# Descent-inversion statistics in riffle shuffles

@article{Islak2013DescentinversionSI,
title={Descent-inversion statistics in riffle shuffles},
author={Umit Islak},
journal={Turkish Journal of Mathematics},
year={2013},
volume={42}
}
• Umit Islak
• Published 10 March 2013
• Mathematics
• Turkish Journal of Mathematics
This paper studies statistics of riffle shuffles by relating them to random word statistics with the use of inverse shuffles. Asymptotic normality of the number of descents and inversions in riffle shuffles with convergence rates of order $1/\sqrt{n}$ in the Kolmogorov distance are proven. Results are also given about the lengths of the longest alternating subsequences of random permutations resulting from riffle shuffles. A sketch of how the theory of multisets can be useful for statistics of… Expand
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