A curious symmetric decomposition of the (des, exc)-Eulerian polynomials
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911912051081216 |
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| author | Ma, Shi-Mei Mansour, Toufik Yeh, Yeong-Nan |
| author_facet | Ma, Shi-Mei Mansour, Toufik Yeh, Yeong-Nan |
| contents | One of the most central result in combinatorics says that the descent statistic and the excedance statistic are equidistribued over the symmetric group. As a continuation of the work of Shareshian-Wachs (Adv. Math., 225(6) (2010), 2921--2966), we provide a curious $t$-symmetric decomposition for the generating polynomial of the joint distribution of the descent and excedance statistics over the symmetric group. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_06365 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A curious symmetric decomposition of the (des, exc)-Eulerian polynomials Ma, Shi-Mei Mansour, Toufik Yeh, Yeong-Nan Combinatorics 05A05 One of the most central result in combinatorics says that the descent statistic and the excedance statistic are equidistribued over the symmetric group. As a continuation of the work of Shareshian-Wachs (Adv. Math., 225(6) (2010), 2921--2966), we provide a curious $t$-symmetric decomposition for the generating polynomial of the joint distribution of the descent and excedance statistics over the symmetric group. |
| title | A curious symmetric decomposition of the (des, exc)-Eulerian polynomials |
| topic | Combinatorics 05A05 |
| url | https://arxiv.org/abs/2406.06365 |