18 papers
A Weak Condition for Limited Augmented Zarankiewicz Numbers
Liqun Qi, Chunfeng Cui, Yi Xu
The authors define a weaker version of the limited augmented Zarankiewicz number by replacing the opposite‑cell condition with an acyclic dependency rule and a simplified local pro…
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 -edges -- triples of cells representing squares of three-term bilinea…
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 satisfies , where is the maximum SOS rank of $m\times…
Sum of Squares Rank of Biquadratic Forms and The Zarankiewicz Number
Chunfeng Cui, Liqun Qi, Yi Xu
Denote the maximum sos rank of sum of squares (SOS) biquadratic forms by . In this paper, we show that and conjecture that $BSR(m, n…
Sum of Squares Decompositions and Rank Bounds for Biquadratic Forms
Liqun Qi, Chunfeng Cui, Yi Xu
We study SOS properties of biquadratic forms. For the class of partially symmetric biquadratic forms, we establish necessary and sufficient conditions for positive semi-definitenes…
Sum of Squares Decompositions for Structured Biquadratic Forms
Yi Xu, Chunfeng Cui, Liqun Qi
This paper studies sum-of-squares (SOS) representations for structured biquadratic forms. We prove that diagonally dominated symmetric biquadratic tensors are always SOS. For the s…