Author

Han-Xin Liu

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Preprint Sep 2026

New Bounds for Limited Zarankiewicz Numbers from $K_{5t}$ Blocks

The restricted augmented Zarankiewicz number $z_L(m,n)$ yields core combinatorial lower bounds for the maximal SOS rank of biquadratic forms. All previously known infinite admissible graph families rely on $K_{4t}$ incidence graphs, attaining an asymptotic relative gap limit of $1/4$. This work develops a new inf...

Han-Xin Liu, Yi-Sheng Song · 1 citation

Preprint Sep 2026

$\mathrm M$-Eigenpairs of Partially Symmetric Tensors: Exact Reformulation and Perturbation Bounds

In this paper, we consider the computation of $M$-eigenpairs of fourth order partially symmetric tensors arising from elasticity theory. First, a lifted fourth order tensor is constructed, and the original $M$-eigenvalue problem is reformulated as a parameterized generalized tensor eigenvalue problem under the $\mathbf...

Zhuo-Lin Du, Han-Xin Liu, Yi-Sheng Song · 0 citations