Incidences Between Points and Lines on Two- and Three-Dimensional Varieties
نویسندگان
چکیده
منابع مشابه
Incidences 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
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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 (
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We show that the number of incidences between m distinct points and n distinct lines in R 4 is O (
متن کاملOn Incidences Between Points and Hyperplanes∗
We show that if the number I of incidences between m points and n planes in R is sufficiently large, then the incidence graph (that connects points to their incident planes) contains a large complete bipartite subgraph involving r points and s planes, so that rs ≥ I2 mn−a(m+n), for some constant a > 0. This is shown to be almost tight in the worst case because there are examples of arbitrarily ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2017
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-017-9940-5