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Combinatorics

Tutorials

  • Combinatorics
  • Combinatorics-1
  • Combinatorics-2

Guides

  • Combinatorics
  • Functions I understand in combinatorics

Tech Notes

  • 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
  • MultisetStrictDescentElements
  • MultisetStrictDescents
  • NarayanaNumber
  • NextPermutation
  • NumberOfTableaux
  • OrderedTupleFromIndex
  • OrderedTupleIndex
  • OrderlessCombinations
  • OrderlessCombinationsOfUnmarkedElements
  • PartialOrderGraphQ
  • PartitionCrank
  • PartitionFromFrobeniusSymbol
  • PartitionPlusNotation
  • PartitionRank
  • PartitionSuperscriptNotation
  • PermutationAscents
  • PermutationCountByInversions
  • PermutationDescents
  • PermutationFromIndex
  • PermutationGraph
  • PermutationIndex
  • PermutationMajorIndex
  • PermutationToTableaux
  • Phitorial
  • PosetQ
  • PosetToTableau
  • Primorial
  • QExponential
  • QMultinomial
  • RandomYoungTableau
  • RationalNumberRepeatingDecimalPeriod
  • ReflexiveGraphQ
  • SecantNumber
  • SelectPermutations
  • SelectSubsets
  • SelectTuples
  • SelfConjugatePartitionQ
  • SignedLahNumber
  • StandardYoungTableaux
  • StrictIntegerPartitions
  • SubsetFromIndex
  • SubsetIndex
  • TableauQ
  • TableauToPoset
  • TableauxToPermutation
  • TangentNumber
  • ToInversionVector
  • TransitiveGraphQ
  • TransposeTableau
  • TupleFromIndex
  • TupleIndex
  • UnsignedLahNumber
  • YoungDiagram
  • ZeckendorfRepresentation
PeterBurbery`Combinatorics`
QMultinomial
​
QMultinomial
[
n
1
,
n
2
,
n
3
,…,q]
gives the
q
-multinomial coefficient for
n1
,
n2
,
n3
that approaches
(n1+n2+n3+…)!/(n1!n2!n3!…)
as
q
goes to 1.
​
Examples  
(3)
Basic Examples  
(3)
Evaluate numerically:
In[1]:=
QMultinomial
[1,2,1,E]
Out[1]=
QGamma[5,]
1+
In[2]:=
N
QMultinomial
[1,2,1,E]
Out[2]=
346.47
The 1, 2, 1 multinomial coefficient appears as the coefficient of
xy^2z
:
In[3]:=
Multinomial[1,2,1]
Out[3]=
12
In[4]:=
Expand[(x+y+z)^4]
Out[4]=
4
x
+4
3
x
y+6
2
x
2
y
+4x
3
y
+
4
y
+4
3
x
z+12
2
x
yz+12x
2
y
z+4
3
y
z+6
2
x
2
z
+12xy
2
z
+6
2
y
2
z
+4x
3
z
+4y
3
z
+
4
z
In[5]:=
Coefficient[%,x
2
y
z]
Out[5]=
12
​
Plot over a subset of the reals:
In[1]:=
Plot
QMultinomial
[x,1/2,3,E],{x,-2,4}
Out[1]=
​
Plot over a subset of the complexes:
In[1]:=
ComplexPlot3D
QMultinomial
[z,1/2,E],{z,-2-2I,2+2I},PlotLegendsAutomatic
Out[1]=
Contents cannot be rendered at this time; please try again later
SeeAlso
QBinomial
 
▪
Binomial
 
▪
Factorial
 
▪
QFactorial
 
▪
QGamma
RelatedGuides
▪
Combinatorics
▪
Functions I understand in combinatorics
RelatedLinks
q-Multinomial Coefficient — Wolfram MathWorld
▪
Sagemath's q-analogues support in combinatorics
▪
Gaussian binomial coefficient — Wikipedia
Multinomial — The Wolfram Functions Site
NKS|Online (A New Kind of Science)
Multinomial Coefficient — MathWorld
""

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