{
  "id": "1504.07265",
  "version": "v1",
  "published": "2015-04-27T20:12:24.000Z",
  "updated": "2015-04-27T20:12:24.000Z",
  "title": "A survey of consecutive patterns in permutations",
  "authors": [
    "Sergi Elizalde"
  ],
  "comment": "Chapter for upcoming IMA volume Recent Trends in Combinatorics",
  "categories": [
    "math.CO"
  ],
  "abstract": "A consecutive pattern in a permutation $\\pi$ is another permutation $\\sigma$ determined by the relative order of a subsequence of contiguous entries of $\\pi$. Traditional notions such as descents, runs and peaks can be viewed as particular examples of consecutive patterns in permutations, but the systematic study of these patterns has flourished in the last 15 years, during which a variety of different techniques have been used. We survey some interesting developments in the subject, focusing on exact and asymptotic enumeration results, the classification of consecutive patterns into equivalence classes, and their applications to the study of one-dimensional dynamical systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-27T20:12:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15",
      "05A16",
      "06A07",
      "05E05",
      "05A19",
      "37E05",
      "37E15",
      "37M10"
    ],
    "keywords": [
      "consecutive pattern",
      "permutation",
      "asymptotic enumeration results",
      "one-dimensional dynamical systems",
      "traditional notions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150407265E"
    }
  }
}