  In this paper we study some properties of flattened partitions and their
canonical forms, as well as the distribution of the statistics of runs and
right-to-left minima over the set of flattened partitions. We show the later
one is given by the shifted distribution of the Stirling number of the second
kind. We also enumerate some interesting sub-classes of the class of flattened
partitions, in particular one class enumerated by powers of $2$. We use one of
the constructive proofs given in the paper to implement an algorithm for the
exhaustive generation of flattened partitions by number of runs.
