Note on sunflowers
Note on sunflowers
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DOI：
10.1016/j.disc.2021.112367
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发表时间：
2021-04-05
影响因子：
0.8
通讯作者：
Warnke, Lutz
中科院分区：
文献类型：
--
作者：
Bell, Tolson;Chueluecha, Suchakree;Warnke, Lutz
一个有p个花瓣的向日葵由p个两两相交的集合组成。向日葵问题的目标是找到最小的r = r（p，k），使得任何r（k）个不同k元集的族都包含一个有p个花瓣的向日葵。在2019年Alweiss、Lovett、Wu和Zhang的突破基础上，Rao证明了r = O（p log（pk））就足够了;这个界限在2020年被Tao重新证明。在这个简短的说明中，我们记录r = O（p log k）就足够了，通过使用这些最近证明的概率部分的一个小变体。(C)2021爱思唯尔有限公司版权所有。
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. (C) 2021 Elsevier B.V. All rights reserved.