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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.10462 |
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Table of Contents:
- In this paper, we present a detailed proof for the exhibition of a cutoff for the one-sided transposition (OST) shuffle on the generalized symmetric group $G_{m,n}$. Our work shows that based on techniques for $m \leq 2$ proven by Matheau-Raven, we can prove the cutoff in total variation distance and separation distance for an unbiased OST shuffle on $G_{m,n}$ for any fixed $m \geq 1$ in time $n \log(n)$. We also prove the branching rules for the simple modules of $G_{m,n}$ and lay down some of the mathematical foundation for proving the conjecture for the cutoff in total variation distance for any general biased OST shuffle on $G_{m,n}$.