Optimal point sets determining few distinct triangles
Epstein, Alyssa · Lott, Adam · Miller, Steven J. · Palsson, Eyvindur A.
Original · EN
We generalize work of Erdos and Fishburn to study the structure of finite point sets that determine few distinct triangles. Specifically, we ask for a given t, what is the maximum number of points that can be placed in the plane to determine exactly t distinct triangles? Denoting this quantity by F(t), we show that F(1) = 4, F(2) = 5, and F(t) < 48(t+1) for all t. We also completely characterize the optimal configurations for t = 1, 2.
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