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Number of points on Convex hull with lattice points
Suppose you have a set of lattice points each of whose coordinates lie in the interval [0, N]. I've heard that the number of points on the convex hull is at most O(N2 / 3). However, I cannot seem to be able to prove this. How can this be proven?
Also, how to generate testcases such that the convex hull contains as many points as possible?
