Limit Theorems for Descents and Inversions of Shelf-Shuffles
Probability
2025-10-02 v1 Combinatorics
Abstract
We prove central limit theorems for the number of descents and the number of inversions after a shelf-shuffle. In particular, we bound the convergence rate for the number of inversions independently of the number of shelves. Along the way, we determine the mean and variance for the number of inversions after a shelf shuffle, which was also an open problem. We also suggest ways to extend our results to biased shelf-shuffles.
Cite
@article{arxiv.2510.00343,
title = {Limit Theorems for Descents and Inversions of Shelf-Shuffles},
author = {Alexander Clay},
journal= {arXiv preprint arXiv:2510.00343},
year = {2025}
}
Comments
10 pages