How often is a permutation an n'th power?

1997/12/03 by Michael Larsen, Larsen, Michael
Biochemistry, Genetics and Molecular Biology · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Genome Rearrangement Algorithms #math.CO

paper · pdf · doi:10.48550/arxiv.math/9712223

2 pages

arxiv created 1997/12/03 · openalex publication_date 1997/12/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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