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Title: Cycle type of random permutations: a toolkit
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.  more » « less
Award ID(s):
1802139
NSF-PAR ID:
10440639
Author(s) / Creator(s):
Editor(s):
Gowers, W. T.
Date Published:
Journal Name:
Discrete analysis
Volume:
2022
Issue:
9
ISSN:
2397-3129
Page Range / eLocation ID:
1-36
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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