论文标题
sylvester-gallai型定理，用于复杂说明的曲霉
A Sylvester-Gallai-type theorem for complex-representable matroids
论文作者
论文摘要
Sylvester-Gallai定理指出，每个排名$ 3 $ $ 3 $真正的可说的Matroid都有两点线。我们证明，对于每个$ k \ ge 2 $，每个具有排名至少$ 4^{k-1} $的复杂代表性的Matroid的排名$ k $ flat，恰好是$ k $。对于$ k = 2 $，这是由于凯利（Kelly）而在证明中使用的众所周知的结果。 Barak，Dvir，Wigderson和Yehudayoff较早证明了类似的结果，后来由DVIR，SARAF和WIGDERSON改进，但是我们获得了更好的界限，并获得了更基本的证据。
The Sylvester-Gallai Theorem states that every rank-$3$ real-representable matroid has a two-point line. We prove that, for each $k\ge 2$, every complex-representable matroid with rank at least $4^{k-1}$ has a rank-$k$ flat with exactly $k$ points. For $k=2$, this is a well-known result due to Kelly, which we use in our proof. A similar result was proved earlier by Barak, Dvir, Wigderson, and Yehudayoff and later refined by Dvir, Saraf, and Wigderson, but we get slightly better bounds with a more elementary proof.
