{
  "annotation_id": "189b2862-c290-4273-9672-bd1e6fd09cff",
  "date_created": "2026-02-17T05:53:12.522000Z",
  "date_modified": "2026-02-17T05:53:12.522000Z",
  "file_hash": "aa424ec9cafa9b71dad5aad9fd44cd088a843902b71e5be5f23c5f554db3f133",
  "private": false,
  "record": {
    "abstract": "In this work, we present a series of bijections that reveal the deep connections between the concepts of tree records, the girth of a connected endofunction, and the genesis sequence, the first sequence in the OEIS. We use these results to derive the generating functions for the tree and forest record numbers, expressing them in terms of the Cayley\u0027s tree function. Finally, we provide a new proof for Cayley\u0027s forest formula.",
    "arxiv_id": "2601.07938",
    "authors": [
      "Enrica Duchi",
      "Adri\u00e1n Lillo",
      "Pablo Puerto",
      "Mercedes Rosas",
      "Stefan Trandafir"
    ],
    "categories": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "title": "The genesis sequence, tree records and endofunctions",
    "url": "https://arxiv.org/abs/2601.07938",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b4c52b59-b12f-49d8-944c-0d338457d481",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}