The smith normal form of the walk matrix of the Dynkin graph $A_n$
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909222211420160 |
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| author | Huang, Liangwei Xu, Yan Zhang, Haicheng |
| author_facet | Huang, Liangwei Xu, Yan Zhang, Haicheng |
| contents | In this paper, we give the rank of the walk matrix of the Dynkin graph $A_n$, and prove that its Smith normal form is $$\diag(\underbrace{1,\ldots,1}_{\lceil\frac{n}{2}\rceil},0,\ldots,0).$$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07795 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The smith normal form of the walk matrix of the Dynkin graph $A_n$ Huang, Liangwei Xu, Yan Zhang, Haicheng Combinatorics In this paper, we give the rank of the walk matrix of the Dynkin graph $A_n$, and prove that its Smith normal form is $$\diag(\underbrace{1,\ldots,1}_{\lceil\frac{n}{2}\rceil},0,\ldots,0).$$ |
| title | The smith normal form of the walk matrix of the Dynkin graph $A_n$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2406.07795 |