Erdős Rado Sunflower (Conjecture) Theorem
arXiv:2606.0266724.2
AI Analysis
Settles a long-standing open problem in combinatorics, providing a definitive bound for sunflower-free families.
The paper proves the Erdős-Rado Sunflower Conjecture, showing that for every s>2, there exists a constant C(s) such that any family of k-sets with size at least C^k contains a sunflower of size s.
Let $f(k,s)$ denote the minimum integer $m$ such that any family $\mathcal{F}$ consisting of $k$-sized sets of cardinality at least $m$ always contain a sunflower of size $s$. The Erdős-Rado Sunflower Conjecture states that for every $s >2$, there is an constant $C=C(s)$ such that $f(k,s) \leq C^k$. In this paper, we prove the conjecture.