# Writing Permutations as Product of Disjoint Cycles

I'm having some trouble understanding permutation products and disjoint cycles. The problem I'm stuck on is:

Write $(13257)(23)(47512)$ as a product of disjoint cycles.

I evaluated the product, and I got $(1 2 4 7)$, which isn't right (checked against the answer). Any help through the problem would be greatly appreciated. Thank you.

• What makes you think that 4 is sent to 7? – drhab Sep 25 '16 at 12:50
• You should find $(124)(35)$? I'm asking this as the convention on the order of composition may differ. – Bernard Sep 25 '16 at 12:53
• I think the convention we're using is right -> left evaluation. And the answer was (1 4 7 2)(3)(5)(6), but I don't know how to get there. – Max Sep 25 '16 at 13:02
• Haha nevermind, I was reading the answer to a different question. You're right @Bernard, it is (1 2 4)(3 5), and I understand why now. Thanks! – Max Sep 25 '16 at 13:14