Open problemChecked July 24, 2026

Erdős-Rado Sunflower Conjecture

A growth-rate conjecture for forcing sunflower structures in uniform set families.

Combinatorics Extremal set theory Theoretical computer science

Mathematical statement

For every number of petals $k$ , there is a constant $c_k$ such that every $n$ -uniform family with more than $c_k^n$ sets contains a $k$ -sunflower.

Statement source: Therefore editorial statement

Statement terms: Source-specific

Editorial wording by Therefore. No statement reuse license is granted.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

Erdos20.erdos_20

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_20 :    answer(sorry) ↔      ∃ c : ℕ → ℕ,        ∀ n k, n > 0 → f n k < (c k) ^ n := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Erdős Problem 20official