  A set partition $\sigma$ of $[n]=\{1,\dots,n\}$ contains another set
partition $\pi$ if restricting $\sigma$ to some $S\subseteq[n]$ and then
standardizing the result gives $\pi$. Otherwise we say $\sigma$ avoids $\pi$.
For all sets of patterns consisting of partitions of $[3]$, the sizes of the
avoidance classes were determined by Sagan and by Goyt. Set partitions are in
bijection with restricted growth functions (RGFs) for which Wachs and White
defined four fundamental statistics. We consider the distributions of these
statistics over various avoidance classes, thus obtaining multivariate
analogues of the previously cited cardinality results. This is the first
in-depth study of such distributions. We end with a list of open problems.

Combinatorics