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You may find answers to your questions by typing, in a Sage session,

Partition?

as well as

Permutation?

and

SymmetricGroupRepresentation?

In particular, you will see that the documentation returned by Partition? says: A partition p of a nonnegative integer n is a non-increasing list of positive integers (the parts of the partition) with total sum n

You may find answers to your questions by typing, in a Sage session,

Partition?
 SymmetricGroupRepresentation?

as well as

Permutation?
Partition?

and

SymmetricGroupRepresentation?

Permutation?

In particular, you will see that the documentation returned by Partition? says: A partition p of a nonnegative integer n is a non-increasing list of positive integers (the parts of the partition) with total sum n

You may find answers to your questions by typing, in a Sage session,

 SymmetricGroupRepresentation?

as well as

Partition?

and

Permutation?

Permutation?

In particular, you will see that the documentation returned by Partition? says: A partition p of a nonnegative integer n is a non-increasing list of positive integers (the parts of the partition) with total sum n