There are not too many magic configurations

E. Ackerman; K. Buchin; C. Knauer; R. Pinchasi; G. Rote

doi:10.1145/1247069.1247098

There are not too many magic configurations

E. Ackerman, K. Buchin, C. Knauer, R. Pinchasi, G. Rote

Algorithms

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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 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.

Original language	English
Title of host publication	Proceedings of the 23rd Annual ACM Symposium on Computational Geometry (SoCG 2007) 6-8 June 2007, Geongju, South Korea
Place of Publication	New York
Publisher	Association for Computing Machinery, Inc.
Pages	142-149
ISBN (Print)	978-1-59593-705-6
DOIs	https://doi.org/10.1145/1247069.1247098
Publication status	Published - 2007
Event	23rd International Symposium on Computational Geometry (SoCG 2007) - Gyeongju, Korea, Republic of Duration: 6 Jun 2007 → 8 Jun 2007 Conference number: 23

Conference

Conference	23rd International Symposium on Computational Geometry (SoCG 2007)
Abbreviated title	SoCG 2007
Country/Territory	Korea, Republic of
City	Gyeongju
Period	6/06/07 → 8/06/07

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10.1145/1247069.1247098

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title = "There are not too many magic configurations",

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 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.",

author = "E. Ackerman and K. Buchin and C. Knauer and R. Pinchasi and G. Rote",

year = "2007",

doi = "10.1145/1247069.1247098",

language = "English",

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booktitle = "Proceedings of the 23rd Annual ACM Symposium on Computational Geometry (SoCG 2007) 6-8 June 2007, Geongju, South Korea",

publisher = "Association for Computing Machinery, Inc.",

address = "United States",

note = "23rd International Symposium on Computational Geometry (SoCG 2007), SoCG 2007 ; Conference date: 06-06-2007 Through 08-06-2007",

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Ackerman, E, Buchin, K, Knauer, C, Pinchasi, R & Rote, G 2007, There are not too many magic configurations. in Proceedings of the 23rd Annual ACM Symposium on Computational Geometry (SoCG 2007) 6-8 June 2007, Geongju, South Korea. Association for Computing Machinery, Inc., New York, pp. 142-149, 23rd International Symposium on Computational Geometry (SoCG 2007), Gyeongju, Korea, Republic of, 6/06/07. https://doi.org/10.1145/1247069.1247098

There are not too many magic configurations. / Ackerman, E.; Buchin, K.; Knauer, C. et al.
Proceedings of the 23rd Annual ACM Symposium on Computational Geometry (SoCG 2007) 6-8 June 2007, Geongju, South Korea. New York: Association for Computing Machinery, Inc., 2007. p. 142-149.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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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.

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DO - 10.1145/1247069.1247098

M3 - Conference contribution

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BT - Proceedings of the 23rd Annual ACM Symposium on Computational Geometry (SoCG 2007) 6-8 June 2007, Geongju, South Korea

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CY - New York

T2 - 23rd International Symposium on Computational Geometry (SoCG 2007)

Y2 - 6 June 2007 through 8 June 2007

ER -

There are not too many magic configurations

Abstract

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