The Subtree Size Profile of Bucket Recursive Trees

Kazemi (2014) introduced a new version of bucket recursive trees as another generalization of recursive trees where buckets have vari- able capacities. In this paper, we get the p-th factorial moments of the random variable Sn,1 which counts the number of subtrees size-1 profile (leaves) and shows a phase change of this random variable. These can be obtained by solving a first order partial differential equation for the generating function correspond to this quantity.