Quotients of Coxeter complexes and buildings with linear diagram (Q1821349)

The author investigates certain subcomplexes of Coxeter complexes and (Tits) buildings, called quotient Coxeter complexes and quotient buildings. It is shown that such a quotient is the order complex of a poset if and only if it has a linear Coxeter diagram. Moreover it is shown that the poset (with a top and bottom element adjoined) is a lattice (for Coxeter complexes and for non-quotient buildings) and is lexicographically shellable (for both quotient Coxeter complexes and quotient buildings).