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Some remarks on the Zarankiewicz problem

Conlon, David (2020) Some remarks on the Zarankiewicz problem. . (Unpublished)

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The Zarankiewicz problem asks for an estimate on z(m,n;s,t), the largest number of 1's in an m×n matrix with all entries 0 or 1 containing no s×t submatrix consisting entirely of 1's. We show that a classical upper bound for z(m,n;s,t) due to Kővári, Sós and Turán is tight up to the constant for a broad range of parameters. The proof relies on a new quantitative variant of the random algebraic method.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Conlon, David0000-0001-5899-1829
Additional Information:I would like to thank Cosmin Pohoata for helpful discussions. I am also grateful to Dhruv Mubayi for drawing my attention to his work with Alon, Mellinger and Verstraëte [1].
Record Number:CaltechAUTHORS:20200914-085046091
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105368
Deposited By: Tony Diaz
Deposited On:14 Sep 2020 16:53
Last Modified:14 Sep 2020 16:53

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