The Bruhat Order of the Symmetric Group is Lexicographically Shellable
Paul H. Edelman · Proceedings of the American Mathematical Society · 1981
The title theorem is proven. It then follows from a theorem of Björner that the simplicial complex of chains of this Bruhat order is shellable and thus Cohen-Macaulay. It is further established that this complex is a double cone over a triangulation of a sphere.