Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 PartitionFromFrobeniusSymbol

Source Notebook

Construct the corresponding partition, given a Frobenius symbol

Contributed by: George Beck

ResourceFunction["PartitionFromFrobeniusSymbol"][f]

gives the partition whose Frobenius symbol is f.

Details and Options

See the documentation for ResourceFunction["FrobeniusSymbolFromPartition"] for illustrative examples.

Examples

Basic Examples (2) 

A Frobenius symbol is matrix with two decreasing rows of nonnegative integers:

In[1]:=
f1 = {{6, 5, 1}, {4, 2, 0}};

This finds the partition corresponding to the Frobenius symbol:

In[2]:=
ResourceFunction["PartitionFromFrobeniusSymbol"]@f1
Out[2]=

Here is another example:

In[3]:=
f2 = {{7, 5, 2, 0}, {5, 4, 1, 0}};
In[4]:=
ResourceFunction["PartitionFromFrobeniusSymbol"]@f2
Out[4]=

Properties and Relations (1) 

Confirm that partitions and Frobenius symbols round-trip as expected:

In[5]:=
f1 == ResourceFunction[ ResourceObject[<|"Name" -> "FrobeniusSymbolFromPartition", "UUID" -> "0216c2ef-f6e6-4aa2-bbcf-2739d7d91255", "ResourceType" -> "Function", "Version" -> "1.0.0", "Description" -> "Get a pair of list representing the Ferrers diagram of a partition", "RepositoryLocation" -> URL[ "https://www.wolframcloud.com/objects/resourcesystem/api/1.0"], "WolframLanguageVersionRequired" -> "10.0", "SymbolName" -> "FunctionRepository`$88f66cb969d04c4089178b997a7ffa12`FrobeniusSymbolFromPartition", "FunctionLocation" -> CloudObject[ "https://www.wolframcloud.com/objects/51b93753-c7d3-4344-8546-0ef539070ccf"], "ShortName" -> "FrobeniusSymbolFromPartition"|>, ResourceSystemBase -> "https://www.wolframcloud.com/objects/resourcesystem/api/1.0"]]@ ResourceFunction["PartitionFromFrobeniusSymbol"]@f1
Out[5]=
In[6]:=
f2 == ResourceFunction[ ResourceObject[<|"Name" -> "FrobeniusSymbolFromPartition", "UUID" -> "0216c2ef-f6e6-4aa2-bbcf-2739d7d91255", "ResourceType" -> "Function", "Version" -> "1.0.0", "Description" -> "Get a pair of list representing the Ferrers diagram of a partition", "RepositoryLocation" -> URL[ "https://www.wolframcloud.com/objects/resourcesystem/api/1.0"], "WolframLanguageVersionRequired" -> "10.0", "SymbolName" -> "FunctionRepository`$88f66cb969d04c4089178b997a7ffa12`FrobeniusSymbolFromPartition", "FunctionLocation" -> CloudObject[ "https://www.wolframcloud.com/objects/51b93753-c7d3-4344-8546-0ef539070ccf"], "ShortName" -> "FrobeniusSymbolFromPartition"|>, ResourceSystemBase -> "https://www.wolframcloud.com/objects/resourcesystem/api/1.0"]]@ ResourceFunction["PartitionFromFrobeniusSymbol"]@f2
Out[6]=

Publisher

George Beck

Version History

  • 3.0.0 – 07 June 2019
  • 2.0.0 – 10 May 2019
  • 1.0.0 – 17 April 2019

Source Metadata

  • Citation:
    George E. Andrews and Kimmo Eriksson, Integer Partitions, Cambridge University Press, 2004, p. 78.

Related Resources

License Information