On the cycle structure of the product of random maximal cycles

The subject of this paper is the cycle structure of the random permutation $σ$ of $[N]$, which is the product of $k$ independent random cycles of maximal length $N$. We use the character-based Fourier transform to study the number of cycles of $σ$ and also the distribution of the elements of the subset $[\ell]$ among the cycles of $σ$.

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