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

Jason Fulman; Gene B. Kim; Sangchul Lee

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

Combinatorics 2019-02-05 v1 Probability

Authors: Jason Fulman , Gene B. Kim , Sangchul Lee

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.

Keywords

central limit theorem peaks of permutations conjugacy class symmetric group analytic combinatorics generating function

Cite

@article{arxiv.1902.00978,
  title  = {Central limit theorem for peaks of a random permutation in a fixed conjugacy class of $S_n$},
  author = {Jason Fulman and Gene B. Kim and Sangchul Lee},
  journal= {arXiv preprint arXiv:1902.00978},
  year   = {2019}
}

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21 pages, 1 figure

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

Abstract

Keywords

Cite

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