How often is a permutation an n'th power?

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Michael Larsen (University of Missouri) This is my paper · ORCID

classification math.CO

keywords permutationpowerargumentasymptoticallyfixedgivelettersoften

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We give a short argument that for any fixed n, the probability that a permutation on m letters is an n'th power is asymptotically C m^{phi(n)/n - 1}.

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Most Words are Geometrically Almost Uniform
math.GR 2019-08 conditional novelty 8.0 of 10

For each fixed simple algebraic group over a finite field, the probability that a random word of length n is geometrically almost uniform tends to 1 as n grows.