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arXiv · 1809.10912

Permutations With Equal Orders

Huseyin Acan·Charles Burnette·Sean Eberhard·Eric Schmutz·James Thomas
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Abstract

Let $P(n)$ be the probability that two independent, uniformly random permutations of $[n]$ have the same order, and let $K(n)$ be the probability that they are in the same conjugacy class. Answering a question of Thibault Godin, we prove that $ P(n)=n^{-2+o(1)}$ and that $\lim\sup \frac{ P(n) }{ K(n) }=\infty.$

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Huseyin Acan, Charles Burnette, Sean Eberhard, Eric Schmutz, James Thomas. 2021-01-01. Permutations With Equal Orders. https://doi.org/10.1017/s0963548321000043

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