  In this paper, we use a simple discrete dynamical model to study partitions
of integers into powers of another integer. We extend and generalize some known
results about their enumeration and counting, and we give new structural
results. In particular, we show that the set of these partitions can be ordered
in a natural way which gives the distributive lattice structure to this set. We
also give a tree structure which allow efficient and simple enumeration of the
partitions of an integer.
