su_bound

Suk [Su17] proved $$ f(n) ≤ 2^{(1+o(1))n}. $$ [Su17] Suk, Andrew, _On the Erdős-Szekeres convex polygon problem_. J. Amer. Math. Soc. (2017), 1047-1053.

theorem su_bound :
    ∃ r : ℕ → ℝ, r =o[atTop] (fun n => (n : ℝ)) ∧
      ∀ n ≥ 3, (f n : ℝ) ≤ 2^(n + r n)

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