{
  "id": "0806.0424",
  "version": "v1",
  "published": "2008-06-03T02:55:17.000Z",
  "updated": "2008-06-03T02:55:17.000Z",
  "title": "Some Enumerations for Parking Functions",
  "authors": [
    "Po-Yi Huang",
    "Jun Ma",
    "Jean Yeh"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, let $\\mathcal{P}_{n,n+k;\\leq n+k}$ (resp. $\\mathcal{P}_{n;\\leq s}$) denote the set of parking functions $\\alpha=(a_1,...,a_n)$ of length $n$ with $n+k$ (respe. $n$)parking spaces satisfying $1\\leq a_i\\leq n+k$ (resp. $1\\leq a_i\\leq s$) for all $i$. Let $p_{n,n+k;\\leq n+k}=|\\mathcal{P}_{n,n+k;\\leq n+k}|$ and $p_{n;\\leq s}=|\\mathcal{P}_{n;\\leq s}|$. Let $\\mathcal{P}_{n;\\leq s}^l$ denote the set of parking functions $\\alpha=(a_1,...,a_n)\\in\\mathcal{P}_{n;\\leq s}$ such that $a_1=l$ and $p_{n;\\leq s}^l=|\\mathcal{P}_{n;\\leq s}^l|$. We derive some formulas and recurrence relations for the sequences $p_{n,n+k;\\leq n+k}$, $p_{n;\\leq s}$ and $p_{n;\\leq s}^l$ and give the generating functions for these sequences. We also study the asymptotic behavior for these sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-06-03T02:55:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parking functions",
      "enumerations",
      "recurrence relations",
      "asymptotic behavior",
      "parking spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.0424H"
    }
  }
}