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Erdős problem 564

Let R3(n)R_3(n) be the minimal mm such that if the edges of the 33-uniform hypergraph on mm vertices are 22-coloured then there is a monochromatic copy of the complete 33-uniform hypergraph on nn vertices.

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FormalConjectures/ErdosProblems/

564.lean

Retained formal statement1 of 1

Let R3(n)R_3(n) be the minimal mm such that if the edges of the 33-uniform hypergraph on mm vertices are 22-coloured then there is a monochromatic copy of the complete 33-uniform hypergraph on nn vertices.

Is there some constant c>0c>0 such that R3(n)≥22cn? R_3(n) \geq 2^{2^{cn}}?

FormalConjectures/ErdosProblems/564.leanErdos564.erdos_5641 lineExact file
True ↔ ∃ c > 0, ∀ᶠ (n : ℕ) in Filter.atTop, 2 ^ 2 ^ (c * n) ≤ ↑(Combinatorics.hypergraphRamsey 3 n)
OpenStatement only, no proof

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