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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.01211 |
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Table of Contents:
- In this paper, we generalise several recent results by Archer and Geary on descents in powers of permutations, and confirm all their conjectures. Specifically, for all $k\in\mathbb{Z}^+$, we prove explicit formulas for the expected numbers of descents and inversions in the $k$-th powers of permutations in $\mathcal{S}_n$ for all $n\geq2k+1$. We also compute the number of Grassmanian permutations in $\mathcal{S}_n$ whose $k$-th powers remain Grassmanian, and the number of permutations in $\mathcal{S}_n$ whose $k$-th powers have the maximum number of descents.