Metrical shellings of simplicial complexes
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.
metrical shelling of simplicial complexes
scientific article; zbMATH DE number 3927791