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Combinatorics

Guides

  • Combinatorics
  • Functions I understand in combinatorics

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  • Combinatorics

Symbols

  • CanonicalMultiset
  • CentralBinomialCoefficient
  • ConjugatePartition
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  • DivisorHasseDiagram
  • DominatingIntegerPartitionQ
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  • SelfConjugatePartitionQ
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  • StirlingPermutations
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PeterBurbery`Combinatorics`
StirlingPermutations
​
StirlingPermutations
[n]
generates all Stirling permutations of order
n
.
​
Examples  
(2)
Basic Examples  
(1)
In[1]:=
FromDigits/@
StirlingPermutations
[1]
Out[1]=
{11}
In[2]:=
FromDigits/@
StirlingPermutations
[2]
Out[2]=
{2211,1221,1122}
In[3]:=
FromDigits/@
StirlingPermutations
[3]
Out[3]=
{332211,233211,223311,221331,221133,331221,133221,123321,122331,122133,331122,133122,113322,112332,112233}
A list:
In[4]:=
StirlingPermutations
[3]
Out[4]=
{{3,3,2,2,1,1},{2,3,3,2,1,1},{2,2,3,3,1,1},{2,2,1,3,3,1},{2,2,1,1,3,3},{3,3,1,2,2,1},{1,3,3,2,2,1},{1,2,3,3,2,1},{1,2,2,3,3,1},{1,2,2,1,3,3},{3,3,1,1,2,2},{1,3,3,1,2,2},{1,1,3,3,2,2},{1,1,2,3,3,2},{1,1,2,2,3,3}}
In[5]:=
FromDigits/@
StirlingPermutations
[4]
Out[5]=
{44332211,34432211,33442211,33244211,33224411,33221441,33221144,44233211,24433211,23443211,23344211,23324411,23321441,23321144,44223311,24423311,22443311,22344311,22334411,22331441,22331144,44221331,24421331,22441331,22144331,22134431,22133441,22133144,44221133,24421133,22441133,22144133,22114433,22113443,22113344,44331221,34431221,33441221,33144221,33124421,33122441,33122144,44133221,14433221,13443221,13344221,13324421,13322441,13322144,44123321,14423321,12443321,12344321,12334421,12332441,12332144,44122331,14422331,12442331,12244331,12234431,12233441,12233144,44122133,14422133,12442133,12244133,12214433,12213443,12213344,44331122,34431122,33441122,33144122,33114422,33112442,33112244,44133122,14433122,13443122,13344122,13314422,13312442,13312244,44113322,14413322,11443322,11344322,11334422,11332442,11332244,44112332,14412332,11442332,11244332,11234432,11233442,11233244,44112233,14412233,11442233,11244233,11224433,11223443,11223344}
The function works on lists.
In[6]:=
StirlingPermutations
[Range[3]]
Out[6]=
{{{1,1}},{{2,2,1,1},{1,2,2,1},{1,1,2,2}},{{3,3,2,2,1,1},{2,3,3,2,1,1},{2,2,3,3,1,1},{2,2,1,3,3,1},{2,2,1,1,3,3},{3,3,1,2,2,1},{1,3,3,2,2,1},{1,2,3,3,2,1},{1,2,2,3,3,1},{1,2,2,1,3,3},{3,3,1,1,2,2},{1,3,3,1,2,2},{1,1,3,3,2,2},{1,1,2,3,3,2},{1,1,2,2,3,3}}}
Make a list of digits.
In[7]:=
MapFromDigits,
StirlingPermutations
[Range[3]],{2}
Out[7]=
{{11},{2211,1221,1122},{332211,233211,223311,221331,221133,331221,133221,123321,122331,122133,331122,133122,113322,112332,112233}}
Properties & Relations  
(1)

SeeAlso
EulerianNumberOfTheSecondKind
 
▪
EulerianNumber
RelatedGuides
▪
Combinatorics
RelatedLinks
▪
How to visually display the Stirling permutations of
kth
order?
▪
Stirling permutation — Wikipedia
""

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