{
  "id": "1812.01682",
  "version": "v1",
  "published": "2018-12-04T21:05:36.000Z",
  "updated": "2018-12-04T21:05:36.000Z",
  "title": "On pattern-avoiding Fishburn permutations",
  "authors": [
    "Juan B. Gil",
    "Michael D. Weiner"
  ],
  "comment": "15 pages, 5 tables",
  "categories": [
    "math.CO"
  ],
  "abstract": "The class of permutations that avoid the bivincular pattern (231, {1}, {1}) is known to be enumerated by the Fishburn numbers. In this paper, we call them Fishburn permutations and study their pattern avoidance. For classical patterns of length 3, we give a complete enumerative picture for regular and indecomposable Fishburn permutations. For patterns of length 4, we focus on a Wilf equivalence class of Fishburn permutations that are enumerated by the Catalan numbers. In addition, we also discuss a class enumerated by the binomial transform of the Catalan numbers and give conjectures for other equivalence classes of pattern-avoiding Fishburn permutations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-04T21:05:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05"
    ],
    "keywords": [
      "pattern-avoiding fishburn permutations",
      "catalan numbers",
      "wilf equivalence class",
      "binomial transform",
      "complete enumerative picture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}