Limit Theorems for Descents and Inversions of Shelf-Shuffles
Alexander Clay
Published: 2025/9/30
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.