{
  "id": "1102.5568",
  "version": "v1",
  "published": "2011-02-28T01:41:42.000Z",
  "updated": "2011-02-28T01:41:42.000Z",
  "title": "Counting (3+1) - Avoiding permutations",
  "authors": [
    "M. D. Atkinson",
    "Bruce E. Sagan",
    "Vincent Vatter"
  ],
  "comment": "17 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A poset is {\\it $(\\3+\\1)$-free} if it contains no induced subposet isomorphic to the disjoint union of a 3-element chain and a 1-element chain. These posets are of interest because of their connection with interval orders and their appearance in the $(\\3+\\1)$-free Conjecture of Stanley and Stembridge. The dimension 2 posets $P$ are exactly the ones which have an associated permutation $\\pi$ where $i\\prec j$ in $P$ if and only if $i<j$ as integers and $i$ comes before $j$ in the one-line notation of $\\pi$. So we say that a permutation $\\pi$ is {\\it $(\\3+\\1)$-free} or {\\it $(\\3+\\1)$-avoiding} if its poset is $(\\3+\\1)$-free. This is equivalent to $\\pi$ avoiding the permutations 2341 and 4123 in the language of pattern avoidance. We give a complete structural characterization of such permutations. This permits us to find their generating function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-28T01:41:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15"
    ],
    "keywords": [
      "avoiding permutations",
      "complete structural characterization",
      "interval orders",
      "free conjecture",
      "induced subposet isomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.5568A"
    }
  }
}