3-edges extend the 2-edge Zarankiewicz framework to prove SOS rank equals edge count in generalized-C4-free biquadratic forms, improving z_3L(5,3) to 10, z_3L(6,4) to at least 16, and z_3L(5,5) to at least 16.
The Sum of squares rank of biquadratic forms and the Zarankiewicz number
2 Pith papers cite this work. Polarity classification is still indexing.
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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).
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Three-Edges and the SOS Rank of Biquadratic Forms: Extending the Augmented Zarankiewicz Framework
3-edges extend the 2-edge Zarankiewicz framework to prove SOS rank equals edge count in generalized-C4-free biquadratic forms, improving z_3L(5,3) to 10, z_3L(6,4) to at least 16, and z_3L(5,5) to at least 16.
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Biquadratic SOS Rank and Augmented Zarankiewicz Number
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).