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Partitions(outer=Partition([3,2,2])) is broken #39922

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@mantepse

Description

@mantepse

Steps To Reproduce

sage: P = Partitions(outer=Partition([3,2,2]))
sage: list(P)
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)
Cell In[130], line 1
----> 1 list(P)

File ~/sage/src/sage/categories/enumerated_sets.py:499, in EnumeratedSets.ParentMethods.__len__(self)
    497     c = self.cardinality()
    498     if c is Infinity:
--> 499         raise NotImplementedError('infinite set')
    500     return int(c)
    501 except AttributeError:

NotImplementedError: infinite set
sage: P.cardinality()
+Infinity
sage: P = Partitions(outer=[oo,2,2])
TypeError: unhashable type: 'list'

Expected Behavior

  • the argument passed via outer should be allowed to be a list
  • if it can be converted to a partition, the cardinality is not infinity

Actual Behavior

broken

Additional Information

No response

Environment

irrelevant

Checklist

  • I have searched the existing issues for a bug report that matches the one I want to file, without success.
  • I have read the documentation and troubleshoot guide

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