Problem 857

Erdős Problem #857: declared status 'open'. Formalized: yes. Let $m=m(n,k)$ be minimal such that in any collection of sets $A_1,\ldots,A_m\subseteq \{1,\ldots,n\}$ there must exist a sunflower of size $k$ - that is, some collection of $k$ of the $A_i$ which pairwise have the same intersection. Estimate $m(n,k)$, or even better, give an asymptotic formula. Prize: no. Tags: combinatorics.