Incidences between points and lines in R 4 ∗ Micha Sharir
نویسندگان
چکیده
We show that the number of incidences between m distinct points and n distinct lines in R 4 is O (
منابع مشابه
Incidences between Points and Lines in Three Dimensions
We give a fairly elementary and simple proof that shows that the number of incidences between m points and n lines in R, so that no plane contains more than s lines, is O (
متن کاملIncidences Between Points and Lines on Two- and Three-Dimensional Varieties
Let P be a set of m points and L a set of n lines in R, such that the points of P lieon an algebraic three-dimensional surface of degree D that does not contain hyperplaneor quadric components, and no 2-flat contains more than s lines of L. We show thatthe number of incidences between P and L is
متن کاملIncidences between points and lines on a two-dimensional variety
We present a direct and fairly simple proof of the following incidence bound: Let P be a set of m points and L a set of n lines in R, for d ≥ 3, which lie in a common algebraic two-dimensional surface of degree D that does not contain any 2-flat, so that no 2-flat contains more than s ≤ D lines of L. Then the number of incidences between P and L is
متن کاملOn lines, joints, and incidences in three dimensions
We extend (and somewhat simplify) the algebraic proof technique of Guth and Katz [7], to obtain several sharp bounds on the number of incidences between lines and points in three dimensions. Specifically, we show: (i) The maximum possible number of incidences between n lines in R and m of their joints (points incident to at least three non-coplanar lines) is Θ(mn) for m ≥ n, and Θ(mn+m+n) for m...
متن کاملIncidences with Curves in ℝ d
We prove that the number of incidences between m points and n bounded-degree curves with k degrees of freedom in R is
متن کامل