{
  "abstract": "We prove that the full Kolakoski shift---namely, the subshift of all smooth sequences over the alphabet $\\{1,2\\}$---is topologically transitive. Consequently, we demonstrate the existence of a smooth sequence whose factors are invariant under both reversal and bitwise complementation. As a further application, we prove the existence of arbitrarily long smooth words containing an equal number of occurrences of the symbols $1$ and $2$, providing evidence in support of Keane's conjecture. Our approach leverages the hierarchical structure of the full Kolakoski shift to reimagine the shift action in terms of a self-similar semigroup, which allows techniques from group theory and combinatorics to be applied.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06878",
  "author_total": 3,
  "authors": [
    {
      "name": "Andrew C. Mitchell"
    },
    {
      "name": "James J. Walton"
    },
    {
      "name": "Michael F. Whittaker"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7trrrwkj859yd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06878",
  "fulltext_url": null,
  "id": "7trrrwkj859yd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06878",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.GR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06878",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7trrrwkj859yd.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06878",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06878"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "The full Kolakoski shift is topologically transitive",
  "title_text": "The full Kolakoski shift is topologically transitive",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:31Z",
  "url": "https://research.draconitic.com/paper/7trrrwkj859yd",
  "venue": "arXiv",
  "versions": []
}