文摘
A set partition 33b9924fc2805691cdde" title="Click to view the MathML source">σ of [n]={1,…,n} contains another set partition π if restricting 33b9924fc2805691cdde" title="Click to view the MathML source">σ to some S⊆[n] and then standardizing the result gives π. Otherwise we say 33b9924fc2805691cdde" title="Click to view the MathML source">σ avoids π. 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.