{
  "abstract": "A pair $(\\mathcal{A}, \\mathcal{B})$ of families of subsets of $[n]$ is cancellative if whenever $A, A' \\in \\mathcal{A}, B \\in \\mathcal{B}$ satisfy $A \\cup B=A' \\cup B$, then $A=A'$, and whenever $A \\in \\mathcal{A}, B, B' \\in \\mathcal{B}$ satisfy $A \\cup B=A \\cup B'$, then $B=B'$. We show that for every cancellative pair $(\\mathcal{A}, \\mathcal{B})$, the inequality $|\\mathcal{A}||\\mathcal{B}| \\le 2.25^n$ holds, matching Tolhuizen's $(2.25-o(1))^n$ lower bound construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01483",
  "author_total": 2,
  "authors": [
    {
      "name": "Yijia Fang"
    },
    {
      "name": "Hao Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5mwwjr6s3dq7c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01483",
  "fulltext_url": null,
  "id": "5mwwjr6s3dq7c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01483",
  "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": "W7206158364",
  "pdf_url": "https://arxiv.org/pdf/2609.01483",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5mwwjr6s3dq7c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.01483",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01483"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On cancellative pairs of families of subsets",
  "title_text": "On cancellative pairs of families of subsets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/5mwwjr6s3dq7c",
  "venue": "arXiv",
  "versions": []
}