Matching theorems for Coxeter systems of a finitely generated Coxeter group
by
John Ratcliffe
Vanderbilt University
Coauthors: Michael Mihalik and Steven Tschantz

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.

We prove that any two Coxeter systems of maximum rank for a finitely generated Coxeter group have the same number of visual subgroups of each complete system isomorphism type; in other words, the presentation diagrams of two Coxeter systems of maximum rank for a finitely generated Coxeter group have the same number of complete subdiagrams of each isomorphism type.

Date received: March 30, 2006