迭代阴影的交点

arXiv - MATH - Combinatorics Pub Date : 2024-09-09 DOI:arxiv-2409.05487

Hou Tin Chau, David Ellis, Marius Tiba

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引用次数: 0

摘要

我们证明，如果 $\mathcal{A}\子集 {[n] \choose n/2}$ 的度量离零和离一都有界，那么 $\Omega(\sqrt{n})$-iterated upper shadowsof $\mathcal{A}$ 和 $\mathcal{A}^c$ 在一个正度量集合中相交。这可以看作是克鲁斯卡尔--卡托纳定理的可证实性结果。

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Intersections of iterated shadows

We show that if $\mathcal{A} \subset {[n] \choose n/2}$ with measure bounded away from zero and from one, then the $\Omega(\sqrt{n})$-iterated upper shadows of $\mathcal{A}$ and $\mathcal{A}^c$ intersect in a set of positive measure. This confirms (in a strong form) a conjecture of Friedgut. It can be seen as a stability result for the Kruskal--Katona theorem.

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arXiv - MATH - Combinatorics

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