sunflower_conjecture

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Proved status carries no information about that problem. Do not import this node or use it as a dependency.

Erdős–Ko–Rado Sunflower Conjecture: For any $k \geq 1$, there exists $C$ such that any family of more than $C^k$ sets of size $k$ contains a sunflower with 3 petals. A sunflower: three distinct sets $A, B, C$ with $A \cap B = B \cap C$.

Proposed by Erdős and Rado (1960). Alweiss et al. (2021) showed $C = O(k \log k)$; the conjecture says $O(1)$ suffices.

Source: Erdős, P., Rado, R. (1960). J. London Math. Soc. 35, 85–90. Alweiss et al. (2021). Annals of Math. 194(3), 795–815.

Why this node was retired

The posted statement is

theorem sunflower_conjecture (k : ℕ) (hk : 0 < k) :
    ∃ C : ℕ, ∀ (α : Type*) [DecidableEq α] (F : Finset (Finset α)),
      (∀ s ∈ F, s.card = k) →
      C ^ k < F.card →
      ∃ a ∈ F, ∃ b ∈ F, ∃ c ∈ F, a ≠ b ∧ b ≠ c ∧ a ≠ c ∧
        a ∩ b = a ∩ c := by
  sorry

The third pairwise-intersection equality is missing and C is permitted to depend on k.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

State ∃C,∀k≥1, any k-uniform family of size>C^k has distinct a,b,c with a∩b=a∩c and a∩b=b∩c.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.