{
  "abstract": "A universal framework for Hopf algebras in combinatorics provides a unified understanding of combinatorial objects. To establish such a framework, we dualize the theory of combinatorial Hopf algebras developed by Aguiar, Bergeron, and Sottile, obtaining the category of rooted Hopf algebras. An object in this category is a graded connected Hopf algebra equipped with a group-like element, called a root, in its completion. These roots dualize the character theory of combinatorial Hopf algebras and provide a natural way to extend Bernstein and raising operators to other rooted Hopf algebras. The resulting constructions extend Schur, Hall--Littlewood, and Macdonald functions to rooted Hopf algebras. As an application, we develop these constructions for symmetric functions in noncommuting variables.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21289",
  "author_total": 2,
  "authors": [
    {
      "name": "Farid Aliniaeifard"
    },
    {
      "name": "Stephanie van Willigenburg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5fm0v0d4c4zey.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21289",
  "fulltext_url": null,
  "id": "5fm0v0d4c4zey",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21289",
  "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.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.21289",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5fm0v0d4c4zey.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21289",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21289"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A universal framework for Hopf algebras in combinatorics",
  "title_text": "A universal framework for Hopf algebras in combinatorics",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/5fm0v0d4c4zey",
  "venue": "arXiv",
  "versions": []
}