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- W3212605836 abstract "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 of them. Erdős 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 with $r$ petals. The famous sunflower conjecture states 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 $mathrm{log} w)^w$. In fact, we prove the result for a robust notion of sunflowers, for which the bound we obtain is sharp up to lower order terms." @default.
- W3212605836 created "2021-11-22" @default.
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- W3212605836 date "2021-11-01" @default.
- W3212605836 modified "2023-10-16" @default.
- W3212605836 title "Improved bounds for the sunflower lemma" @default.
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- W3212605836 doi "https://doi.org/10.4007/annals.2021.194.3.5" @default.
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