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!
Dear All.
Can I ask something?
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?