{
  "id": "1211.7110",
  "version": "v1",
  "published": "2012-11-29T22:38:57.000Z",
  "updated": "2012-11-29T22:38:57.000Z",
  "title": "Algorithms for discovering and proving theorems about permutation patterns",
  "authors": [
    "Hjalti Magnusson",
    "Henning Ulfarsson"
  ],
  "comment": "13 pages, 3 figures",
  "categories": [
    "math.CO",
    "cs.DM",
    "cs.DS",
    "cs.MS"
  ],
  "abstract": "We present an algorithm, called BiSC, that describes the patterns avoided by a given set of permutations. It automatically conjectures the statements of known theorems such as the descriptions of stack-sortable (Knuth 1975) and West-2-stack-sortable permutations (West 1990), smooth (Lakshmibai and Sandhya 1990) and forest-like permutations (Bousquet-Melou and Butler 2007), and simsun permutations (Branden and Claesson 2011). The algorithm has also been used to discover new theorems and conjectures related to Young tableaux, Wilf-equivalences and sorting devices. We further give algorithms to prove a complete description of preimages of pattern classes under certain sorting devices. These generalize an algorithm of Claesson and Ulfarsson (2012) and allow us to prove a linear time algorithm for finding occurrences of the pattern 4312.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-29T22:38:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05"
    ],
    "keywords": [
      "permutation patterns",
      "proving theorems",
      "sorting devices",
      "linear time algorithm",
      "discovering"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.7110M"
    }
  }
}