Erdős problem 107 · problems.science

Let $f(n)$ be minimal such that any $f(n)$ points in $ℝ^2$ , no three on a line, contain $n$ points which form the vertices of a convex $n$ -gon. Prove that $f(n) = 2^{n-2} + 1$ .

Sources

Browse retained paths and inspect the exact material available for this Problem.

7 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

107.lean

Retained formal statement7 of 7

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.

FormalConjectures/ErdosProblems/107.leanErdos107.variants.su_bound1 lineExact file

1∃ r, (r =o[Filter.atTop] fun n => ↑n) ∧ ∀ n ≥ 3, ↑(Erdos107.f n) ≤ 2 ^ (↑n + r n)

SolvedStatement only, no proof

Sources

Search problems.science