{
  "abstract": "Given a weakly decreasing positive integer sequence $\\lambda = (\\lambda_1,\\dotsc,\\lambda_\\ell)$ summing to $n$, let $\\chi^\\lambda$ denote the irreducible character of the symmetric group $\\mathfrak{S}_n$ indexed by $\\lambda$. This representation has dimension $\\chi^\\lambda(e)$, where $e$ is the identity element of $\\mathfrak{S}_n$. Let $\\mathrm{Imm}_{\\chi^\\lambda}$ denote the corresponding irreducible character immanant, the function on $n \\times n$ matrices $A = (a_{i,j})$ defined by$$\\mathrm{Imm}_{\\chi^\\lambda}(A) := \\negthickspace \\sum_{w \\in \\mathfrak{S}_n} \\negthickspace \\chi^\\lambda(w) \\hspace{.5mm} a_{1,w_1} \\cdots a_{n,w_n}.$$Merris conjectured [Linear Multilinear Algebra 14 (1983) pp. 21--35] and Heyfron proved [Linear Multilinear Algebra 24 (1988) pp. 65--78] that irreducible character immanants indexed by \"hook\" sequences $(k, 1, \\dotsc, 1)$ satisfy the inequalities$$\\frac{\\mathrm{Imm}_{\\chi^n}(A)}{\\chi^{n}(e)}\\geq \\frac{\\mathrm{Imm}_{\\chi^{n-1,1}}(A)}{\\chi^{n-1,1}(e)}\\geq \\frac{\\mathrm{Imm}_{\\chi^{ n-2,1,1}}(A)}{\\chi^{n-2,1,1}(e)}\\geq \\cdots \\geq \\frac{\\mathrm{Imm}_{\\chi^{1,\\dotsc,1}}(A)}{\\chi^{1,\\dotsc,1}(e)},$$whenever $A$ is an $n \\times n$ Hermitian positive semidefinite matrix. We prove that the same inequalities hold whenever $A$ is an $n \\times n$ totally nonnegative matrix.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Mark Skandera"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/30n447593qnt3.bib",
  "cited_by": 0,
  "doi": "10.37236/14684",
  "fulltext_url": null,
  "id": "30n447593qnt3",
  "issns": [
    "1077-8926"
  ],
  "landing_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/p33i4p23",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W4414806413",
  "pdf_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/download/p33i4p23/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": "The Electronic Journal of Combinatorics",
  "ris": "https://research.draconitic.com/paper/30n447593qnt3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:24Z",
      "native_id": "10.37236/14684",
      "source": "crossref",
      "url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/p33i4p23"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2607|Advanced Combinatorial Mathematics",
      "subfield": "combinatorics"
    }
  ],
  "title": "Hook Immanantal Inequalities for Totally Nonnegative Matrices",
  "title_text": "Hook Immanantal Inequalities for Totally Nonnegative Matrices",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:24Z",
  "url": "https://research.draconitic.com/paper/30n447593qnt3",
  "venue": "The Electronic Journal of Combinatorics",
  "versions": []
}