论文标题
设置系统爆炸
Set System Blowups
论文作者
论文摘要
我们证明，给定一个常数$ k \ ge 2 $和一个大的集合系统$ \ nathcal {f} $的大小最多，最多是$ w $，一种典型的$ k $ -k $ -k $ - sets $（s_1，\ cdots，s_k）$的$ \ \ \ \ \ \ \ \ mathcal {f} $都可以从$ ne $ a ply s plance plance up le he w we le le le， $ \ Mathcal {f} _i $包含$ s_i $，因此对于$ i \ neq j $，如果$ t_i \ in \ Mathcal {f} _i $ $ $ $ t_i $和$ t_j \ in \ in \ nathcal {f}向日葵猜想的版本与原始的答案相同，最多是指数因素。
We prove that given a constant $k \ge 2$ and a large set system $\mathcal{F}$ of sets of size at most $w$, a typical $k$-tuple of sets $(S_1, \cdots, S_k)$ from $\mathcal{F}$ can be ``blown up" in the following sense: for each $1 \le i \le k$, we can find a large subfamily $\mathcal{F}_i$ containing $S_i$ so that for $i \neq j$, if $T_i \in \mathcal{F}_i$ and $T_j \in \mathcal{F}_j$ , then $T_i \cap T_j=S_i \cap S_j$. We also show that the answer to the multicolor version of the sunflower conjecture is the same as the answer for the original, up to an exponential factor.
