Eyal Ackerman, Kevin Buchin, Christian Knauer, Rom Pinchasi, and Günter Rote:

There are not too many magic configurations

  1. In: Proceedings of the 23rd Annual Symposium on Computational Geometry, Gyeongju, South Korea, June 6-8, 2007. Association for Computing Machinery, 2007, pp. 142-149. doi:10.1145/1247069.1247098
  2. Discrete and Computational Geometry 39 (2008), pp. 3-16. doi:10.1007/s00454-007-9023-0

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 a magic configuration consists either of points in general position, or all points are collinear, with the possible exception of one point, or they form a special configuration of 7 points.

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Last update: August 14, 2017.