{
  "abstract": "A square is a word $xx$, where $x$ is nonempty. We show that a circular word of length $n$ contains at most $\\lfloor 3n/2 \\rfloor$ distinct squares of length at most $n$. The proof combines known results relating squares to circuits in Rauzy graphs. The coefficient $3/2$ agrees with the known lower bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32084",
  "author_total": 1,
  "authors": [
    {
      "name": "Rikuya Hamai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1m979m6qcg0d1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32084",
  "fulltext_url": null,
  "id": "1m979m6qcg0d1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32084",
  "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",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|semigroups and automata theory"
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  ],
  "openalex": "W7214758226",
  "pdf_url": "https://arxiv.org/pdf/2609.32084",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1m979m6qcg0d1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.32084",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32084"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Tight Upper Bound on the Number of Distinct Squares in Circular Words",
  "title_text": "The Tight Upper Bound on the Number of Distinct Squares in Circular Words",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/1m979m6qcg0d1",
  "venue": "arXiv",
  "versions": []
}