{
  "id": "0909.5459",
  "version": "v1",
  "published": "2009-09-29T22:28:05.000Z",
  "updated": "2009-09-29T22:28:05.000Z",
  "title": "On the Generalized Climbing Stairs Problem",
  "authors": [
    "Edray Herber Goins",
    "Talitha M. Washington"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\mathcal S$ be a subset of the positive integers, and $M$ be a positive integer. Mohammad K. Azarian, inspired by work of Tony Colledge, considered the number of ways to climb a staircase containing $n$ stairs using \"step-sizes\" $s \\in \\mathcal S$ and multiplicities at most $M$. In this exposition, we find a solution via generating functions, i.e., an expression which counts the number of partitions $n = \\sum_{s \\in \\mathcal S} m_s s$ satisfying $0 \\leq m_s \\leq M$. We then use this result to answer a series of questions posed by Azarian, thereby showing a link with ten sequences listed in the On-Line Encyclopedia of Integer Sequences. We conclude by posing open questions which seek to count the number of compositions of $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-29T22:28:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A17"
    ],
    "keywords": [
      "generalized climbing stairs problem",
      "positive integer",
      "tony colledge",
      "on-line encyclopedia",
      "integer sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.5459H"
    }
  }
}