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 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

TableauQ  ▪  DeleteFromTableau

LastLexicographicTableau  ▪  LongestIncreasingSubsequence