Let $m = m (n, k)$ be minimal such that in any collection of sets $A_{1}, \dots, A_{m} \subseteq {1, \dots, n}$ there must exist a sunflower of size $k$ - that is, some collection of $k$ of the $A_{i}$ which pairwise have the same intersection.Estimate $m (n, k)$ , or even better, give an asymptotic formula.

Worked, still open.

combinatorics · open · possible · formalized (Lean) · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

[ F_k(n):=\max{|\mathcal F|:\ \mathcal F\subseteq 2^{[n]}\text{ contains no (k)-sunflower}}. ]

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

AMS 5 · open (literature)

theorem erdos_857 :
    let f : ℕ → ℕ → ℝ := answer(sorry)
    ∀ k : ℕ, 3 ≤ k → Tendsto (fun n : ℕ => (m n k : ℝ) / f k n) atTop (nhds 1)

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