Combinatorics and Graph Theory

    

A New Upper Bound for the Heilbronn Triangle Problem

Authors: Theophilus Agama

Using ideas from the geometry of compression, we improve on the current upper bound of Heilbronn's triangle problem. In particular, by letting $Delta(s)$ denotes the minimal area of the triangle induced by $s$ points in a unit disc, then we have the upper bound $$Delta(s)ll frac{1}{s^{frac{3}{2}-epsilon}}$$ for small $epsilon:=epsilon(s)>0$.

Comments: 10 Pages.

Download: PDF

Submission history

[v1] 2024-06-18 20:53:41

Unique-IP document downloads: 368 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus