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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/2402.07798 |
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| _version_ | 1866910326984802304 |
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| author | Banaian, Esther Hoang, Anh Trong Nam Kelley, Elizabeth Miller, Weston Stack, Jason Stephen, Carolyn Williams, Nathan |
| author_facet | Banaian, Esther Hoang, Anh Trong Nam Kelley, Elizabeth Miller, Weston Stack, Jason Stephen, Carolyn Williams, Nathan |
| contents | We construct a bijection between certain Deodhar components of a braid variety constructed from an affine Kac-Moody group of type $A_{n-1}$ and vertex-labeled trees on $n$ vertices. By an argument of Galashin, Lam, and Williams using Opdam's trace formula in the affine Hecke algebra and an identity due to Haglund, we obtain an elaborate new proof for the enumeration of the number of vertex-labeled trees on $n$ vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07798 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An elaborate new proof of Cayley's formula Banaian, Esther Hoang, Anh Trong Nam Kelley, Elizabeth Miller, Weston Stack, Jason Stephen, Carolyn Williams, Nathan Combinatorics We construct a bijection between certain Deodhar components of a braid variety constructed from an affine Kac-Moody group of type $A_{n-1}$ and vertex-labeled trees on $n$ vertices. By an argument of Galashin, Lam, and Williams using Opdam's trace formula in the affine Hecke algebra and an identity due to Haglund, we obtain an elaborate new proof for the enumeration of the number of vertex-labeled trees on $n$ vertices. |
| title | An elaborate new proof of Cayley's formula |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2402.07798 |