{
  "abstract": "Fang and Huang proved that every cancellative pair $(\\mathcal{A},\\mathcal{B})$ of families of subsets of $[n]$ satisfies $|\\mathcal{A}|\\cdot|\\mathcal{B}|\\leq(\\frac{9}{4})^n$. Their proof uses entropy. We give a Fourier-analytic proof based on Lifshitz's one-sided noise operator $\\mathrm{T}^{1/4\\to1/2}$. The main tool is a near-$L^1$ hypercontractive estimate for this operator.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09105",
  "author_total": 1,
  "authors": [
    {
      "name": "Fan Chang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/00mdrzp1946jg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09105",
  "fulltext_url": null,
  "id": "00mdrzp1946jg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09105",
  "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"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7212044638",
  "pdf_url": "https://arxiv.org/pdf/2609.09105",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/00mdrzp1946jg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.09105",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09105"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A hypercontractive proof of the sharp bound for cancellative pairs",
  "title_text": "A hypercontractive proof of the sharp bound for cancellative pairs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/00mdrzp1946jg",
  "venue": "arXiv",
  "versions": []
}