{
  "id": "0806.0435",
  "version": "v2",
  "published": "2008-06-03T05:10:48.000Z",
  "updated": "2008-06-05T02:05:14.000Z",
  "title": "Enumerations for Permutations by Circular Peak Sets",
  "authors": [
    "Pierre Bouchard",
    "Hungyung Chang",
    "Jun Ma",
    "Jean Yeh"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The circular peak set of a permutation $\\sigma$ is the set $\\{\\sigma(i)\\mid \\sigma(i-1)<\\sigma(i)>\\sigma(i+1)\\}$. In this paper, we focus on the enumeration problems for permutations by circular peak sets. Let $cp_n(S)$ denote the number of the permutations of order $n$ which have the circular peak set $S$. For the case with $|S|=0,1,2$, we derive the explicit formulas for $cp_n(S)$. We also obtain some recurrence relations for the sequence $cp_n(S)$ and give the formula for $cp_n(S)$ in the general case.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-06-05T02:05:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "circular peak set",
      "permutation",
      "recurrence relations",
      "general case",
      "enumeration problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.0435B"
    }
  }
}