Matching theorems for systems of a finitely generated Coxeter group
  In this paper we prove a series of matching theorems for two sets of Coxeter generators of a finitely generated Coxeter group that identify common features of the two sets of generators. As an application, we describe an algorithm for finding a set of Coxeter generators of maximum rank for a finitely generated Coxeter group. 
Michael Mihalik, John Ratcliffe, Steven Tschantz