### Abstract

Let $S$ be a set of $n$ points in the plane in general position. In this note we study the so-called triangle vector $ of~$S$. For each cardinality $i$, $0 leq i leq n-3$, $i)$ is the number of triangles spanned by points of $S$ which contain exactly $i$ points of $S$ in their interior. We show relations of this vector to other combinatorial structures and derive tight upper bounds for several entries of $, including $n-6)$ to $n-3)$.

Original language | Undefined/Unknown |
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Title of host publication | Proc. XVIII Encuentros de Geometría Computacional |

Place of Publication | Girona, Spain |

Pages | 55-58 |

Number of pages | 4 |

Publication status | Published - 2019 |

### Fields of Expertise

- Information, Communication & Computing

## Cite this

Aichholzer, O., Fabila-Monroy, R., & Obmann, J. (2019). On the Triangle Vector. In

*Proc. XVIII Encuentros de Geometría Computacional*(pp. 55-58). Girona, Spain.