9 papers
A transfer principle for Steklov eigenvalue estimates of graphs
Xiongfeng Zhan, Jin-Xin Zhou
In this paper, we establish a new variant of the Burger-Brooks transfer principle, which allows us to apply spectral estimates for measured Riemannian surfaces to obtain the follow…
Higher Steklov eigenvalues of graphs on surfaces
Xiongfeng Zhan, Zhe You
In this paper, we study the higher Steklov eigenvalues of graphs on surfaces. We obtain the upper bound of higher Steklov eigenvalues of a finite graph with boundary and ge…
A note on the Björner--Kalai theorem
Xiongfeng Zhan, Xueyi Huang
In 1988, Björner and Kalai used combinatorial shadow functions to characterize the maximal Betti sequence for a given -vector and the minimal -vector for a given Betti seque…
Eigenvalue bounds for combinatorial Laplacians and an application to random complexes
Xiongfeng Zhan, Xueyi Huang, Jin-Xin Zhou
This paper establishes new eigenvalue bounds for combinatorial Laplacians of simplicial complexes, extending previous results for flag complexes by Lew (2024) and general complexes…
Combinatorial Laplacians and Relative Homology of Complex Pairs
Xiongfeng Zhan, Xueyi Huang, Lu Lu
As a discretization of the Hodge Laplacian, the combinatorial Laplacian of simplicial complexes has garnered significant attention. In this paper, we study combinatorial Laplacians…
Fractional revival on quasi-abelian Cayley graphs
Yi Fang, Xueyi Huang, Xiaogang Liu +1
Fractional revival, a quantum transport phenomenon critical to entanglement generation in quantum spin networks, generalizes the notion of perfect state transfer on graphs. A Cayle…