Augmented Zarankiewicz numbers satisfy BSR(m,n) ≥ z_A(m,n) ≥ z_L(m,n) ≥ z(m,n) and deliver exact values for z_L in cases (m,2), (3,3), (4,3), (4,4) plus new lower bounds for (5,3)-(5,5).
The Sum of squares rank of biquadratic forms and the Zarankiewicz number
3 Pith papers cite this work. Polarity classification is still indexing.
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Introduces 3-edges and generalized cycle-free conditions to prove that SOS rank equals total edge count for triply simple biquadratic forms and applies the method to improve lower bounds on z_3L and BSR.
Reports exact z_L(6,4)=14 and z_L(10,5)=26 plus lower bounds z_L(15,6)≥43, z_L(21,7)≥64, z_L(28,8)≥88 obtained via ILP and verified admissible families.
citing papers explorer
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Three-Edges and the SOS Rank of Biquadratic Forms
Introduces 3-edges and generalized cycle-free conditions to prove that SOS rank equals total edge count for triply simple biquadratic forms and applies the method to improve lower bounds on z_3L and BSR.
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A Computational Study of Limited Augmented Zarankiewicz Numbers in the Incidence-Graph Family of Complete Graphs
Reports exact z_L(6,4)=14 and z_L(10,5)=26 plus lower bounds z_L(15,6)≥43, z_L(21,7)≥64, z_L(28,8)≥88 obtained via ILP and verified admissible families.