{
  "id": "1312.2051",
  "version": "v1",
  "published": "2013-12-07T02:24:18.000Z",
  "updated": "2013-12-07T02:24:18.000Z",
  "title": "Cyclically consecutive permutation avoidance",
  "authors": [
    "Richard Ehrenborg"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give an explicit formula for the number of permutations avoiding cyclically a consecutive pattern in terms of the spectrum of the associated operator of the consecutive pattern. As an example, the number of cyclically consecutive $123$-avoiding permutations in ${\\mathfrak S}_{n}$ is given by $n!$ times the convergent series ${\\displaystyle \\sum_{k=-\\infty}^{\\infty} \\left(\\frac{\\sqrt{3}}{2\\pi(k+1/3)}\\right)^{n}}$ for $n \\geq 2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-07T02:24:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15",
      "45C05"
    ],
    "keywords": [
      "cyclically consecutive permutation avoidance",
      "explicit formula",
      "convergent series",
      "consecutive pattern",
      "associated operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.2051E"
    }
  }
}