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math.CO2023
The spectra of Laplace operators on covering simplicial complexes
Yi-Zheng Fan, Yi-Min Song, Yi Wang
We give a decomposition of the Laplace operator (in matrix form) of a covering simplicial complex as a direct sum of several matrices, one of which is the Laplace operator of the b…
math.CO2023
Hypergraph coverings and Ramanujan Hypergraphs
Yi-Min Song, Yi-Zheng Fan, Zhengke Miao
In this paper we investigate Ramanujan hypergraphs by using hypergraph coverings. We first show that the spectrum of a -fold covering of a connected hypergraph con…
math.AG2023
Asymptotic Behavior of the Zhang--Kawazumi's phi-invariant
Yinchong Song
The phi-invariant was introduced by Shou-Wu Zhang and Nariya Kawazumi. We study the continuity property of the phi-invariants for degenerating graphs, and show that this continuity…