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Optimal Point Sets Determining Few Distinct Triangles by Epstein, Alyssa; Lott, Adam; Miller, Steven J.; Palsson, Eyvindur A. is a scholarly article available to read on EtoBox.

What is Optimal Point Sets Determining Few Distinct Triangles about?

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 $t = 1, 2$.

Author

Epstein, Alyssa; Lott, Adam; Miller, Steven J.; Palsson, Eyvindur A.

Published

2016

Language

EN