SetPartitionListViaRGF[n]

lists all set partitions of the first n natural numbers by first listing all restricted growth functions (RGFs) on these and then mapping the RGFs to corresponding set partitions.

SetPartitionListViaRGF[n,k]

lists all RGFs on the first n natural numbers whose maximum element is k and then maps these RGFs into the corresponding set partitions, all of which contain exactly k blocks.