Growth functions associated with Artin monoids of finite type

摘要

We prove that the growth functions associated with Artin-monoids of finitetype~*)are rational functions whose numerators is equal to 1. We give an explicit formula for thedenominator polynomial N_M(t)and give three conjectures on it: 1.N_is irreducible up to afactor 1-t, 2. there are l-1 real distinct roots of N_M(t)on the interval (0,1), and 3. smallest realroot on (0,1) is the unique smallest absolute values of all roots of N_M(t).