SetPartitions[set] returns the list of set partitions of set. SetPartitions[n] returns the list of set partitions of {1, 2, ..., n}.

SetPartitionToRGF[sp, set] converts the set partition sp of set into the corresponding restricted growth function.

TableauClasses[p] partitions the elements of permutation p into classes according to their initial columns during Young tableaux construction.

TableauQ[t] yields True if and only if t represents a Young tableau.

Tableaux[p] constructs all tableaux having a shape given by integer partition p.

TableauxToPermutation[t_1, t_2] constructs the unique permutation associated with Young tableaux t_1 and t_2, where both tableaux have the same shape.

TransposePartition[p] reflects a partition p of k parts along the main diagonal, creating a partition with maximum part k.

TransposeTableau[t] reflects a Young tableau t along the main diagonal, creating a different tableau.

UnrankSetPartition[r, s, k] finds a k-block set partition of s with rank r. UnrankSetPartition[r, n, k] finds a k-block set partition of {1, 2, ..., n} with rank r.

UnrankRGF[r, n] returns a restricted growth function defined on the first n natural numbers whose rank is r.