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Combinatorics

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  • Combinatorics

Symbols

  • CanonicalMultiset
  • CentralBinomialCoefficient
  • ConjugatePartition
  • DescendingSublists
  • DivisorHasseDiagram
  • DominatingIntegerPartitionQ
  • DurfeeSquare
  • EnumerateMultisetPartialDerangements
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  • FerrersDiagram
  • Fibbinary
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  • FindAscentElements
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  • FrobeniusSymbolFromPartition
  • FromInversionVector
  • FromPartitionPlusNotation
  • FromPartitionSuperscriptNotation
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PeterBurbery`Combinatorics`
FrobeniusSymbolFromPartition
​
FrobeniusSymbolFromPartition
[p]
gives a pair of lists that count dots in the rows and columns relative to the diagonal of the Durfee square in the Ferrers diagram of the partition
p
.
​
Details and Options

Examples  
(9)
Basic Examples  
(4)
Compute the Frobenius symbol of a partition:
In[1]:=
FrobeniusSymbolFromPartition
[{7,7,4,2,1}]
Out[1]=
{{6,5,1},{4,2,0}}
​
Here we use a partition of 8 consisting of only one large part:
In[1]:=
FrobeniusSymbolFromPartition
[{8}]
Out[1]=
{{7},{0}}
​
Here the partition is 11111111, with many small parts:
In[1]:=
FrobeniusSymbolFromPartition
[{1,1,1,1,1,1,1,1}]
Out[1]=
{{0},{7}}
​
Here is an intermediate case:
In[1]:=
FrobeniusSymbolFromPartition
[{7,6,5,4,3,2,1}]
Out[1]=
{{6,4,2,0},{6,4,2,0}}
Scope  
(4)

Properties & Relations  
(1)

SeeAlso
IntegerPartitions
 
▪
PartitionsP
 
▪
FerrersDiagram
 
▪
DurfeeSquare
 
▪
PartitionFromFrobeniusSymbol
RelatedGuides
▪
Combinatorics
RelatedLinks
FrobeniusSymbolFromPartition
Resource Function created by George Beck
""

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