Equilateral triangles in finite metric spaces
type: Item
instance of: scholarly article
title: Equilateral triangles in finite metric spaces
zbMATH Open document ID: 1054.05070
author: Vania Mascioni
published in: The Electronic Journal of Combinatorics
publication date: 2004-10-13T00:00:00Z
full work available at URL: https://eudml.org/doc/124094
full work available at URL: v11i1r18.html
review text: Summary: In the context of finite metric spaces with integer distances, we investigate the new Ramsey-type question of how many points can a space contain and yet be free of equilateral triangles. In particular, for finite metric spaces with distances in the set \(\{1,\dots, n\}\), the number \(D_n\) is defined as the least number of points the space must contain in order to be sure that there will be an equilateral triangle in it. Several issues related to these numbers are studied, mostly focusing on low values of \(n\). Apart from the trivial \(D_1=3\), \(D_2=6\), we prove that \(D_3=12\), \(D_4=33\) and \(81\leq D_5\leq 95\).
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 2107460
zbMATH Keywords: finite metric spaces
zbMATH Keywords: distances
zbMATH Keywords: Ramsey-type question
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2107460