{
  "abstract": "We prove the conjecture of Prellberg and Stanton (2003) that $\\frac{1-q}{(q^n;q)_m}\\genfrac{[}{]}{0pt}{}{n}{m}_{q}$ has nonnegative power-series coefficients for $0<m<n$, except when $n$ is even and $m\\in\\{2,n-2\\}$. We obtain a polynomial version by bounding a Möbius correction by first differences of Gaussian coefficients. The proof uses partitions and quadratic and cubic semi-invariants of binary forms. An extension of this bound proves the Reiner--Stanton--White conjecture on positivity of orbit polynomials for flags of subspaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26878",
  "author_total": 1,
  "authors": [
    {
      "name": "Thomas Prellberg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/90ewkqw1wn8m2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26878",
  "fulltext_url": null,
  "id": "90ewkqw1wn8m2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26878",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7223146769",
  "pdf_url": "https://arxiv.org/pdf/2610.26878",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/90ewkqw1wn8m2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.26878",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26878"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A positivity conjecture of Prellberg and Stanton",
  "title_text": "A positivity conjecture of Prellberg and Stanton",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/90ewkqw1wn8m2",
  "venue": "arXiv",
  "versions": []
}