{
  "abstract": "We show that for all positive, nonincreasing, convex functions $f : (0, \\infty) \\to (0,\\infty)$ and for any collection of $n$ points $x_i \\in \\mathbb{R}$ with $x_1 < x_2 < \\ldots < x_n$ and $n$ even, the Pfaffian of the skew matrix defined by $f(x_j - x_i)$ above the diagonal is positive. More generally, we establish coefficientwise nonnegativity for Pfaffians arising from interval decompositions, which also yields quantitative lower bounds for singly and doubly bordered Pfaffians. Choosing $f(r) = r^{-2}$ proves the three nonvanishing assertions in the conjecture of Albouy and Moeckel. Further, we show that the rainbow bound (the product over the nested matching $\\{1,n\\}, \\{2,n-1\\}, \\ldots \\{n/2, n/2 + 1\\}$) is the unique single-matching product that bounds $\\mathrm{Pf}(A_f(x))$ below uniformly over $x$ and $f$ positive, nonincreasing, convex.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24371",
  "author_total": 1,
  "authors": [
    {
      "name": "William Johnson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/93anw0efymdzz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24371",
  "fulltext_url": null,
  "id": "93anw0efymdzz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24371",
  "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.DS"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7223051877",
  "pdf_url": "https://arxiv.org/pdf/2610.24371",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/93anw0efymdzz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24371",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24371"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Pfaffian Positivity for Convex Kernels and Optimal Matching Bounds",
  "title_text": "Pfaffian Positivity for Convex Kernels and Optimal Matching Bounds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/93anw0efymdzz",
  "venue": "arXiv",
  "versions": []
}