# Levon Kolesnikov

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New bounds on the number of similar or directly similar copies of a pattern within a finite subset of the line or the plane are proved. The number of equilateral triangles whose vertices all lie within an n-point subset of the plane is shown to be no more than ⌊(4n − 1)(n − 1)/18⌋. The number of k-term arithmetic progressions that lie within an n-point… (More)

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