Abstract
The Erdös-Szekeres convexn-gon theorem states that for anyn≥3, there is a smallest integerf(n) such that any set of at leastf(n) points in the planeE 2, no three collinear, contains the vertices of a convexn-gon. We consider three versions of this result as applied to convexly independent points and convex polytopes inE d>,d≥2.
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