{
  "abstract": "Let $A=(a_{ij})$ be an $n\\times n$ real matrix and let $λ$ be a partition of $n$. Let $ϕ^λ$ be the class function dual to the Young permutation character, and let $$ ϕ^λ[A] = \\sum_{σ\\in\\mathfrak{S}_n}ϕ^λ(σ) \\prod_{i=1}^{n}a_{iσ(i)} $$ be the corresponding monomial immanant. Stembridge [Canad. J. Math. 44 (1992), pp. 1079-1099] posed the following open problem: If all minors of $A$ of order at most $r$ are nonnegative, and the partition $λ$ has length at most $r$, is it true that $ϕ^λ[A]\\ge 0$? This paper solves the problem for all hook partitions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36665",
  "author_total": 3,
  "authors": [
    {
      "name": "Xiangshuai Dong"
    },
    {
      "name": "Tingzeng Wu"
    },
    {
      "name": "Xing Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4gsczebadby3g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36665",
  "fulltext_url": null,
  "id": "4gsczebadby3g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36665",
  "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",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7214892635",
  "pdf_url": "https://arxiv.org/pdf/2609.36665",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4gsczebadby3g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36665",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36665"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the nonnegativity of monomial immanants for hook partitions",
  "title_text": "On the nonnegativity of monomial immanants for hook partitions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/4gsczebadby3g",
  "venue": "arXiv",
  "versions": []
}