# Math Help - permutation questions

1. ## permutation questions

Dear All.

There are two permutations

x = (1 2 3 4 5 6 7 8)
(3 5 2 1 4 6 8 7)

y = (1 2 3 4 5 6 7 8)
(6 1 5 7 3 2 8 4)

Can I ask how I can express these as a product of transposition?
I got a disjoint cycle for x (1 3 2 5 4) (7 8), then transposition is just (1 3) (3 2) (2 5) (5 4) (7 8)?
And what is signature of both of them? I got odd for both of them.
Is this correct?

2. ## Re: permutation questions

Since (7 8) is already a transposition, we just need to focus on (1 3 2 5 4).

I find that:

(1 3)(3 2)(2 5)(5 4) = (1 3)(3 2)(2 5 4) = (1 3)(2 5 4 3) = (1 3 2 5 4), so you are correct. If you did y the same way congratulations!