  Heinz Huber (1956) considered the following problem on the the hyperbolic
plane H. Consider a strictly hyperbolic subgroup of automorphisms on H with
compact quotient, and choose a conjugacy class in this group. Count the number
of vertices inside an increasing ball, which are images of a fixed point x in H
under automorphisms in the chosen conjugacy class, and describe the asymptotic
behaviour of this number as the size of the ball goes to infinity. We use a
well-known analogy between the hyperbolic plane and the regular tree to solve
this problem on the regular tree.
