The range of the des statistic for conjugacy classes in $S_n$
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918037623406592 |
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| author | Kares, Yisca |
| author_facet | Kares, Yisca |
| contents | We determine the range of the des statistic on every conjugacy class in the symmetric group $S_n$, prove that the minimum is $1$ (except for the identity class), and show that every intermediate value from $1$ to the maximum value is attained. We also demonstrate a constructive method to achieve every value in the range and discuss its combinatorial implications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22828 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The range of the des statistic for conjugacy classes in $S_n$ Kares, Yisca Combinatorics We determine the range of the des statistic on every conjugacy class in the symmetric group $S_n$, prove that the minimum is $1$ (except for the identity class), and show that every intermediate value from $1$ to the maximum value is attained. We also demonstrate a constructive method to achieve every value in the range and discuss its combinatorial implications. |
| title | The range of the des statistic for conjugacy classes in $S_n$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2505.22828 |