The Sunflower Conjecture Proven

Abstract

We demonstrate the truth of the sunflower conjecture by showing that a family $\mathcal{F}$ of sets each of cardinality at most $m$ includes a $k$-sunflower, if $|\mathcal{F}| > ( c k^4 )^{m}$ for a constant $c>0$ independent of $m$ and $k$, where $k$-sunflower means a family of $k$ different sets with a common pairwise intersection.