{
  "id": "1812.10738",
  "version": "v1",
  "published": "2018-12-27T15:02:22.000Z",
  "updated": "2018-12-27T15:02:22.000Z",
  "title": "Revisiting pattern avoidance and quasisymmetric functions",
  "authors": [
    "Jonathan Bloom",
    "Bruce Sagan"
  ],
  "comment": "25 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let S_n be the nth symmetric group. Given a set of permutations Pi we denote by S_n(Pi) the set of permutations in S_n which avoid Pi in the sense of pattern avoidance. Consider the generating function Q_n(Pi) = sum_pi F_{Des pi} where the sum is over all pi in S_n(Pi) and F_{Des pi} is the fundamental quasisymmetric function corresponding to the descent set of pi. Hamaker, Pawlowski, and Sagan introduced Q_n(Pi) and studied its properties, in particular, finding criteria for when this quasisymmetric function is symmetric or even Schur nonnegative for all n >= 0. The purpose of this paper is to continue their investigation answering some of their questions, proving one of their conjectures, as well as considering other natural questions about Q_n(Pi). In particular we look at Pi of small cardinality, superstandard hooks, partial shuffles, Knuth classes, and a stability property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-27T15:02:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "05A05"
    ],
    "keywords": [
      "revisiting pattern avoidance",
      "nth symmetric group",
      "fundamental quasisymmetric function",
      "descent set",
      "stability property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}