On the Triangle Vector

Oswin Aichholzer; Ruy Fabila-Monroy; Julia Obmann

On the Triangle Vector

Oswin Aichholzer
, Ruy Fabila-Monroy
, Julia Obmann

Institute of Software Engineering and Artificial Intelligence (7160)

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

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
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

Access to Document

http://imae.udg.edu/egc2019/doc/BookAbstractsEGC2019.pdf

Cite this

@inproceedings{1ed7f43bb2f74af1902770af5c7f073e,

title = "On the Triangle Vector",

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\textasciitilde{}\$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)\$.",

author = "Oswin Aichholzer and Ruy Fabila-Monroy and Julia Obmann",

year = "2019",

language = "undefiniert/unbekannt",

pages = "55--58",

booktitle = "Proc. XVIII Encuentros de Geometr{\'i}a Computacional",

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TY - GEN

T1 - On the Triangle Vector

AU - Aichholzer, Oswin

AU - Fabila-Monroy, Ruy

AU - Obmann, Julia

PY - 2019

Y1 - 2019

N2 - 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 $n-3)$.

AB - 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 $n-3)$.

M3 - Beitrag in einem Konferenzband

SP - 55

EP - 58

BT - Proc. XVIII Encuentros de Geometría Computacional

CY - Girona, Spain

ER -