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I came across the following question which I haven’t seen before: Question. Fix $ k\ge 3$ . For infinitely many $ n$ , does there exists a generating set $ \langle R_n \rangle = S_n$ , $ |R_n|=k$ , such that the corresponding (undirected) Cayley graph $ \Gamma(S_n,R_n)$ is edge-transitive? Perhaps, there a simple explicitRead more

I apologize in advance if this is too amateur, this is not really my area, but I’m very curious. We have a permutation $ \pi \in S_n$ and we want to represent it as a product of $ (1\;2)$ and $ (1\;2\;\ldots\; n)$ . What is the minimum number of transpositions needed to do it?Read more