SetPartitionListViaRGF

SetPartitionListViaRGF[n]
lists all set partitions of the first

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

natural numbers whose maximum element is

and then maps these RGFs into the corresponding set partitions, all of which contain exactly

blocks.

To use SetPartitionListViaRGF, you first need to load the Combinatorica Package using Needs["Combinatorica`"].