Steps To Reproduce

sage: S = Permutations(range(5), 2)
sage: S.cardinality()
120
sage: len(S.list())
20
sage: S.cardinality()
20

Similar to #20317.

Expected Behavior

The correct cardinality of permutations with a given length is returned, and in an efficient manner.

Actual Behavior

It seems that the class Permutations_setk in permutation.py does not override the cardinality() method from its parent class. After calling .list(), the generic _cardinality_from_list method from the category framework is used.

Replacing range(5) with [0,1,2,3,4] or even [99,1,2,3,4] gives the same result. But replacing it with 5 or [1,2,3,4,5] gives the correct behavior, since the class of S is now Permutations_nk, whose cardinality() method computes a quotient of factorials (maybe falling_factorial(n,k) is better there).

Additional Information

Somewhat related, there are some naive cardinality() methods in https://github.com/sagemath/sage/blob/develop/src/sage/combinat/permutation.py for other classes.

Environment

• OS: Linux
• Sage Version: 10.7

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