Xiangshuai Dong

activity

20242026

collaborators

6 papers

math.CO2026

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

T. Wu, S. Lu, X. Dong

Let $G$ be a simple graph on $n$ vertices, and let $F (G)$ denote the number of its spanning forests. Bencs and Csikvári [Upper bound for the number of spanning forests of regular g…

math.CO2026

Solution to an open problem on the computational complexity of immanant

Xiangshuai Dong, Tingzeng Wu, Xing Gao

Immanants are a class of generalized matrix functions associated with the irreducible characters of the symmetric group. Bürgisser [SIAM J. Comput., 30 (2000), pp. 1023--1040] prov…

math.CO2026

Immanantal polynomials of the linear combination matrices of graphs

Xiangshuai Dong, Tingzeng Wu

The immanant is a generalized matrix function associated with irreducible characters of the symmetric group. The immanantal polynomial of matrix $M$ is defined as the immanant of m…

math.CO2025

Hook immanantal equalities for linear combination matrices of (di)graphs and their applications

Xiangshuai Dong, Tingzeng Wu, HongJian Lai

Let $χ_{λ}$ be an irreducible character of the symmetric group $S_{n}$ . For an $n \times n$ matrix $M = (m_{ij})$ , define the immanant of $M$ corresponding to $χ_{λ}$ by \begin{eqnarray*…

math.CO2025

Brualdi-Goldwasser-Michael problem for maximum permanents of {\rm(0,1)}-matrices

Tingzeng Wu, Xiangshuai Dong, Huazhong Lü

Let $U (n, τ)$ be the set of all {\rm(0,1)}-matrices of order $n$ with exactly $τ$ 0's. Brualdi et al. investigated the maximum permanents of all matrices in $\mathscr{U}(n…

math.CO2024

Solution to an open problem on Laplacian ratio

T. Wu

Let G be a graph. The Laplacian ratio of G is the permanent of the Laplacian matrix of G divided by the product of degrees of all vertices. The computational complexity of Laplacia…