On The Number of Similar Instances of a Pattern in a Finite Set

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 \(\lfloor{(4 n-1)(n-1)/18}\rfloor\)...

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Veröffentlicht in:	arXiv.org 2016-11
Hauptverfasser:	Abrego, Bernardo, Fernandez-Merchant, Silvia, Katz, Daniel J, Kolesnikov, Levon
Format:	Artikel
Sprache:	eng
Schlagworte:	Apexes Arithmetic Configurations Progressions Upper bounds
Online-Zugang:	Volltext
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