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Improved bounds for the sunflower lemma
arXiv - CS - Computational Complexity Pub Date : 2019-08-22 , DOI: arxiv-1908.08483
Ryan Alweiss; Shachar Lovett; Kewen Wu; Jiapeng Zhang

A sunflower with $r$ petals is a collection of $r$ sets so that the intersection of each pair is equal to the intersection of all. Erd\H{o}s and Rado proved the sunflower lemma: for any fixed $r$, any family of sets of size $w$, with at least about $w^w$ sets, must contain a sunflower. The famous sunflower conjecture is that the bound on the number of sets can be improved to $c^w$ for some constant $c$. In this paper, we improve the bound to about $(\log w)^w$. In fact, we prove the result for a robust notion of sunflowers, for which the bound we obtain is tight up to lower order terms.
更新日期:2020-03-18

 

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