{
  "abstract": "Let $A=(a_{ij})$ be a nonnegative row-stochastic or column-stochastic $n\\times n$ matrix of rank at most $k$, where $1\\le k\\le n$. Write $n=qk+s$, where $0\\le s<k$. The author conjectured in 2018 that, for every permutation $σ$ of $\\{1,\\ldots,n\\}$, $\\prod_{i=1}^n a_{i,σ(i)}\\le q^{-q(k-s)}(q+1)^{-(q+1)s}$. We prove this bound and classify all equality cases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01763",
  "author_total": 1,
  "authors": [
    {
      "name": "Yair Lavi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/568q32rwarg2w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01763",
  "fulltext_url": null,
  "id": "568q32rwarg2w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01763",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01763",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/568q32rwarg2w.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01763",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01763"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Maximum Diagonal Product of a Stochastic Matrix of Bounded Rank",
  "title_text": "The Maximum Diagonal Product of a Stochastic Matrix of Bounded Rank",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/568q32rwarg2w",
  "venue": "arXiv",
  "versions": []
}