Is it true that $f(n,k) 0$ and for all $n > 0$?

Erdős problem 20

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Is it true that $f(n,k) < c_k^n$ for some constant $c_k>0$ and for all $n > 0$ ?

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The source's own material, retained exactly.

3 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

20.lean

Retained formal statement2 of 3

Erdős and Rado [ErRa60] proved the factorial upper bound for the $k$ -sunflower threshold: any family of $n$ -uniform sets with more than $(k-1)^n \, n!$ members contains a $k$ -sunflower, hence $f(n,k) \le (k-1)^n \, n! + 1$ .

FormalConjectures/ErdosProblems/20.leanErdos20.erdos_20.variants.erdos_rado_bound1 lineExact file

1∀ (n k : ℕ), n > 0 → 2 ≤ k → Erdos20.f n k ≤ (k - 1) ^ n * n.factorial + 1

SolvedStatement only, no proof