TY - GEN

T1 - There are not too many magic configurations

AU - Ackerman, Eyal

AU - Buchin, Kevin

AU - Knauer, Christian

AU - Pinchasi, Rom

AU - Rote, Günter

PY - 2007

Y1 - 2007

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 everyline 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.

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 everyline 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.

KW - Discharging method

KW - Magic configurations

UR - http://www.scopus.com/inward/record.url?scp=35348817335&partnerID=8YFLogxK

U2 - 10.1145/1247069.1247098

DO - 10.1145/1247069.1247098

M3 - Conference contribution

AN - SCOPUS:35348817335

SN - 1595937056

SN - 9781595937056

T3 - Proceedings of the Annual Symposium on Computational Geometry

SP - 142

EP - 149

BT - Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07

T2 - 23rd Annual Symposium on Computational Geometry, SCG'07

Y2 - 6 June 2007 through 8 June 2007

ER -