Real Zeros and Normal Distribution for statistics on Stirling permutations defined by Gessel and Stanley

Miklos Bona

Real Zeros and Normal Distribution for statistics on Stirling permutations defined by Gessel and Stanley

Combinatorics 2008-03-12 v2 Probability

Authors: Miklos Bona

Abstract

We study Stirling permutations defined by Gessel and Stanley. We prove that their generating function according to the number of descents has real roots only. We use that fact to prove that the distribution of these descents, and other, equidistributed statistics on these objects converge to a normal distribution.

Keywords

Stirling permutations real zeros normal distribution generating function descents equidistributed statistics Gessel and Stanley

Cite

@article{arxiv.0708.3223,
  title  = {Real Zeros and Normal Distribution for statistics on Stirling permutations defined by Gessel and Stanley},
  author = {Miklos Bona},
  journal= {arXiv preprint arXiv:0708.3223},
  year   = {2008}
}

Comments

8 pages

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