On k-Sets in Four Dimensions
نویسندگان
چکیده
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.
منابع مشابه
An Improved Bound for k-Sets in Four Dimensions
We show that the number of halving sets of a set of n points in R is O ( n ) , improving the previous bound of [9] with a simpler (albeit similar) proof.
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