A. Beker

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math.CO2026

The RÃ©nyi entropy of the order of a random permutation

Adrian Beker

We study the distribution of the order of a random permutation of $[n]$ through the lens of RÃ©nyi entropy. In particular, we obtain an asymptotic for the RÃ©nyi $q$ -entropy of the…

math.CO2025

The most probable order of a random permutation

Adrian Beker

Given positive integers $n$ and $m$ , let $p_{n} (m)$ be the probability that a uniform random permutation of $[n]$ has order exactly $m$ . We show that, as $n \to \infty$ , the maximum…