Author

N. Lebedev

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Preprint Sep 2026

Density and separation for augmented Zarankiewicz numbers

We study the augmented Zarankiewicz problem, in which disjoint pairs of cells are added to a binary matrix with no all-one $2\times2$ submatrix. The pairs must satisfy compatibility conditions, and the objective counts each original occupied cell and each added pair once. We show that starting with a maximum $C_4$-free...

N. Lebedev · 4 citations · ⚡1

Preprint Oct 2026

Asymptotic equivalence and exact values for second-order Zarankiewicz numbers

The recursive-line and signed Zarankiewicz numbers maximize the number of squares in augmentations of a maximum $C_4$-free base, subject to two sufficient irreducibility criteria. The count includes one square per base cell and one per selected pair of unused cells. We compare these parameters with the second-order num...

N. Lebedev · 0 citations