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.
Bibliographical noteFunding Information:
The research by Rom Pinchasi was supported by a Grant from the G.I.F., the German-Israeli Foundation for Scientific Research and Development.
- Discharging method
- Euclidean plane
- Euler's formula
- Magic configuration
- Murty's conjecture
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics