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Combinatorics

Tutorials

  • Combinatorics

Guides

  • Combinatorics
  • Functions I understand in combinatorics

Tech Notes

  • Combinatorics
  • Stirling permutation

Symbols

  • CanonicalMultiset
  • CentralBinomialCoefficient
  • ConjugatePartition
  • DescendingSublists
  • DivisorHasseDiagram
  • DominatingIntegerPartitionQ
  • DurfeeSquare
  • EnumerateMultisetPartialDerangements
  • EulerianCatalanNumber
  • EulerianNumber
  • EulerianNumberOfTheSecondKind
  • FerrersDiagram
  • Fibbinary
  • FibonacciEncode
  • FindAscentElements
  • FindAscentPositions
  • FindDescentElements
  • FindDescentPositions
  • FrobeniusSymbolFromPartition
  • FromInversionVector
  • FromPartitionPlusNotation
  • FromPartitionSuperscriptNotation
  • GaussFactorial
  • GrayCode
  • HasseDiagram
  • HookLengths
  • HuffmanCodeWords
  • HuffmanDecode
  • HuffmanEncode
  • IntegerPartitionQ
  • InverseFibonacci
  • InverseGrayCode
  • InversionCount
  • InversionVectorQ
  • LehmerCodeFromPermutation
  • LucasNumberU1
  • LucasNumberV2
  • ModifiedCentralBinomialCoefficient
  • Multichoose
  • MultisetAssociation
  • MultisetPartialDerangements
  • NarayanaNumber
  • NextPermutation
  • NumberOfTableaux
  • OrderedTupleFromIndex
  • OrderedTupleIndex
  • OrderlessCombinations
  • OrderlessCombinationsOfUnmarkedElements
  • PartialOrderGraphQ
  • PartitionCrank
  • PartitionFromFrobeniusSymbol
  • PartitionPlusNotation
  • PartitionRank
  • PartitionSuperscriptNotation
  • PermutationCountByInversions
  • PermutationFromIndex
  • PermutationGraph
  • PermutationIndex
  • PermutationMajorIndex
  • PermutationToTableaux
  • Phitorial
  • PosetQ
  • PosetToTableau
  • Primorial
  • QExponential
  • QMultinomial
  • RandomYoungTableau
  • RationalNumberRepeatingDecimalPeriod
  • ReflexiveGraphQ
  • SecantNumber
  • SelectPermutations
  • SelectSubsets
  • SelectTuples
  • SelfConjugatePartitionQ
  • SignedLahNumber
  • StandardYoungTableaux
  • StirlingPermutationGraph
  • StirlingPermutations
  • StrictIntegerPartitions
  • SubsetFromIndex
  • SubsetIndex
  • TableauQ
  • TableauToPoset
  • TableauxToPermutation
  • TangentNumber
  • ToInversionVector
  • TransitiveGraphQ
  • TransposeTableau
  • TupleFromIndex
  • TupleIndex
  • UnsignedLahNumber
  • YoungDiagram
  • ZeckendorfRepresentation
PeterBurbery`Combinatorics`
TableauToPoset
​
TableauToPoset
[young]
converts the Young tableau
young
to a partially ordered set of coordinates.
​
Details and Options

Examples  
(2)
Basic Examples  
(1)
All Young tableaux of shape (3,2):
In[1]:=
young=
StandardYoungTableaux
[{3,2}]
Out[1]=
{{{1,2,3},{4,5}},{{1,2,4},{3,5}},{{1,2,5},{3,4}},{{1,3,4},{2,5}},{{1,3,5},{2,4}}}
Convert the Young tableaux to posets:
In[2]:=
posets=
TableauToPoset
/@young
Out[2]=
{{{1,1},{2,1},{3,1},{1,2},{2,2}},{{1,1},{2,1},{1,2},{3,1},{2,2}},{{1,1},{2,1},{1,2},{2,2},{3,1}},{{1,1},{1,2},{2,1},{3,1},{2,2}},{{1,1},{1,2},{2,1},{2,2},{3,1}}}
Show the Young tableaux with their corresponding poset diagrams:
In[3]:=
Row[Column/@Transpose[{​​Style[Grid[Map[Function[i,Item[i,FrameTrue]],Reverse[#],{2}]],24]&/@young,​​Graphics[{Arrowheads[Medium],Arrow/@Partition[#,2,1]}]&/@posets}],Spacer[20]]
Out[3]=
4
5
​
1
2
3
3
5
​
1
2
4
3
4
​
1
2
5
2
5
​
1
3
4
2
4
​
1
3
5
Scope  
(1)

SeeAlso
StandardYoungTableaux
 
▪
TableauQ
 
▪
TransposeTableau
 
▪
HookLengths
 
▪
NumberOfTableaux
 
▪
RandomYoungTableau
 
▪
PermutationToTableaux
 
▪
TableauxToPermutation
 
▪
FerrersDiagram
 
▪
HasseDiagram
RelatedGuides
▪
Combinatorics
RelatedLinks
TableauToPoset
Resource Function contributed by Ed Pegg Jr.
""

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