Metrical shellings of simplicial complexes
type: Item
instance of: scholarly article
title: Metrical shellings of simplicial complexes
zbMATH Open document ID: 0579.51012
DOI: 10.1016/S0195-6698(85)80037-8
author: Rudolf Scharlau
published in: European Journal of Combinatorics
publication date: 1985-01-01T00:00:00Z
review text: Let \(\Delta\) be the Coxeter complex of a Coxeter group, \({\mathcal C}\) the set of chambers of \(\Delta\), then a shelling of \(\Delta\) is a map \(R: {\mathcal C}\to \Delta\) together with a partial ordering \(\leq\) of \({\mathcal C}\) such that R(C)\(\subseteq C\) for all \(C\in {\mathcal C}\), \(\Delta =\cup_{C\in {\mathcal C}}\{A\in \Delta /R(C)\subseteq A\subseteq C\},\) \(R(C)\subseteq D \Rightarrow C\leq D\) and such that \(\leq admits\) an extension to a well ordering. A. Björner proved that a building is shellable. This work shows that the proof only depends on a metrical property of the complex, namely the existence of certain projection maps from the set of all chambers (maximal simplices) onto the set of chambers containing a fixed simplex.
Mathematics Subject Classification ID: 51E25
Mathematics Subject Classification ID: 51D10
Mathematics Subject Classification ID: 51G05
zbMATH DE Number: 3927791
zbMATH Keywords: metrical shelling of simplicial complexes
zbMATH Keywords: shellable building
zbMATH Keywords: projection maps
reviewed by: Elena Broží ková
MaRDI profile type: Publication
cites work: Q3952144
cites work: Q5580319
cites work: Q5619224
cites work: Buildings of spherical type and finite BN-pairs
cites work: Q3961400
cites work: A Characterization of Tits Buildings by Metrical Properties
description: scientific article; zbMATH DE number 3927791