An analog of the Furstenberg-Katznelson-Weiss theorem on triangles in sets of positive density in finite field geometries

Details An analog of the Furstenberg-Katznelson-Weiss theorem on triangles in sets of positive density in finite field geometries An analog of the Furstenberg-Katznelson-Weiss theorem on triangles in sets of positive density in finite field geometries

2008-04-30

arxiv.org/abs/0804.4894v1

Mathematics

Combinatorics

Scientific paper

We prove that if the cardinality of a subset of the 2-dimensional vector
space over a finite field with $q$ elements is $\ge \rho q^2$, with
$\frac{1}{\sqrt{q}}<<\rho \leq 1$, then it contains an isometric copy of $\ge
c\rho q^3$ triangles.

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