{
  "id": "2506.15800",
  "version": "v1",
  "published": "2025-06-18T18:36:03.000Z",
  "updated": "2025-06-18T18:36:03.000Z",
  "title": "Odd-indexed Fibonacci numbers via pattern-avoiding permutations",
  "authors": [
    "Juan B. Gil",
    "Felix H. Xu",
    "William Y. Zhu"
  ],
  "comment": "16 pages. Accepted for publication",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we consider several combinatorial problems whose enumeration leads to the odd-indexed Fibonacci numbers, including certain types of Dyck paths, block fountains, directed column-convex polyominoes, and set partitions with no crossings and no nestings. Our goal is to provide bijective maps to pattern-avoiding permutations and derive generating functions that track certain positional statistics at the permutation level.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-06-18T18:36:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19",
      "05A05",
      "05A15"
    ],
    "keywords": [
      "odd-indexed fibonacci numbers",
      "pattern-avoiding permutations",
      "permutation level",
      "directed column-convex polyominoes",
      "combinatorial problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}