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Let the cycle type of a permutation α ∈ S_n be the decreasing list of integers...

Let the cycle type of a permutation α ∈ S_n be the decreasing list of integers giving the lengths of the disjoint cycles in α. (e.g. the cycle type of (6 8)(3 7 2)(1 5 9)(4) = (3, 3, 2, 1) ) Show the cycle type of α and (β^-1)αβ are equivalent ∀ α, β in S_n.

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