide the combinatorial proofs of the log-convexity for the derangement numbers in the symmetric group $\\mathfrak{S}_n$, hyperoctahedral group $\\mathfrak{B}_n$, and the demihyperoctahedral group $\\mathfrak{D}_n$. We also show that the sequences of the even and odd derangement numbers in $\\mathfrak{S}_n$ and $\\mathfrak{B}_n$ are log-convex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-18T21:02:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A20",
      "05A05"
    ],
    "keywords": [
      "combinatorial proof",
      "coxeter groups",
      "log-convexity",
      "odd derangement numbers",
      "symmetric group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}