{
  "abstract": "In 1994, Friedman, Joichi and Stanton conjectured that coefficients of the power-series $q+(1-q)\\prod_{i=n}^{2n-1}\\frac{1}{1-q^{i}}$ are nonnegative for $n\\geq3$ and $n$ being odd. Let $\\qbinom nm$ denote the Gaussian polynomial. In 2003, Prellberg and Stanton conjectured that coefficients of the power-series $(1-q)\\qbinom nm\\prod_{i=0}^{m-1}\\frac{1}{1-q^{i+m}}$ are nonnegative for $0<m<n$, except when $n$ is even and $m\\in\\{2,n-2\\}$. The latter conjecture implies the former. In this paper, we prove a stronger result concerning coefficientwise nonnegativity of another power series, which implies the conjecture of Prellberg and Stanton. The proof uses a Möbius correction from Gaussian polynomials, weight-preserving injections on partitions, explicit linearly independent vectors in the kernel of a derivation operator and the KOH identity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18377",
  "author_total": 3,
  "authors": [
    {
      "name": "Hong-Zhang Ai"
    },
    {
      "name": "Lili Mu"
    },
    {
      "name": "Bao-Xuan Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6wkkqjxj7mqcg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18377",
  "fulltext_url": null,
  "id": "6wkkqjxj7mqcg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18377",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7221814253",
  "pdf_url": "https://arxiv.org/pdf/2610.18377",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6wkkqjxj7mqcg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18377",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18377"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Proof of a nonnegativity conjecture of Prellberg--Stanton",
  "title_text": "Proof of a nonnegativity conjecture of Prellberg--Stanton",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/6wkkqjxj7mqcg",
  "venue": "arXiv",
  "versions": []
}