Partitions and Compositions
Integer Partitions
Partitions — list partitions of a positive integer
NextPartition — next partition in lexicographic ordering
FerrersDiagram — visualize a partition
PartitionQ ▪ RandomPartition ▪ TransposePartition ▪ NumberOfPartitions
Distribution — list the frequency of each element in a list
Compositions
Compositions — list all compositions of integer 
into 
parts
RandomComposition — construct a random composition
NumberOfCompositions ▪ NextComposition
Set Partitions
SetPartitions — partition a set
ToCanonicalSetPartition — reorder a set partition into a canonical order
KSetPartitions — partition a set into 
parts
SetPartitionQ ▪ RandomSetPartition ▪ RandomKSetPartition
CoarserSetPartitionQ ▪ SetPartitionToRGF ▪ SetPartitionListViaRGF
RankSetPartition — rank the set partition in a list of all partitions of a given set
UnrankSetPartition ▪ RankKSetPartition ▪ UnrankKSetPartition
RGFs — list restricted growth functions
RankRGF — find the rank of a restricted growth function
RandomRGF — random restricted growth function
RGFToSetPartition ▪ SetPartitionToRGF ▪ RGFQ ▪ UnrankRGF
Young Tableaux
Tableaux — construct Young tableaux from integer partition
RandomTableau — construct a random tableau
PermutationToTableaux — construct tableaux from a permutation
NumberOfTableaux ▪ ConstructTableau ▪ NextTableau
TableauxToPermutation ▪ TableauClasses
InsertIntoTableau — insert an integer into a tableau
TransposeTableau — transpose a tableau
FirstLexicographicTableau — first Young tableau in lexicographic ordering
LastLexicographicTableau ▪ LongestIncreasingSubsequence