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- W4310921805 abstract "The Sylvester-Gallai Theorem states that every rank-$3$ real-representable matroid has a two-point line. We prove that, for each $kge 2$, 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." @default.
- W4310921805 created "2022-12-21" @default.
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- W4310921805 date "2022-12-06" @default.
- W4310921805 modified "2023-10-16" @default.
- W4310921805 title "A Sylvester-Gallai-type theorem for complex-representable matroids" @default.
- W4310921805 doi "https://doi.org/10.48550/arxiv.2212.03307" @default.
- W4310921805 hasPublicationYear "2022" @default.
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