{
  "abstract": "We prove a strengthening of Füredi's conjecture on strong Bollobás $t$-systems. For nonnegative integers $t$ and $s$, a family of $m\\ge2$ pairs of finite sets $(A_i,B_i)$ satisfying $|A_i\\cap B_i|\\le t$ and $|A_i\\cap B_j|>t+s$ for all $i\\ne j$ satisfies \\[ \\sum_{i=1}^{m} \\frac{\\binom{|B_i|-t+s}{s}} {\\binom{|A_i|+|B_i|-2t}{|A_i|-t}}\\le1. \\] When $s=0$, this is precisely Füredi's conjectured weighted inequality. The proof is based on a local growth inequality for graded exterior ideals, a basis-exchange construction, and a common-section reduction. The same method gives the corresponding inequality for subspaces over arbitrary fields. We also determine a best possible upper bound for the Füredi weight sum, construct equality examples with an arbitrary prescribed number of pairs, and derive further inequalities from two-sided basis exchanges.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11742",
  "author_total": 2,
  "authors": [
    {
      "name": "Zihao Huang"
    },
    {
      "name": "Suijie Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/39ayzt77yz9me.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11742",
  "fulltext_url": null,
  "id": "39ayzt77yz9me",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11742",
  "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|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7212290830",
  "pdf_url": "https://arxiv.org/pdf/2609.11742",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/39ayzt77yz9me.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.11742",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11742"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Füredi's Conjecture and a Sharp Strengthening",
  "title_text": "Füredi's Conjecture and a Sharp Strengthening",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/39ayzt77yz9me",
  "venue": "arXiv",
  "versions": []
}