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Combinatorics

Tutorials

  • Combinatorics

Guides

  • Combinatorics
  • Functions I understand in combinatorics

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  • Combinatorics
  • Stirling permutation

Symbols

  • CanonicalMultiset
  • CentralBinomialCoefficient
  • ConjugatePartition
  • DescendingSublists
  • DivisorHasseDiagram
  • DominatingIntegerPartitionQ
  • DurfeeSquare
  • EnumerateMultisetPartialDerangements
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  • EulerianNumberOfTheSecondKind
  • FerrersDiagram
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  • FindAscentElements
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  • FindDescentPositions
  • FrobeniusSymbolFromPartition
  • FromInversionVector
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  • GaussFactorial
  • GrayCode
  • HasseDiagram
  • HookLengths
  • HuffmanCodeWords
  • HuffmanDecode
  • HuffmanEncode
  • IntegerPartitionQ
  • InverseFibonacci
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  • InversionCount
  • InversionVectorQ
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  • LucasNumberU1
  • LucasNumberV2
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  • PartialOrderGraphQ
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PeterBurbery`Combinatorics`
HasseDiagram
​
HasseDiagram
[f,s]
constructs a Hasse diagram of the partial order set (poset) defined by the binary relation
f
and set
s
.
​
Details and Options

Examples  
(5)
Basic Examples  
(3)
The Hasse diagram of the set of all subsets of a three-element set, ordered by inclusion:
In[1]:=
HasseDiagram
[SubsetQ,Subsets[{"x","y","z"}],VertexShapeFunction"Name"]
Out[1]=
​
Permutations differing by one transposition, ordered by the number of inversions:
In[1]:=
HasseDiagram
Count[#1-#2,0]2&&
InversionCount
[#1]>
InversionCount
[#2]&,Permutations[{1,2,3,4}],VertexShapeFunction"Name"
Out[1]=
​
Positive integers ordered by divisibility:
In[1]:=
HasseDiagram
[(Mod[#1,#2]0)&,Range[12],VertexLabels"Name"]
Out[1]=
Applications  
(1)

Properties & Relations  
(1)

SeeAlso
Graph
 
▪
RelationGraph
 
▪
TransitiveReductionGraph
 
▪
PartialOrderGraphQ
 
▪
DivisorHasseDiagram
RelatedGuides
▪
Combinatorics
RelatedLinks
HasseDiagram
Resource Function contributed by Wolfram Staff (original content by Sriram V. Pemmaraju and Steven S. Skiena)
""

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