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Combinatorics

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  • Combinatorics-1
  • Combinatorics-2

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  • Combinatorics

Symbols

  • CanonicalMultiset
  • CentralBinomialCoefficient
  • ConjugatePartition
  • DescendingSublists
  • DivisorHasseDiagram
  • DominatingIntegerPartitionQ
  • DurfeeSquare
  • EnumerateMultisetPartialDerangements
  • EulerianCatalanNumber
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  • EulerianNumberOfTheSecondKind
  • FerrersDiagram
  • Fibbinary
  • FibonacciEncode
  • FindAscentElements
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  • FrobeniusSymbolFromPartition
  • FromInversionVector
  • FromPartitionPlusNotation
  • FromPartitionSuperscriptNotation
  • GaussFactorial
  • GrayCode
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  • HookLengths
  • HuffmanCodeWords
  • HuffmanDecode
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  • IntegerPartitionQ
  • InverseFibonacci
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  • InversionCount
  • InversionVectorQ
  • LehmerCodeFromPermutation
  • LucasNumberU1
  • LucasNumberV2
  • ModifiedCentralBinomialCoefficient
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  • NarayanaNumber
  • NextPermutation
  • NumberOfTableaux
  • OrderedTupleFromIndex
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  • OrderlessCombinations
  • OrderlessCombinationsOfUnmarkedElements
  • PartialOrderGraphQ
  • PartitionCrank
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PeterBurbery`Combinatorics`
OrderlessCombinationsOfUnmarkedElements
​
OrderlessCombinationsOfUnmarkedElements
[list,nspec]
gives orderless combinations for
list
and
nspec
with the constraint that the elements of
list
are unmarked by replacing the elements with integers.
​
Details and Options

Examples  
(2)
Basic Examples  
(1)
Up to 7 elements:
In[1]:=
Take
OrderlessCombinationsOfUnmarkedElements

,
,
,7,7
Out[1]=
{{1},{1,1},{1,2},{1,1,1},{1,1,2},{1,2,2},{1,2,3}}
Exactly 7 elements:
In[2]:=
Take
OrderlessCombinationsOfUnmarkedElements

,
,
,
,{7},7
Out[2]=
{{1,1,1,1,1,1,1},{1,1,1,1,1,1,2},{1,1,1,1,1,2,2},{1,1,1,1,1,2,3},{1,1,1,1,2,2,2},{1,1,1,1,2,2,3},{1,1,1,1,2,3,3}}
Between 3 and 5 elements:
In[3]:=
OrderlessCombinationsOfUnmarkedElements

,
,
,
,
,
,
,{3,5}
Out[3]=
{{1,1,1},{1,1,2},{1,2,2},{1,2,3},{1,1,1,1},{1,1,1,2},{1,1,2,2},{1,1,2,3},{1,2,2,2},{1,2,2,3},{1,2,3,3},{1,2,3,4},{1,1,1,1,1},{1,1,1,1,2},{1,1,1,2,2},{1,1,1,2,3},{1,1,2,2,2},{1,1,2,2,3},{1,1,2,3,3},{1,1,2,3,4},{1,2,2,2,2},{1,2,2,2,3},{1,2,2,3,3},{1,2,2,3,4},{1,2,3,3,3},{1,2,3,3,4},{1,2,3,4,4},{1,2,3,4,5}}
Use step size 2 from 1 to 7:
In[4]:=
Table[n,{n,1,7,2}]
Out[4]=
{1,3,5,7}
The lengths selected are 1, 3, 5, and 7:
In[5]:=
Take
OrderlessCombinationsOfUnmarkedElements

,
,
,
,
,
,
,{1,7,2},17
Out[5]=
{{1},{1,1,1},{1,1,2},{1,2,2},{1,2,3},{1,1,1,1,1},{1,1,1,1,2},{1,1,1,2,2},{1,1,1,2,3},{1,1,2,2,2},{1,1,2,2,3},{1,1,2,3,3},{1,1,2,3,4},{1,2,2,2,2},{1,2,2,2,3},{1,2,2,3,3},{1,2,2,3,4}}
A custom length specification:
In[6]:=
Take
OrderlessCombinationsOfUnmarkedElements

,
,
,
,
,
,
,{{1,2,3,5}},17
Out[6]=
{{1},{1,1},{1,2},{1,1,1},{1,1,2},{1,2,2},{1,2,3},{1,1,1,1,1},{1,1,1,1,2},{1,1,1,2,2},{1,1,1,2,3},{1,1,2,2,2},{1,1,2,2,3},{1,1,2,3,3},{1,1,2,3,4},{1,2,2,2,2},{1,2,2,2,3}}
Properties & Relations  
(1)

SeeAlso
OrderlessCombinations
RelatedGuides
▪
Combinatorics
▪
Functions I understand in combinatorics
""

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