1 citations · 1 across the 13 of their papers we have counts for
13 papers
Sharp dispersive estimates for wave equation on lattice graphs with high dimension
Zhe You, Xiongfeng Zhan
Schultz [Comm.~Pure~Appl.~Math., 1998] first established dispersive estimates for the fundamental solution of the discrete wave equation on lattice graphs for , which…
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…
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…
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 sequen…
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…
An Extension of Pólya's Enumeration Theorem
Xiongfeng Zhan, Xueyi Huang
In combinatorics, Pólya's Enumeration Theorem is a powerful tool for solving a wide range of counting problems, including the enumeration of groups, graphs, and chemical compounds.…
Proof of Lew's conjecture on the spectral gaps of simplicial complexes
Xiongfeng Zhan, Xueyi Huang, Huiqiu Lin
As a generalization of graph Laplacians to higher dimensions, the combinatorial Laplacians of simplicial complexes have garnered increasing attention. Let be a simplicial compl…
Fourier analysis on distance-regular Cayley graphs over abelian groups
Xiongfeng Zhan, Xueyi Huang, Lu Lu
The problem of constructing or characterizing strongly regular Cayley graphs (or equivalently, regular partial difference sets) has garnered significant attention over the past hal…
Distance-regular Cayley graphs over (pseudo-) semi-dihedral groups
Xueyi Huang, Lu Lu, Xiongfeng Zhan
Distance-regular graphs are a class of regualr graphs with pretty combinatorial symmetry. In 2007, Miklavič and Potočnik proposed the problem of charaterizing distance-regular Cayl…
Distance-regular Cayley graphs over
Xiongfeng Zhan, Lu Lu, Xueyi Huang
In [Distrance-regular Cayley graphs on dihedral groups, J. Combin. Theory Ser B 97 (2007) 14--33], Miklavič and Potočnik proposed the problem of characterizing distance-regular Cay…
Generalized Wave Operators in von Neumann Algebras
Xiongfeng Zhan, Yifei Ruan, Henanbei Huang +1
Let be a countable decomposable properly infinite von Neumann algebra with a faithful normal semifinite tracial weight $…