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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/2406.09369 |
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| _version_ | 1866911916343951360 |
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| author | Archer, Kassie Geary, Aaron |
| author_facet | Archer, Kassie Geary, Aaron |
| contents | We consider a few special cases of the more general question: How many permutations $π\in\mathcal{S}_n$ have the property that $π^2$ has $j$ descents for some $j$? In this paper, we first enumerate Grassmannian permutations $π$ by the number of descents in $π^2$. We then consider all permutations whose square has exactly one descent, fully enumerating when the descent is "small" and providing a lower bound in the general case. Finally, we enumerate permutations whose square or cube has the maximum number of descents, and finish the paper with a few future directions for study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09369 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Descents in powers of permutations Archer, Kassie Geary, Aaron Combinatorics We consider a few special cases of the more general question: How many permutations $π\in\mathcal{S}_n$ have the property that $π^2$ has $j$ descents for some $j$? In this paper, we first enumerate Grassmannian permutations $π$ by the number of descents in $π^2$. We then consider all permutations whose square has exactly one descent, fully enumerating when the descent is "small" and providing a lower bound in the general case. Finally, we enumerate permutations whose square or cube has the maximum number of descents, and finish the paper with a few future directions for study. |
| title | Descents in powers of permutations |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2406.09369 |