论文标题
关于向日葵的注意
Note on Sunflowers
论文作者
论文摘要
带有P pet的向日葵由P组组成，其成对相交相同的P组。向日葵问题的目的是找到最小的R = R（P，K），以便任何R^K不同的K-Element套件都包含带有P花瓣的向日葵。在2019年的Alweiss，Lovett，Wu和Zhang的突破之下，Rao证明R = O（P LOG（PK））就足够了；该界限在2020年被陶（Tao）重复。在此简短的说明中，我们记录了r = o（p log k）足够的足够，通过使用这些最近证明的概率部分的次要变体。
A sunflower with p petals consists of p sets whose pairwise intersections are identical. The goal of the sunflower problem is to find the smallest r=r(p,k) such that any family of r^k distinct k-element sets contains a sunflower with p petals. Building upon a breakthrough of Alweiss, Lovett, Wu and Zhang from 2019, Rao proved that r=O(p log(pk)) suffices; this bound was reproved by Tao in 2020. In this short note we record that r=O(p log k) suffices, by using a minor variant of the probabilistic part of these recent proofs.
