Chapter 4: Constant-degree Polynomial Partitioning
نویسنده
چکیده
To see the issues that arise when studying incidence problems in higher dimensions, we consider one of the simplest cases: Incidences between m points and n planes in R. To see that this problem is not interesting, we consider the following point-plane configuration. Let l ⊂ R be a line, let P be a set of m points on l, and let H be a set of n planes that contain l (e.g., see Figure 1). This construction satisfies I(P,H) = mn, implying that the problem is trivial.
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