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

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arXiv
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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.

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