{
  "abstract": "We briefly visit the theory of polynomial and semipolynomial maps defined on an arbitrary monoid, with range a commutative group. Then we characterize the space $\\mathcal{P}(S,\\mathbb{C})$ of polynomial maps $f:S\\to \\mathbb{C}$, where $S=\\mathcal{A}^*$ is the monoid of words based on an arbitrary alphabet $\\mathcal{A}$ under concatenation, and we use this characterization to prove that if there exists a monoid $S\\not\\in\\mathcal{CS}$ such that $\\mathcal{SP}(S,\\mathbb{C})\\neq \\mathcal{P}(S,\\mathbb{C})$, then also $\\mathcal{SP}(\\mathcal{A}^*,\\mathbb{C})\\neq\\mathcal{P}(\\mathcal{A}^*,\\mathbb{C})$ for a certain alphabet $\\mathcal{A}$. We propose as an open problem to prove or disprove that $\\mathcal{SP}(\\mathcal{A}^*,\\mathbb{C})=\\mathcal{P}(\\mathcal{A}^*,\\mathbb{C})$ for arbitrary alphabets $\\mathcal{A}$. Our results are motivated by previous work of Shulman.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.05077",
  "author_total": 1,
  "authors": [
    {
      "name": "J. M. Almira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a2d0b7gjw0pb6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.05077",
  "fulltext_url": null,
  "id": "a2d0b7gjw0pb6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.05077",
  "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.GR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.05077",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a2d0b7gjw0pb6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2606.05077",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.05077"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Polynomial maps on the monoid of words",
  "title_text": "Polynomial maps on the monoid of words",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/a2d0b7gjw0pb6",
  "venue": "arXiv",
  "versions": []
}