Yi-Min Song

activity

20242026

collaborators

6 papers

math.CO2026

Degree Majorization and Laplacian Eigenvalue Sums for Simplicial Complexes

Huan-Zhi Zhang, Yi-Min Song, Yi-Zheng Fan

Let $K$ be an $r$ -dimensional simplicial complex. We prove that the spectrum of its $(r - 1)$ -dimensional up-Laplacian is majorized by the conjugate degree sequence of its $(r - 1)…

math.CO2026

Spectral radius of $2$ -dimensional simplicial complexes with given Betti number

Chuan-Ming She, Yi-Zheng Fan, Yi-Min Song

In this paper we establish an asymptotic formula for the signless Laplacian spectral radius of a $2$ -dimensional simplicial complex with given $2$ -th Betti number. Furthermore, we…

math.AG2025

Parametrization of geometric Beilinson--Bloch heights via adelic line bundles

Yinchong Song

Let $S$ be a quasi-projective smooth variety over complex field $C$ . For a smooth projective morphism $I ¨ : X \to S$ , we will introduce a new height pairing \begin{alig…

math.CO2025

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.GT2025

Counting components of moduli space of HCMU spheres via weighted trees

Yi Song

HCMU surfaces are compact Riemann surfaces equipped with the Calabi extremal KÃ¤hler metric and a finite number of singularities. By using both the classical football decomposition…

math.CO2024

The largest normalized Laplacian eigenvalue and incidence balancedness of simplicial complexes

Yi-min Song, Hui-Feng Wu, Yi-Zheng Fan

Let $K$ be a simplicial complex, and let $I^_{i}^{u p} (K)$ be the $i$ -th up normalized Laplacian of $K$ . Horak and Jost showed that the largest eigenvalue of $I^_{i}^{u p} (K)$ is at most…