Cycle type of random permutations: A toolkit

Abstract

We prove a number of results, new and old, about the cycle type of a random permutation on S_n. Underlying our analysis is the idea that the number of cycles of size k is roughly Poisson distributed with parameter 1/k. In particular, we establish strong results about the distribution of the number of cycles whose lengths lie in a fixed but arbitrary set I. Our techniques are motivated by the theory of sieves in number theory.

arXiv commentFinal published version for in Discrete Analysis

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• Euler's constant: Euler's work and modern developments
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Cited by in corpus (1)

• Crystalline Spectral Form Factors