k-Sets in Four Dimensions
Tóm tắt
We show, with an elementary proof, that the number of halving simplices
in a set of n points in ℝ4 in general position is
O(n4-2/45). This improves the previous bound of
O(n4-1/13^{4}). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane.