Year: 2026
Type: preprint
Abstract: In the 1970s, Erdős and Szemerédi conjectured that for any $n \ge k-1\ge 2$, any collection of subsets of $[n]$ not containing a $k$-sunflower has size at most $c_k^n$ for some $c_k<2$. In the $k=3$ case, this follows from the work of Croot, Lev, and Pach and Ellenberg and Gijswijt on the cap-set problem, through a reduction due to Alon, Shpilka, and Umans. We prove the conjecture for every $k \ge 3$.
Source: arXiv (Cornell University)
Authors: Bucić, Matija, He, Fankang, Lee, Hyunwoo
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223013679