Sets of points determining only acute angles and some related colouring problems
type: Item
instance of: scholarly article
title: Sets of points determining only acute angles and some related colouring problems
zbMATH Open document ID: 1081.05103
published in: The Electronic Journal of Combinatorics
publication date: 2006-02-16T00:00:00Z
full work available at URL: https://eudml.org/doc/125587
full work available at URL: v13i1r12.html
review text: Summary: We present both probabilistic and constructive lower bounds on the maximum size of a set of points \({\mathcal S} \subseteq \mathbb R^d\) such that every angle determined by three points in \({\mathcal S}\) is acute, considering especially the case \({\mathcal S} \subseteq \{0,1\}^d\). These results improve upon a probabilistic lower bound of \textit{P. Erdős} and \textit{Z. Füredi} [Ann. Discrete Math. 17, 275--283 (1983; Zbl 0534.52007)]. We also present lower bounds for some generalisations of the acute angles problem, considering especially some problems concerning colourings of sets of integers.
Mathematics Subject Classification ID: 05D40
Mathematics Subject Classification ID: 51M16
zbMATH DE Number: 5006925
zbMATH Keywords: probabilistic
author: David Bevan
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5006925