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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.07131 |
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| _version_ | 1866911284052623360 |
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| author | Wan, Zheyan |
| author_facet | Wan, Zheyan |
| contents | In this article, we construct matrices associated to Pachner $\frac{n-1}{2}$-$\frac{n-1}{2}$ moves for odd $n$ and matrices associated to Pachner $(\frac{n}{2}-1)$-$\frac{n}{2}$ moves for even $n$. The entries of these matrices are rational functions of formal variables in a field. We prove that these matrices satisfy the $n$-gon equation for any $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07131 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A matrix solution to any polygon equation Wan, Zheyan Mathematical Physics Combinatorics Quantum Algebra In this article, we construct matrices associated to Pachner $\frac{n-1}{2}$-$\frac{n-1}{2}$ moves for odd $n$ and matrices associated to Pachner $(\frac{n}{2}-1)$-$\frac{n}{2}$ moves for even $n$. The entries of these matrices are rational functions of formal variables in a field. We prove that these matrices satisfy the $n$-gon equation for any $n$. |
| title | A matrix solution to any polygon equation |
| topic | Mathematical Physics Combinatorics Quantum Algebra |
| url | https://arxiv.org/abs/2407.07131 |