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I am a little confused about an example. By definition,

A cycle of m symbols CAN be written as a product of m - 1 transpositions.

(x1 x2 x3 ... xn) = (x1 x2)(x1 x3)...(x1 xn)

Now

Express the permutation (23) on S = {1,2,3,4,5} as a product of transpositions.

(23) = (12) o (23) o (13) = (12) o (13) o (12)

I can see how it works. But based on the def. I don't see how they came up with the answer. I know this is simple but I don't see it. What the hey?

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# Permutations and Transpositions

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