Liqun Qi

activity

20232026

most citedEigenvalues of Dual Hermitian Matrices with Application in Formation Control

1 citations · 2 across the 34 of their papers we have counts for

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9 papers · 1 filter

math.CO2026

The Second-Order Augmented Zarankiewicz Number

Liqun Qi, Chunfeng Cui

The second-order Zarankiewicz number $z_{2} (m, n)$ and the biquadratic sum-of-squares rank $BSR (m, n)$ are related by the unconditional hierarchy \[ \mathrm{BSR}(m,n)\ \ge\ z_…

math.CO2026

Exact Second-Order Zarankiewicz Numbers for Complete-Graph Incidence Families

Yannan Chen, Liqun Qi, Johan Löfberg

For $n \geq 6$ , $m = (2 n)$ , let the complete-graph incidence family on $K_{n}$ have the vertices of $K_{n}$ as columns, its edges as rows, and the incidence graph as one-edge graph. Th…

math.CO2026

Is the Signed Zarankiewicz Number the Same as the Recursive-line Zarankiewicz Number?

Zhiwei Chen, Yannan Chen, Liqun Qi

Löfberg and Qi introduced the second order Zarankiewicz number $z_2$, the recursive-line Zarankiewicz number $z_{RL}$, and the signed Zarankiewicz number $z_{SL}$ for doubly…

math.CO2026

Second Order Zarankiewicz Number

Johan Löfberg, Liqun Qi

We introduce the \emph{second order Zarankiewicz number} $z_{2} (m, n)$ for irreducible doubly simple biquadratic forms with $∣ E_{1} ∣ = z (m, n)$ , together with the intermediate recursive-li…

math.CO2026

A Weak Condition for Limited Augmented Zarankiewicz Numbers

Liqun Qi, Chunfeng Cui, Yi Xu

This paper introduces the weak augmented Zarankiewicz number $z_{w A} (m, n)$ and the weak limited augmented Zarankiewicz number $z_{w L} (m, n)$ , which are combinatorial extensions of t…

math.CO2026

Three-Edges and the SOS Rank of Biquadratic Forms

Liqun Qi, Chunfeng Cui, Yi Xu

We extend the augmented bipartite graph framework for biquadratic sum-of-squares (SOS) ranks by introducing $3$ -edges -- triples of cells representing squares of three-term bilinea…

math.CO2026

Optimization Models and Computational Bounds for Limited Augmented Zarankiewicz Numbers in the Incidence-Graph Family of Complete Graphs

Yi Xu, Gaohang Yu, Liqun Qi

Let $G_{1}$ denote the incidence graph of the complete graph $K_{q + 1}$ . We study limited augmented Zarankiewicz numbers in this family through structured 0--1 optimization models for…

math.CO2026

A General Lower Bound for the Limited Augmented Zarankiewicz Number based upon Complete Graphs

Liqun Qi, Chunfeng Cui, Yi Xu

The limited augmented Zarankiewicz number $z_{L} (m, n)$ satisfies $BSR (m, n) \geq z_{L} (m, n) \geq z (m, n)$ , where $BSR (m, n)$ is the maximum SOS rank of $m\times…

math.CO2024

Spectral Properties of Dual Unit Gain Graphs

Chunfeng Cui, Yong Lu, Liqun Qi +1

In this paper, we study dual quaternion and dual complex unit gain graphs and their spectral properties in a unified frame of dual unit gain graphs. Unit dual quaternions represent…