Triangulations with very few geometric bistellar neighbors
type: Item
instance of: scholarly article
title: Triangulations with very few geometric bistellar neighbors
zbMATH Open document ID: 0956.52016
DOI: 10.1007/PL00009489
published in: Discrete \& Computational Geometry
publication date: 2000-01-30T00:00:00Z
review text: A regular (or coherent) triangulation of a configuration \({\mathcal A}\) of \(m\) points which spans \(\mathbb{R}^d\) affinely arises from a particular kind of projection from an \((m-1)\)-simplex, and so has at least \(m-d-1\) bistellar neighbours, in which one of the two ways of triangulating some \(d+1\) of the points is replaced by the other. This property fails for non-regular triangulations. In this paper, the author gives some striking examples. When \(d=3\) there is, for each even \(n\), a configuration with \(m= n^2+ 2n+ 2\) points and only \(4n- 3\) bistellar neighbours. For \(d= 4\), there are configurations with arbitrarily many points but a bounded number of bistellar neighbours.
Mathematics Subject Classification ID: 52B45
zbMATH DE Number: 1394713
zbMATH Keywords: point configuration
zbMATH Keywords: regular
zbMATH Keywords: coherent
zbMATH Keywords: bistellar flip
zbMATH Keywords: triangulation
zbMATH Keywords: bistellar neighbours
reviewed by: Peter McMullen
MaRDI profile type: Publication
full work available at URL: pl00009489
OpenAlex ID: W2019017480
author: Francisco Santos
description: scientific article; zbMATH DE number 1394713