From the 1 of 13 linked papers with an AI index.
13 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…
Biquadratic SOS Rank and Augmented Zarankiewicz Number
Liqun Qi, Chunfeng Cui, Yi Xu
This paper introduces the concepts of the augmented Zarankiewicz number and the limited augmented Zarankiewicz number , which are natural combinatorial extensi…
Narrowing the Gap: SOS Ranks of Biquadratic Forms and a Lower Bound of
Yi Xu, Chunfeng Cui, Liqun Qi
We investigate the maximum sum-of-squares (SOS) rank of biquadratic forms in the critical case of variables, where the general bounds are currently $7 \leq \mathrm{BSR…
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…