Linear dependencies, polynomial factors in the Duke--Erd\H os forbidden sunflower problem

Andrey Kupavskii, Fedor Noskov

We call a family of $s$ sets $\{F_1,\dots ,F_s\}$ a \textit{sunflower with $s$ petals} if, for any distinct $i,j\in [s]$, one has $F_i\cap F_j={\cap }_{u=1}^s{F}_u$. The set $…