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.
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The research by Rom Pinchasi was supported by a Grant from the G.I.F., the German-Israeli Foundation for Scientific Research and Development.
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Ackerman, E., Buchin, K., Knauer, C. et al. There Are Not Too Many Magic Configurations. Discrete Comput Geom 39, 3–16 (2008). https://doi.org/10.1007/s00454-007-9023-0
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DOI: https://doi.org/10.1007/s00454-007-9023-0