Permutation of a set

Stub grade: A*

This page is a stub

This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:

Very important to get some work on the symmetric group in play, then this may be demoted. Demote to grade A once the notation section has been added, there's a lot to say there.

Note: permutation on a set redirects here.

Definition

Let [ilmath]X[/ilmath] be any non-empty set, [ilmath]X[/ilmath]. A permutation on [ilmath]X[/ilmath] is:

• A bijective function, [ilmath]f:X\rightarrow X[/ilmath]. Recall that bijective means injective (1:1) and surjective (onto).

Claims:

The collection of all permutations of a set forms a group under function composition - see the permutation group. The symmetric group is a special case of the permutation group when the set is finite.