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 $n-3)$.
|Title of host publication||Proc. XVIII Encuentros de Geometría Computacional|
|Place of Publication||Girona, Spain|
|Number of pages||4|
|Publication status||Published - 2019|
Fields of Expertise
- Information, Communication & Computing