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Abstract
Let m be a positive integer and let ρ (m; n) be the proportion of permutations of the symmetric group Sym(n) whose order is coprime to m. In 2002, Pouyanne proved that (Formula Presented) where K_{m} is a complicated (unbounded) function of m. We show that there exists a positive constant C(m) such that, for all n > m, (Formula Presented) where ϕ is Euler's totient function.
Original language  English 

Article number  P1.6 
Number of pages  14 
Journal  Electronic Journal of Combinatorics 
Volume  27 
Issue number  1 
DOIs  
Publication status  Published  2020 
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Dive into the research topics of 'Permutations with orders coprime to a given integer'. Together they form a unique fingerprint.Projects
 1 Finished

Complexity of group algorithms and statistical fingerprints of groups
Praeger, C. & Niemeyer, A.
21/02/19 → 31/12/22
Project: Research