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 -