{
  "abstract": "We prove that every recovering pair $(\\mathcal{A},\\mathcal{B})$ of nonempty families of subsets of an $n$-element set satisfies $$|\\mathcal{A}||\\mathcal{B}|\\le\\left(\\frac{223949}{100000}\\right)^n=(2.23949)^n.$$ A result of Mond, Souza and Versteegen, combined with the sharp $(9/4)^n$ bound of Fang and Huang for cancellative pairs, gives $(2.2499)^n$ for recovering pairs. We improve this to $(2.23949)^n$. The proof combines two entropy inequalities. One is derived directly from the recovering property, while the other applies the Fang-Huang bound to families obtained from the original pair by a construction of Mond, Souza and Versteegen. The two inequalities are then combined by a convex combination.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03851",
  "author_total": 1,
  "authors": [
    {
      "name": "Simone Costa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/abntv9p0qdt22.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03851",
  "fulltext_url": null,
  "id": "abntv9p0qdt22",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03851",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7220709274",
  "pdf_url": "https://arxiv.org/pdf/2610.03851",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/abntv9p0qdt22.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.03851",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03851"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An Improved Upper Bound for Recovering Pairs",
  "title_text": "An Improved Upper Bound for Recovering Pairs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/abntv9p0qdt22",
  "venue": "arXiv",
  "versions": []
}