关于最大相交族的大小

Combinatorics, Probability and Computing Pub Date : 2020-10-06 DOI:10.1017/s0963548323000287

D. Zakharov

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引用次数: 4

摘要

我们证明了$n$ -一致极大相交族的大小不超过$e^{-n^{0.5+o(1)}}n^n$。这改进了Frankl (2019) Comb最近的一项研究。Probab。Comput.28(5), 733 - 739年)。Alweiss et al.(2020)第52届ACM SIGACT计算理论研讨会论文集)的Spread引理在证明中发挥了重要作用。

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On the size of maximal intersecting families

We show that an $n$ -uniform maximal intersecting family has size at most $e^{-n^{0.5+o(1)}}n^n$ . This improves a recent bound by Frankl ((2019) Comb. Probab. Comput.28(5) 733–739.). The Spread Lemma of Alweiss et al. ((2020) Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing.) plays an important role in the proof.

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Combinatorics, Probability and Computing

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