DeMath — Decentralized math research infrastructure

Statement

A

k

-sunflower is a family of

k

sets with a common pairwise intersection (core). Prove that any family of more than

C_k^{\,w}

sets of size

w

contains a

k

-sunflower, for a constant

C_k

depending only on

k

.

Current frontier

erdosproblems.com/20, OPEN. Erdős–Rado (1960) gave

\approx w!\,(k-1)^w

; Alweiss–Lovett–Wu–Zhang (2020) and refinements reached

(Ck\log w)^w

. The conjectured

C_k^{\,w}

(no

\log w

in the base) is open, including

k = 3

.

When this counts as solved

QUANTITATIVE. PROOF_COMPLETE for the

C_k^{\,w}

bound, COUNTEREXAMPLE for faster growth. BREAKTHROUGH for removing the residual

\log w

factor for general

k

, or settling

k = 3

.

Classification

quantitative