Talagrand 创建大型集合猜想的证明

Xuan Fang; Tianyu Wang

Talagrand 创建大型集合猜想的证明

组合数学 2025-12-08 v2 离散数学概率论

作者: Xuan Fang , Tianyu Wang

摘要

Talagrand 猜想指出：若集合族 $\mathcal{F}$ 关于 $X = \{ 1,2,\cdots, N \}$ 的测度较大，则常数倍的 $\mathcal{F}$ 中集合的并将覆盖幂集 $X$ 的大部分。该猜想是组合论与概率论交叉领域的核心难题，Talagrand 将其称为个人最喜欢的难题。本文提供了确认此猜想的证明。

关键词

Talagrand 猜想大型集合组合论概率论测度论

引用

@article{arxiv.2511.17336,
  title  = {A Proof of Talagrand's Creating Large Sets Conjecture},
  author = {Xuan Fang and Tianyu Wang},
  journal= {arXiv preprint arXiv:2511.17336},
  year   = {2025}
}

备注

This manuscript has been withdrawn by the authors. Upon further review, we have identified critical flaws in the analysis that invalidates the main conclusions presented. The authors intend to address these concerns and may submit a corrected version in the future. We apologize for any inconvenience this may have caused

Talagrand 创建大型集合猜想的证明

摘要

关键词

引用

备注

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