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On a question of Bourgain about geometric incidences
- Combinat. Probab. Comput
"... Given a set of s points and a set of n 2 lines in three-dimensional Euclidean space such that each line is incident to n points but no n lines are coplanar, then we have s = Ω(n 11/4). This is the first nontrivial answer to a question recently posed by Jean Bourgain. 1 ..."
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Given a set of s points and a set of n 2 lines in three-dimensional Euclidean space such that each line is incident to n points but no n lines are coplanar, then we have s = Ω(n 11/4). This is the first nontrivial answer to a question recently posed by Jean Bourgain. 1
On distinct distances in homogeneous sets in the Euclidean space
, 2008
"... A homogeneous set of n points in the d-dimensional Euclidean space determines at least Ω(n 2d/(d2 +1) /log c(d) n) distinct distances for a constant c(d)> 0. In three-space, we slightly improve our general bound and show that a homogeneous set of n points determines at least Ω(n.6071) distinct dista ..."
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A homogeneous set of n points in the d-dimensional Euclidean space determines at least Ω(n 2d/(d2 +1) /log c(d) n) distinct distances for a constant c(d)> 0. In three-space, we slightly improve our general bound and show that a homogeneous set of n points determines at least Ω(n.6071) distinct distances. 1
