The Sunflower Conjecture Proven

TL;DR

This paper proves the sunflower conjecture by establishing that large enough set families necessarily contain a k-sunflower, with bounds independent of set size and sunflower size.

Contribution

It provides a proof of the sunflower conjecture with bounds that do not depend on the set size or the number of sets in the sunflower.

Findings

A family of sets with size greater than (ck)^{2m} contains a k-sunflower.

The proof applies to families of sets each of size at most m.

The sunflower conjecture is confirmed for the specified bounds.

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 $|\mathcal{F}| > ( c k )^{2m}$ 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.