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Xiang-Shuai Dong

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Preprint Oct 2026

A sharp upper bound on the number of spanning forests of regular graphs

Let $G$ be a simple graph on $n$ vertices, and let $F(G)$ denote the number of its spanning forests. Bencs and Csikv\'ari [Upper bound for the number of spanning forests of regular graphs, European J. Combin. 110 (2023) 103677] proved that every $r$-regular graph $G$ with $r\geq 2$ satisfies $F(G) \leq r^{n}$. They fur...

Ting-Zeng Wu, S. Lu, Xiang-Shuai Dong · 0 citations

Preprint Sep 2026

On the nonnegativity of monomial immanants for hook partitions

Let $A=(a_{ij})$ be an $n\times n$ real matrix and let $\lambda$ be a partition of $n$. Let $\phi^\lambda$ be the class function dual to the Young permutation character, and let $$ \phi^\lambda[A] = \sum_{\sigma\in\mathfrak{S}_n}\phi^\lambda(\sigma) \prod_{i=1}^{n}a_{i\sigma(i)} $$ be the corresponding monomial immanan...

Xiang-Shuai Dong, Ting-Zeng Wu, Xing Gao · 0 citations