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摘要
We prove a quantitative version of the multi-colored Motzkin-Rabin theorem in the spirit of Barak et al. (Proceedings of the National Academy of Sciences, 2012): Let be disjoint sets of points (of 'colors'). Suppose that for every and every point there are at least other points so that the line connecting and contains a third point of another color. Then the union of the points in all sets is contained in a subspace of dimension bounded by a function of and alone.
- 出版日期2015-1
