{
  "abstract": "A $D$-diffsequence is a sequence of integers $x_1 < \\dots < x_k$ such that $x_{i+1} -x_i \\in D$ for $1 \\le i \\le k-1$. The set $D$ is called $r$-accessible if every $r$-coloring of the positive integers contains arbitrarily long monochromatic $D$-diffsequences. This note proves that the set of Fibonacci numbers is not 3-accessible, resolving an open problem of Landman and Robertson from 2007.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33744",
  "author_total": 1,
  "authors": [
    {
      "name": "William J. Wesley"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f3hgyxdh5x1vt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33744",
  "fulltext_url": null,
  "id": "f3hgyxdh5x1vt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33744",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7214765984",
  "pdf_url": "https://arxiv.org/pdf/2609.33744",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f3hgyxdh5x1vt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33744",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33744"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Fibonacci numbers are not 3-accessible",
  "title_text": "The Fibonacci numbers are not 3-accessible",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/f3hgyxdh5x1vt",
  "venue": "arXiv",
  "versions": []
}