{
  "abstract": "Bang (1976) proved the inequality for matrix permanents $\\mathrm{per}^2(A) \\geq 2^{-2n}\\mathrm{per}(A \\otimes J_2)$, where $J_2$ is the $2 \\times 2$ all-ones matrix and $A$ is any $n \\times n$ matrix with non-negative entries. We show that, if $A$ is any $n \\times n$ real-valued matrix with rank at most two (possibly having negative entries), this inequality can be sharpened, replacing the constant $2^{-2n}$ by $1 / \\binom{2n}{n} = (n!)^2 / (2n)! > 2^{-2n}$. We then show that this sharpened inequality also implies new inequalities for finite free convolutions of polynomials: if $p$ and $q$ are monic real-rooted polynomials of degree $n$, then $(p \\boxplus_n q)(x)^2 \\geq (p^2 \\boxplus_{2n} q^2)(x)$ and $(p \\boxtimes_n q)(x)^2 \\geq (p^2 \\boxtimes_{2n} q^2)(x)$ for all $x \\in \\mathbb{R}$, for $\\boxplus_n$ and $\\boxtimes_n$ the finite free additive and multiplicative convolution operations, respectively, on polynomials of degree $n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28520",
  "author_total": 3,
  "authors": [
    {
      "name": "Dmitriy Kunisky"
    },
    {
      "name": "Daniel A. Spielman"
    },
    {
      "name": "Xifan Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2hs8kz74tqh1z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28520",
  "fulltext_url": null,
  "id": "2hs8kz74tqh1z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28520",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7204758424",
  "pdf_url": "https://arxiv.org/pdf/2608.28520",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2hs8kz74tqh1z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.28520",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28520"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Inequalities for rank-two permanents and finite free convolutions",
  "title_text": "Inequalities for rank-two permanents and finite free convolutions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/2hs8kz74tqh1z",
  "venue": "arXiv",
  "versions": []
}