Growth in Right-Angled Groups and Monoids
  We derive functional relationships between spherical generating functions of graph monoids, right-angled Artin groups and right-angled Coxeter groups. We use these relationships to express the spherical generating function of a right-angled Artin group in terms of the clique polynomial of its defining graph. We also describe algorithms for computing the geodesic generating functions of these structures. 
Jayadev S. Athreya and Amritanshu Prasad
math.GR math.CO