The distribution of the root degree of a random permutation
Abstract
Given a permutation ω of {1, n}, let R(ω) be the root degree of ω, i.e. the smallest (prime) integer r such that there is a permutation σ with ω = σ r. We show that, for ω chosen uniformly at random, R(ω) = (lnlnn - 3lnlnln n + O p (1)) -1 lnn, and find the limiting distribution of the remainder term. © 2009 János Bolyai Mathematical Society and Springer Verlag.
Publication Title
Combinatorica
Recommended Citation
Bollobás, B., & Pittel, B. (2009). The distribution of the root degree of a random permutation. Combinatorica, 29 (2), 131-151. https://doi.org/10.1007/s00493-009-2343-3
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