On the Number of Order Types in Integer Grids of Small Size

11/06/2018

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by   Luis E. Caraballo, et al.

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Let {p_1,...,p_n} and {q_1,...,q_n} be two sets of n labeled points in general position in the plane. We say that these two point sets have the same order type if for every triple of indices (i,j,k), p_k is above the directed line from p_i to p_j if and only if q_k is above the directed line from q_i to q_j. In this paper we give the first non-trivial lower bounds on the number of different order types of n points that can be realized in integer grids of polynomial