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arXiv · 2406.07795

The smith normal form of the walk matrix of the Dynkin graph $A_n$

Liangwei Huang·Yan Xu·Haicheng Zhang
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Abstract

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 $$\diag(\underbrace{1,\ldots,1}_{\lceil\frac{n}{2}\rceil},0,\ldots,0).$$

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Liangwei Huang, Yan Xu, Haicheng Zhang. 2024-06-12. The smith normal form of the walk matrix of the Dynkin graph $A_n$. https://arxiv.org/abs/2406.07795

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