{
  "id": "2505.05651",
  "version": "v1",
  "published": "2025-05-08T21:16:22.000Z",
  "updated": "2025-05-08T21:16:22.000Z",
  "title": "Characterizing avoidance in cycles via vincular patterns",
  "authors": [
    "Robert P. Laudone"
  ],
  "comment": "16 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that cyclic permutations avoiding $321$ are precisely those permutations whose image under the fundamental bijection avoid a set of vincular patterns. We do this by using pattern functions and arrow patterns, in combination with the characterization of $321$ avoidance in terms of equality of the upper bound of the Daiconis-Graham inequalities. We then explore some consequences of this result, including upper and lower bound results on the growth rate of $321$ avoiding cycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-08T21:16:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15"
    ],
    "keywords": [
      "vincular patterns",
      "characterizing avoidance",
      "fundamental bijection avoid",
      "lower bound results",
      "cyclic permutations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}