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In: Advanced Math

Write down every permutation in S3 as a product of 2-cycles in the most efficient way...

Write down every permutation in S3 as a product of 2-cycles in the most efficient way you can find (i.e., use the fewest possible transpositions). Now, write every permutation in S3 as a product of adjacent 2-cycles, but don’t worry about whether your decomposition are efficient. Any observations about the number of transpositions you used in each case? Think about even versus odd.

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