Basic Examples

In[]:=
A Frobenius symbol is matrix with two decreasing rows of nonnegative integers:
f1={{6,5,1},{4,2,0}};
In[]:=
This finds the partition corresponding to the Frobenius symbol:
[◼]
PartitionFromFrobeniusSymbol
@f1
In[]:=
{7,7,4,2,1}
Out[]=
Here is another example:
f2={{7,5,2,0},{5,4,1,0}};
In[]:=
[◼]
PartitionFromFrobeniusSymbol
@f2
In[]:=
{8,7,5,4,2,2}
Out[]=

Properties and Relations

In[]:=
Confirm that partitions and Frobenius symbols round-trip as expected:
f1==
[◼]
FrobeniusSymbolFromPartition
@
[◼]
PartitionFromFrobeniusSymbol
@f1
In[]:=
True
Out[]=
f2==
[◼]
FrobeniusSymbolFromPartition
@
[◼]
PartitionFromFrobeniusSymbol
@f2
In[]:=
True
Out[]=