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Combinatorics

Tutorials

  • Combinatorics
  • Combinatorics-1
  • Combinatorics-2

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  • Combinatorics
  • Functions I understand in combinatorics

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  • Combinatorics

Symbols

  • CanonicalMultiset
  • CentralBinomialCoefficient
  • ConjugatePartition
  • DescendingSublists
  • DivisorHasseDiagram
  • DominatingIntegerPartitionQ
  • DurfeeSquare
  • EnumerateMultisetPartialDerangements
  • EulerianCatalanNumber
  • EulerianNumber
  • EulerianNumberOfTheSecondKind
  • FerrersDiagram
  • Fibbinary
  • FibonacciEncode
  • FindAscentElements
  • FindAscentPositions
  • FrobeniusSymbolFromPartition
  • FromInversionVector
  • FromPartitionPlusNotation
  • FromPartitionSuperscriptNotation
  • GaussFactorial
  • GrayCode
  • HasseDiagram
  • HookLengths
  • HuffmanCodeWords
  • HuffmanDecode
  • HuffmanEncode
  • IntegerPartitionQ
  • InverseFibonacci
  • InverseGrayCode
  • InversionCount
  • InversionVectorQ
  • LehmerCodeFromPermutation
  • LucasNumberU1
  • LucasNumberV2
  • ModifiedCentralBinomialCoefficient
  • Multichoose
  • MultisetAssociation
  • MultisetPartialDerangements
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  • NarayanaNumber
  • NextPermutation
  • NumberOfTableaux
  • OrderedTupleFromIndex
  • OrderedTupleIndex
  • OrderlessCombinations
  • OrderlessCombinationsOfUnmarkedElements
  • PartialOrderGraphQ
  • PartitionCrank
  • PartitionFromFrobeniusSymbol
  • PartitionPlusNotation
  • PartitionRank
  • PartitionSuperscriptNotation
  • PermutationAscents
  • PermutationCountByInversions
  • PermutationDescents
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  • Phitorial
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  • RationalNumberRepeatingDecimalPeriod
  • ReflexiveGraphQ
  • SecantNumber
  • SelectPermutations
  • SelectSubsets
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  • SelfConjugatePartitionQ
  • SignedLahNumber
  • StandardYoungTableaux
  • StrictIntegerPartitions
  • SubsetFromIndex
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  • TableauQ
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  • TransitiveGraphQ
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  • TupleFromIndex
  • TupleIndex
  • UnsignedLahNumber
  • YoungDiagram
  • ZeckendorfRepresentation
PeterBurbery`Combinatorics`
IntegerPartitionQ
​
IntegerPartitionQ
[x]
checks whether
x
is a weakly decreasing list of positive integers.
​
​
IntegerPartitionQ
[x,n]
checks whether
x
is an integer partition of
n
.
​
Details and Options

Examples  
(2)
Basic Examples  
(2)
Check an integer partition:
In[1]:=
IntegerPartitionQ
[{3,2,1}]
Out[1]=
True
Check whether it is an integer partition of 6:
In[2]:=
IntegerPartitionQ
[{3,2,1},6]
Out[2]=
True
​
Here are the 5 integer partitions of 4:
In[1]:=
IntegerPartitions[4]
Out[1]=
{{4},{3,1},{2,2},{2,1,1},{1,1,1,1}}
They all pass the test for being an integer partition:
In[2]:=
IntegerPartitionQ
/@IntegerPartitions[4]
Out[2]=
{True,True,True,True,True}
SeeAlso
IntegerPartitions
 
▪
PartitionsP
 
▪
PartitionsQ
 
▪
ConjugatePartition
 
▪
FrobeniusSymbolFromPartition
 
▪
PartitionFromFrobeniusSymbol
 
▪
PartitionCrank
 
▪
PartitionRank
 
▪
FerrersDiagram
 
▪
TableauQ
RelatedGuides
▪
Combinatorics
RelatedLinks
IntegerPartitionQ
Resource Function by Wolfram Staff
""

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