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

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