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arXiv · 2310.06659

On the average number of cycles in conjugacy class products

Jesse Campion Loth·Amarpreet Rattan
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Abstract

We show that for the product of two fixed point free conjugacy classes, the average number of cycles is always very similar. Specifically, our main result is that for a randomly chosen pair of fixed point free permutations of cycle types $α$ and $β$, the average number of cycles in their product is between $H_n-3$ and $H_n+1$, where $H_n$ is the harmonic number.

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Jesse Campion Loth, Amarpreet Rattan. 2024-10-22. On the average number of cycles in conjugacy class products. https://arxiv.org/abs/2310.06659

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