{
  "abstract": "Let $A$ be a stochastic $n\\times n$ matrix with $\\operatorname{rank}A\\leq k$, where $1\\leq k\\leq n$. Write $n=qk+s$, where $0\\leq s<k$. The author conjectured in 2018 that $\\operatorname{per}A\\leq (q!/q^q)^{k-s}((q+1)!/(q+1)^{q+1})^s$, with equality if and only if $A=P(J_q^{\\oplus(k-s)}\\oplus J_{q+1}^{\\oplus s})Q$, where $P,Q$ are permutation matrices and $J_t$ is the $t\\times t$ matrix with every entry $1/t$. We prove this conjecture in full.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27911",
  "author_total": 1,
  "authors": [
    {
      "name": "Yair Lavi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6yvmm6njy8cbg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27911",
  "fulltext_url": null,
  "id": "6yvmm6njy8cbg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27911",
  "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",
      "1703|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7214157211",
  "pdf_url": "https://arxiv.org/pdf/2609.27911",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6yvmm6njy8cbg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27911",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27911"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Maximum Permanent of a Stochastic Matrix of Bounded Rank",
  "title_text": "The Maximum Permanent of a Stochastic Matrix of Bounded Rank",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/6yvmm6njy8cbg",
  "venue": "arXiv",
  "versions": []
}