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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
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  • FindAscentElements
  • FindAscentPositions
  • FindDescentElements
  • FindDescentPositions
  • FrobeniusSymbolFromPartition
  • FromInversionVector
  • FromPartitionPlusNotation
  • FromPartitionSuperscriptNotation
  • GaussFactorial
  • GrayCode
  • HasseDiagram
  • HookLengths
  • HuffmanCodeWords
  • HuffmanDecode
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  • IntegerPartitionQ
  • InverseFibonacci
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  • OrderlessCombinations
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  • PartitionCrank
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  • PartitionPlusNotation
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PeterBurbery`Combinatorics`
FromPartitionPlusNotation
​
FromPartitionPlusNotation
[λ]
returns a list of weakly decreasing integers representing the integer partition
λ
written in partition plus notation.
​
Examples  
(1)
Basic Examples  
(1)
Write {2,2,1} in partition plus notation.
In[1]:=
PartitionPlusNotation
[{2,2,1}]
Out[1]=
2+2+1
Go back to {2,2,1}:
In[2]:=
FromPartitionPlusNotation
[2+2+1]
Out[2]=
{2,2,1}
List@@ would also work here:
In[3]:=
List@@2+2+1
Out[3]=
2+2+1
There is one time when List@@ will not work. That time is for a single integer.
In[4]:=
List@@5
Out[4]=
5
We wanted to return {5}, the way IntegerPartitions[5] does.
In[5]:=
IntegerPartitions[5]
Out[5]=
{{5},{4,1},{3,2},{3,1,1},{2,2,1},{2,1,1,1},{1,1,1,1,1}}
We can use FromPartitionPlusNotation for this edge case.
In[6]:=
PartitionPlusNotation
/@IntegerPartitions[5]
Out[6]=
{5,4+1,3+2,3+1+1,2+2+1,2+1+1+1,1+1+1+1+1}
In[7]:=
FromPartitionPlusNotation
/@
PartitionPlusNotation
/@IntegerPartitions[5]
Out[7]=
{{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 PartitionPlusNotation.
In[8]:=
FromPartitionPlusNotation
/@
PartitionPlusNotation
/@IntegerPartitions[5]===IntegerPartitions[5]
Out[8]=
True
SeeAlso
PartitionPlusNotation
RelatedGuides
▪
Combinatorics
""

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