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arXiv · 1902.00978

Central limit theorem for peaks of a random permutation in a fixed conjugacy class of $S_n$

Jason Fulman·Gene B. Kim·Sangchul Lee
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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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Jason Fulman, Gene B. Kim, Sangchul Lee. 2019-02-03. Central limit theorem for peaks of a random permutation in a fixed conjugacy class of $S_n$. https://arxiv.org/abs/1902.00978

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