{
  "abstract": "We study versions of binomial and multichoose coefficients for finite $G$-sets, extending a result of Siebeneicher from the 1970s concerning the duality between these operations. If the group $G$ comes from a finite Galois extension of fields, the Dress map provides a bridge from $G$-sets to quadratic forms over the base field. We show that this Dress map is compatible with binomial coefficients of finite $G$-sets and a particular operation on quadratic forms we define. This allows us to extend the definition of Brugallé and Wickelgren's quadratically enriched binomial coefficients to arbitrary Grothendieck--Witt classes. This allows for a new proof that quadratically enriched binomial coefficients depend only on the trace form of the inputted étale algebra, as well as an elegant reproof of a result of Chen and Wickelgren about binomial coefficients over finite fields.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23758",
  "author_total": 2,
  "authors": [
    {
      "name": "Thomas Brazelton"
    },
    {
      "name": "Ben Spitz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a1c3hpbh4e5xy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23758",
  "fulltext_url": null,
  "id": "a1c3hpbh4e5xy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23758",
  "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.AT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
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  ],
  "openalex": "W7222956525",
  "pdf_url": "https://arxiv.org/pdf/2610.23758",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a1c3hpbh4e5xy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23758",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23758"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Operations on $G$-sets and the Dress map",
  "title_text": "Operations on G-sets and the Dress map",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/a1c3hpbh4e5xy",
  "venue": "arXiv",
  "versions": []
}