A proof of Xin-Zhang's tridiagonal determinant conjecture (extended version)
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910042085654528 |
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| author | Hu, Jiaqiang Zhang, Chen |
| author_facet | Hu, Jiaqiang Zhang, Chen |
| contents | We confirm a recent conjecture of Xin and Zhang, which establishes a simple product formula for the characteristic polynomial of an $(n-1) \times (n-1)$ tridiagonal matrix $C$. This characteristic polynomial arises from a recurrence relation that enumerates $n \times n$ nonnegative integer matrices with all row and column sums equal to $t$, also called the Ehrhart polynomial of the $n$th Birkhoff polytope. Moreover, we extend our method to broader families of tridiagonal matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03082 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A proof of Xin-Zhang's tridiagonal determinant conjecture (extended version) Hu, Jiaqiang Zhang, Chen Combinatorics We confirm a recent conjecture of Xin and Zhang, which establishes a simple product formula for the characteristic polynomial of an $(n-1) \times (n-1)$ tridiagonal matrix $C$. This characteristic polynomial arises from a recurrence relation that enumerates $n \times n$ nonnegative integer matrices with all row and column sums equal to $t$, also called the Ehrhart polynomial of the $n$th Birkhoff polytope. Moreover, we extend our method to broader families of tridiagonal matrices. |
| title | A proof of Xin-Zhang's tridiagonal determinant conjecture (extended version) |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.03082 |