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Sep 20, 2017 at 9:46 comment added Mark Wildon The proportion of permutations of $\{1,\ldots,N\}$ commuting with an $N$-cycle is $1/N$, so small if $N$ is large. But +1 for the idea of looking at the (position-dependent) conjugate of $S_\pi$.
Sep 15, 2017 at 1:38 history answered zabroshenie goroda CC BY-SA 3.0