论文标题
关于Zarankiewicz问题的一些评论
Some remarks on the Zarankiewicz problem
论文作者
论文摘要
Zarankiewicz问题要求对$ z（m，n; s，t）$进行估算，这是$ m \ times n $矩阵中的$ 1 $的最大数量，所有条目$ 0 $ 0 $或$ 1 $包含no $ s \ times t $ submatrix，完全由$ 1 $ $ $ 1 $组成。我们表明，由于KőVári，Sós和Turán导致的$ z（m，n; s，t）$的经典上限紧密到广泛的参数。证明依赖于随机代数方法的新定量变体。
The Zarankiewicz problem asks for an estimate on $z(m, n; s, t)$, the largest number of $1$'s in an $m \times n$ matrix with all entries $0$ or $1$ containing no $s \times t$ 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.
