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Combinatorics

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  • Combinatorics

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  • Combinatorics
  • Functions I understand in combinatorics

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  • Combinatorics
  • Stirling permutation

Symbols

  • CanonicalMultiset
  • CentralBinomialCoefficient
  • ConjugatePartition
  • DescendingSublists
  • DivisorHasseDiagram
  • DominatingIntegerPartitionQ
  • DurfeeSquare
  • EnumerateMultisetPartialDerangements
  • EulerianCatalanNumber
  • EulerianNumber
  • EulerianNumberOfTheSecondKind
  • FerrersDiagram
  • Fibbinary
  • FibonacciEncode
  • FindAscentElements
  • FindAscentPositions
  • FindDescentElements
  • FindDescentPositions
  • FrobeniusSymbolFromPartition
  • FromInversionVector
  • FromPartitionPlusNotation
  • FromPartitionSuperscriptNotation
  • GaussFactorial
  • GrayCode
  • HasseDiagram
  • HookLengths
  • HuffmanCodeWords
  • HuffmanDecode
  • HuffmanEncode
  • IntegerPartitionQ
  • InverseFibonacci
  • InverseGrayCode
  • InversionCount
  • InversionVectorQ
  • LehmerCodeFromPermutation
  • LucasNumberU1
  • LucasNumberV2
  • ModifiedCentralBinomialCoefficient
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  • OrderlessCombinations
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  • PartialOrderGraphQ
  • PartitionCrank
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  • PartitionPlusNotation
  • PartitionRank
  • PartitionSuperscriptNotation
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PeterBurbery`Combinatorics`
FromPartitionSuperscriptNotation
​
FromPartitionSuperscriptNotation
[λ]
goes from λ represented with partition superscript notation to λ represented as a weakly decreasing list of strictly positive integers.
​
Examples  
(1)
Basic Examples  
(1)
Here are the integer partitions of 5:
In[1]:=
IntegerPartitions[5]
Out[1]=
{{5},{4,1},{3,2},{3,1,1},{2,2,1},{2,1,1,1},{1,1,1,1,1}}
Here is a list of integer partitions in superscript notation:
In[2]:=
PartitionSuperscriptNotation
/@IntegerPartitions[5]
Out[2]=
{
1
5
,
1
4
1
1
,
1
3
1
2
,
1
3
2
1
,
2
2
1
1
,
1
2
3
1
,
5
1
}
Go back to the integer partitions of 5:
In[3]:=
FromPartitionSuperscriptNotation
/@
PartitionSuperscriptNotation
/@IntegerPartitions[5]
Out[3]=
{{5},{4,1},{3,2},{3,1,1},{2,2,1},{2,1,1,1},{1,1,1,1,1}}
This is the inverse of PartitionSuperscriptNotation.
In[4]:=
FromPartitionSuperscriptNotation
/@
PartitionSuperscriptNotation
/@IntegerPartitions[5]===IntegerPartitions[5]
Out[4]=
True
SeeAlso
PartitionSuperscriptNotation
RelatedGuides
▪
Combinatorics
""

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