{
  "id": "1303.3767",
  "version": "v1",
  "published": "2013-03-15T13:22:23.000Z",
  "updated": "2013-03-15T13:22:23.000Z",
  "title": "Algebraic and Affine Pattern Avoidance",
  "authors": [
    "Tom Denton"
  ],
  "comment": "Modified from a chapter of the author's dissertation, currently submitted for review for publication",
  "journal": "S\\'eminaire Lotharingien de Combinatoire, B69c (2013), 40 pp",
  "categories": [
    "math.CO"
  ],
  "abstract": "We investigate various connections between the 0-Hecke monoid, Catalan monoid, and pattern avoidance in permutations, providing new tools for approaching pattern avoidance in an algebraic framework. In particular, we characterize containment of a class of `long' patterns as equivalent to the existence of a corresponding factorization. We then generalize some of our constructions to the affine setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-15T13:22:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine pattern avoidance",
      "catalan monoid",
      "algebraic framework",
      "connections",
      "permutations"
    ],
    "tags": [
      "dissertation",
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.3767D"
    }
  }
}