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Central Limit Theorem for Peaks of a Random Permutation in a Fixed Conjugacy Class of \(S_n\)

Abstract

The number of peaks of a random permutation is known to be asymptotically normal. We give a new proof of this and prove a central limit theorem for the distribution of peaks in a fixed conjugacy class of the symmetric group. Our technique is to apply analytic combinatorics to study a complicated but exact generating function for peaks in a given conjugacy class.

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Acknowledgements

We are very grateful to two referees for many detailed comments. Fulman was supported by Simons Foundation Grant 400528.

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Correspondence to Jason Fulman.

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Fulman, J., Kim, G.B. & Lee, S. Central Limit Theorem for Peaks of a Random Permutation in a Fixed Conjugacy Class of \(S_n\). Ann. Comb. 26, 97–123 (2022). https://doi.org/10.1007/s00026-021-00561-4

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  • DOI: https://doi.org/10.1007/s00026-021-00561-4