{
  "abstract": "Given power series $f_1,\\dots,f_r\\in z^2K[[z]]$ over a field $K$, we show that the semigroup $\\langle f_1,\\dots,f_r\\rangle$ generated by the $f$'s under composition is free of rank $r$ whenever the multiplicative semigroup $\\langle\\mathrm{lc}(f_1),\\dots,\\mathrm{lc}(f_r)\\rangle$ in $K^\\times$ is free commutative of rank $r$; here $\\mathrm{lc}(f)$ denotes the first nonzero coefficient of $f$. To do this, we associate an affine linear transformation to every $F\\in\\langle f_1,\\dots,f_r\\rangle$ and then apply a ping-pong lemma. In particular, combining this with work of Pappalardi, Sha, Shparlinski, and Stewart, it follows that most semigroups of polynomials over a number field $K$ are free, and we make this statement precise through a counting argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31582",
  "author_total": 1,
  "authors": [
    {
      "name": "Wade Hindes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/70715t3r6hq2x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31582",
  "fulltext_url": null,
  "id": "70715t3r6hq2x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31582",
  "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.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214620375",
  "pdf_url": "https://arxiv.org/pdf/2609.31582",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/70715t3r6hq2x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.31582",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31582"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Free semigroups of power series",
  "title_text": "Free semigroups of power series",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/70715t3r6hq2x",
  "venue": "arXiv",
  "versions": []
}