{
  "abstract": "In 1981 Guibas and Odlyzko showed that the set $A$ of all words of a given length $n$ that avoid a given word $p$, and the set $B$ of all words of length $n$ that avoid a given word $q$, have the same cardinality iff $p$ and $q$ have the same self-border lengths. In 2024 Carrigan et. al. asked if there is a \"natural\" bijection between $A$ and $B$. This paper makes partial progress toward answering that question. We provide such a bijection by imposing additional conditions on $p$ and $q$, but we also obtain a stronger conclusion: there is a \"natural\" bijection $Φ$ from the set of all finite words to itself such that a word $Ω$ has a $p$ or $q$ at a given position iff $Φ(Ω)$ has, repectively, a $q$ or a $p$ at that same position. An algorithm is given for converting $Ω$ into $Φ(Ω)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31967",
  "author_total": 1,
  "authors": [
    {
      "name": "Ramin Naimi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7eh5jgymvw686.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31967",
  "fulltext_url": null,
  "id": "7eh5jgymvw686",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31967",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.31967",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7eh5jgymvw686.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.31967",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31967"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Swapping Compatible Words",
  "title_text": "Swapping Compatible Words",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/7eh5jgymvw686",
  "venue": "arXiv",
  "versions": []
}