{
  "id": "math/0309269",
  "version": "v1",
  "published": "2003-09-17T05:51:20.000Z",
  "updated": "2003-09-17T05:51:20.000Z",
  "title": "Finite automata and pattern avoidance in words",
  "authors": [
    "Petter Brändén",
    "Toufik Mansour"
  ],
  "comment": "17 pages, 1 figures, 2 tables",
  "categories": [
    "math.CO"
  ],
  "abstract": "We say that a word $w$ on a totally ordered alphabet avoids the word $v$ if there are no subsequences in $w$ order-equivalent to $v$. In this paper we suggest a new approach to the enumeration of words on at most $k$ letters avoiding a given pattern. By studying an automaton which for fixed $k$ generates the words avoiding a given pattern we derive several previously known results for these kind of problems, as well as many new. In particular, we give a simple proof of the formula \\cite{Reg1998} for exact asymptotics for the number of words on $k$ letters of length $n$ that avoids the pattern $12...(\\ell+1)$. Moreover, we give the first combinatorial proof of the exact formula \\cite{Burstein} for the number of words on $k$ letters of length $n$ avoiding a three letter permutation pattern.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-09-17T05:51:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15",
      "68Q45"
    ],
    "keywords": [
      "finite automata",
      "pattern avoidance",
      "first combinatorial proof",
      "letter permutation",
      "totally ordered alphabet avoids"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......9269B"
    }
  }
}