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On the Set of Diameters of Finite Point-Sets in the Plane

by M. Becheanu and R. A. Todor

(Report number 2003-05)

Abstract
In this note we study the existence of finite point-sets in the plane which have a prescribed set of diameters. We recall a classical result concerning an upper bound for the number of diameters occuring in an n-point set in the plane and we describe the sets (called 'complete') for which this upper bound is attained. We also give an algorithm for the construction of all complete sets. The final section is then devoted to the question of enlarging an arbitrary finite plane set to a 'complete' one.

Keywords:

@Techreport{BT03_317,
  author = {M. Becheanu and R. A. Todor},
  title = {On the Set of Diameters of Finite Point-Sets in the Plane},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2003-05},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2003/2003-05.pdf },
  year = {2003}
}

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