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

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

2007-08-23

arxiv.org/abs/0708.3223v2

Mathematics

Combinatorics

8 pages

Scientific paper

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.

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