{
  "id": "math/0603285",
  "version": "v1",
  "published": "2006-03-13T09:49:56.000Z",
  "updated": "2006-03-13T09:49:56.000Z",
  "title": "Enumeration of 3-letter patterns in compositions",
  "authors": [
    "S. Heubach",
    "T. Mansour"
  ],
  "comment": "20 pages, 1 figure; accepted for the Proceedings of the 2005 Integer Conference",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let A be any set of positive integers and n a positive integer. A composition of n with parts in A is an ordered collection of one or more elements in A whose sum is n. We derive generating functions for the number of compositions of n with m parts in A that have r occurrences of 3-letter patterns formed by two (adjacent) instances of levels, rises and drops. We also derive asymptotics for the number of compositions of n that avoid a given pattern. Finally, we obtain the generating function for the number of k-ary words of length m which contain a prescribed number of occurrences of a given pattern as a special case of our results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-13T09:49:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15",
      "05A16"
    ],
    "keywords": [
      "composition",
      "enumeration",
      "positive integer",
      "generating function",
      "special case"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3285H"
    }
  }
}