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On a Question of Bourgain about Geometric Incidences

Published online by Cambridge University Press:  01 July 2008

JÓZSEF SOLYMOSI  and
CSABA D. TÓTH
JÓZSEF SOLYMOSI
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, CanadaV6T 1Z2 (e-mail: solymosi@math.ubc.ca)
CSABA D. TÓTH
Affiliation:
Department of Mathematics, University of Calgary, 2500 University Drive NW, Calgary, AB, CanadaT2N 1N4 (e-mail: cdtoth@ucalgary.ca)
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Abstract

Given a set of s points and a set of n2 lines in three-dimensional Euclidean space such that each line is incident to n points but no n lines are coplanar, we show that s = Ω(n11/4). This is the first non-trivial answer to a question recently posed by Jean Bourgain.

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 4 , July 2008 , pp. 619 - 625
Copyright
Copyright © Cambridge University Press 2008

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