{
  "id": "2408.06959",
  "version": "v1",
  "published": "2024-08-13T15:15:58.000Z",
  "updated": "2024-08-13T15:15:58.000Z",
  "title": "Self-modified difference ascent sequences",
  "authors": [
    "Giulio Cerbai",
    "Anders Claesson",
    "Bruce E. Sagan"
  ],
  "comment": "22 pages, 2 tables",
  "categories": [
    "math.CO"
  ],
  "abstract": "Ascent sequences play a key role in the combinatorics of Fishburn structures. Difference ascent sequences are a natural generalization obtained by replacing ascents with $d$-ascents. We have recently extended the so-called hat map to difference ascent sequences, and self-modified difference ascent sequences are the fixed points under this map. We characterize self-modified difference ascent sequences and enumerate them in terms of certain generalized Fibonacci polynomials. Furthermore, we describe the corresponding subset of $d$-Fishburn permutations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-13T15:15:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19",
      "05A05"
    ],
    "keywords": [
      "ascent sequences play",
      "characterize self-modified difference ascent sequences",
      "fishburn structures",
      "natural generalization",
      "hat map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}