Optimal point sets determining few distinct triangles
| Autor: | Epstein, Alyssa, Lott, Adam, Miller, Steven J., Palsson, Eyvindur A. |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $t = 1, 2$. Comment: Version 2.0, 15 pages. Minor update |
| Databáze: | arXiv |
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