{
  "id": "0801.2412",
  "version": "v2",
  "published": "2008-01-16T01:00:55.000Z",
  "updated": "2008-05-31T18:44:46.000Z",
  "title": "Generalized permutation patterns -- a short survey",
  "authors": [
    "Einar Steingrimsson"
  ],
  "comment": "11 pages. Added a section on asymptotics (Section 8), added more examples of barred patterns equal to generalized patterns (Section 7) and made a few other minor additions. To appear in ``Permutation Patterns, St Andrews 2007'', S.A. Linton, N. Ruskuc, V. Vatter (eds.), LMS Lecture Note Series, Cambridge University Press",
  "categories": [
    "math.CO"
  ],
  "abstract": "An occurrence of a classical pattern p in a permutation \\pi is a subsequence of \\pi whose letters are in the same relative order (of size) as those in p. In an occurrence of a generalized pattern, some letters of that subsequence may be required to be adjacent in the permutation. Subsets of permutations characterized by the avoidance--or the prescribed number of occurrences--of generalized patterns exhibit connections to an enormous variety of other combinatorial structures, some of them apparently deep. We give a short overview of the state of the art for generalized patterns.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-05-31T18:44:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05E15"
    ],
    "keywords": [
      "generalized permutation patterns",
      "short survey",
      "subsequence",
      "occurrences-of generalized patterns",
      "combinatorial structures"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.2412S"
    }
  }
}