There Are Not Too Many Magic Configurations

  • Authors:

  • Eyal Ackerman;Kevin Buchin;Christian Knauer;Rom Pinchasi;Günter Rote

  • Affiliations:

  • Technion—Israel Institute of Technology, Computer Science Department, 32000, Haifa, Israel;Freie Universität Berlin, Institute of Computer Science, Takustr. 9, 14195, Berlin, Germany;Freie Universität Berlin, Institute of Computer Science, Takustr. 9, 14195, Berlin, Germany;Technion—Israel Institute of Technology, Mathematics Department, 3200, Haifa, Israel;Freie Universität Berlin, Institute of Computer Science, Takustr. 9, 14195, Berlin, Germany

  • Venue:
  • Discrete & Computational Geometry
  • Year:
  • 2008

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Abstract

A finite planar point set P is called a magic configuration if there is an assignment of positive weights to the points of P such that, for every line l determined by P, the sum of the weights of all points of P on l equals 1. We prove a conjecture of Murty from 1971 and show that if a set of n points P is a magic configuration, then P is in general position, or P contains n−1 collinear points, or P is a special configuration of 7 points.