Dear all,

my intention was to fix a small shortcoming, reported in 
https://github.com/sagemath/sage/issues/38897, which surfaced a few further 
small problems.

One thing I'm unsure about is the following:

Partitions currently inherits from UniqueRepresentation.  However, it is 
frequently used to get the cardinality of certain subsets, e.g., Partitions 
of restricted length or restricted part size.  Thus, for each combination 
of restrictions we create an entry in the global cache. In the example 
code, *very* many such parents a created.

I just checked IntegerVectors, which also accepts such a wide range of 
combinations of parameters.  In this class, only certain subclasses have 
UniqueRepresentation.  Should we do the same for Partitions?

It is actually not completely clear to me what UniqueRepresentation is good 
for in this setting.  Wouldn't it make sense only for parents that are 
likely to be used very often?

Have a nice day,

Martin  

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