# Permutations : Parity

Show that $ and %$%^-1 have the same parity for all % and $ in Sn. (Sn is the symmetric group of degree n)

Â© BrainMass Inc. brainmass.com March 4, 2021, 5:51 pm ad1c9bdddfhttps://brainmass.com/math/combinatorics/permutations-parity-functions-14208

#### Solution Preview

We know for any %, % and % have the same parity.

Now we define sgn$=1 if $ ...

#### Solution Summary

Parity in a symmetric group is concisely proven.

$2.49