I am trying to read through and understand about permutations, and I have a couple of questions.(adsbygoogle = window.adsbygoogle || []).push({});

First, How do you write a permutation as a transposition?

The example that I have is (3, 10, 1, 4, 5, 7, 2, 8, 6, 9), and I said that it is equal to (3, 10)(10, 1)(1, 4)(4, 5)(5, 7)(7, 2)(2, 8)(8, 6)(6, 9). I think I followed how the book showed to do this, so I think my answer is corect (right?), but I have no idea WHY this works.

Am I correct in assuming that I use the (3, 10, 1, 4, 5, 7, 2, 8, 6, 9), since the original question writes this as (1 2 3 4 5 6 7 8 9 10

(3, 10, 1, 4, 5, 7, 2, 8, 6, 9).

Also, if you could answer Why this works, it would be very helpful.

Also, how exactly do I compute this long composition problem? I don't understand how it works. I understand that I work from right to left, but if I know that 6 goes to 9 and 9 goes to 6, how do I go backwards to where I started? (Hopefully that question makes sense).

Also, why is the order of two cycles equal to the least common multiple of elements in each cycle?

Am I correct in assuming that in the following cycle:

(1, 3, 10)(2, 4, 5, 7)(6, 8)(9), the order is lcm[3, 4, 2, 1] = 12?

Again, explaining why would be extremely helpful.

Thanks.

Colleen

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# Permutations Question

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