General routines Partitions Comparing partitions Operations on partitions

Operations on partitions

You can add partitions componentwise: A familiar operation on partitions is conjugation, or association, as it is also called. This is done using the the standard routine conjugate, or if you are an expert using the special routine conjugate_partition().
Example:
...
scan(PARTITION,a);
println(a);
conjugate_partition(a,b);
...
Partitions are represented graphically using the Ferrers diagram. The routine to call it is the standard routine ferrers, which then calls the routine ferrers_partition. In the representation theory of symmetric groups you often compute the so-called hooklengths in the Ferrers diagram: Hook lengths are mostly used to compute the dimension of an ireducible representation of the symmetric group, which is labeled by a partition. You can do this directly using the standard routine dimension(), which calls dimension_partition: Another object which is labeled by partitions are the classes and the centralizers of elements in the symmetric group. We can compute their orders: Finally there is a routine for checking the installation of a PARTITIONobject:
harald.fripertinger "at" uni-graz.at, May 26, 2011

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