Let α (alpha) all in S_n be a cycle of length l. Prove that if α = τ_1 · · · τ_s, where τ_i are transpositions, then s geq l − 1.(adsbygoogle = window.adsbygoogle || []).push({});

I'm trying to get a better understanding of how to begin proofs. I'm always a little lost when trying to solve them.

I know that I want to somehow show that s is greater than l - 1 cycles. Does this mean I need to find out or show that any l cycle can be written as a product of l-1 cycles? I wrote that

α = τ_1 · · · τ_s = (τ_1 τ_s)(τ_1 τ_s-1)...(τ_1 τ_2)

But does this qualify as a proof for showing that any l cycle can be written as a product of l-1 cycles? Even so, how does this make sense for s geq l -1? Sorry, I'm just trying to understand this more clearly.

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# Clearer Understanding of Permutation and Transpositions

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