Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903169 | Discrete Mathematics | 2018 | 5 Pages |
Abstract
We consider the number of distinct distances between two finite sets of points in Rk, for any constant dimension kâ¥2, where one set P1 consists of n points on a line l, and the other set P2 consists of m arbitrary points, such that no hyperplane orthogonal to l and no hypercylinder having l as its axis contains more than O(1) points of P2. The number of distinct distances between P1 and P2 is then Ωminn2â3m2â3,n10â11m4â11log2â11m,n2,m2.Without the assumption on P2, there exist sets P1, P2 as above, with only O(m+n) distinct distances between them.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Ariel Bruner, Micha Sharir,