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).
Sums of squares and quadratic persistence on real projective varieties
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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).