Chapter 3: Polynomial Partitioning
نویسنده
چکیده
Consider a set P of m points in R. Given a polynomial f ∈ R[x1, . . . , xd], we define the zero set of f to be Z(f) = {p ∈ R | f(p) = 0}. For any r > 1, we say that f ∈ R[x1, . . . , xd] is an r-partitioning polynomial for P if every connected component of R \ Z(f) contains at most m/r points of P.1 Notice that there is no restriction on the number of points of P that lie in Z(f). Figure 1 depicts a 2-partitioning polynomial for a set of 12 points in R.
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