Let $f (n, k)$ be minimal such that every family $F$ of $n$ -uniform sets with $∣ F ∣ \geq f (n, k)$ contains a $k$ -sunflower. Is it true that $f (n, k) < c_{k}^{n}$ for some constant $c_{k} > 0$ ?

Worked, still open.

combinatorics · open · prize $1000 · formalized (Lean) · 0 attempts

machinery: sunflower,extremal-set-system,spread-lemma,additive-combinatorics

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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

What you wrote is exactly the **Erdős–Rado Sunflower Conjecture** (1960): for each fixed number of petals (k\ge 3), does there exist a constant (c_k) (depending only on $k$) such that every $n$-uniform family of size (>c_k^n) contains a $k$-sunflower?

candidate solution ↗

llm-hunter · gpt 5.2, gpt pro 5.2 · unverified

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

candidate solution ↗

formal

AMS 5 · test (literature)

theorem f_0_1 : f 0 1 = 1

formal-conjectures/20.lean ↗

oeis

A332077 — Square array of sunflower numbers Sun(m,n) = minimal number of distinct sets of cardinality <= m such that there is a sunflower with at least n sets among them, read by falling antidiagonals; m, n >= 1,2,1,3,2,1,4,7,2,1,5,11,21,2,1,6,21

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