TY - JOUR

T1 - There are not too many magic configurations

AU - Ackerman, E.

AU - Buchin, K.

AU - Knauer, C.

AU - Pinchasi, R.

AU - Rote, G.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

U2 - 10.1007/s00454-007-9023-0

DO - 10.1007/s00454-007-9023-0

M3 - Article

VL - 39

SP - 3

EP - 16

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 1-3

ER -