On the Triangle Vector

Oswin Aichholzer, Ruy Fabila-Monroy, Julia Obmann

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageUndefined/Unknown
Title of host publicationProc. XVIII Encuentros de Geometría Computacional
Place of PublicationGirona, Spain
Pages55-58
Number of pages4
Publication statusPublished - 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.