There are not too many magic configurations

Eyal Ackerman; Kevin Buchin; Christian Knauer; Rom Pinchasi; Günter Rote

doi:10.1007/s00454-007-9023-0

There are not too many magic configurations

Eyal Ackerman, Kevin Buchin, Christian Knauer, Rom Pinchasi, Günter Rote

Research output: Contribution to journal › Article › 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 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.

Original language	English
Pages (from-to)	3-16
Number of pages	14
Journal	Discrete and Computational Geometry
Volume	39
Issue number	1-3
DOIs	https://doi.org/10.1007/s00454-007-9023-0
State	Published - Mar 2008
Externally published	Yes

Bibliographical note

Funding Information:
The research by Rom Pinchasi was supported by a Grant from the G.I.F., the German-Israeli Foundation for Scientific Research and Development.

Keywords

Discharging method
Euclidean plane
Euler's formula
Lines
Magic configuration
Murty's conjecture
Points

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Access to Document

10.1007/s00454-007-9023-0

Cite this

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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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AU - Knauer, Christian

AU - Pinchasi, Rom

AU - Rote, Günter

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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.

KW - Discharging method

KW - Euclidean plane

KW - Euler's formula

KW - Lines

KW - Magic configuration

KW - Murty's conjecture

KW - Points

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ER -

There are not too many magic configurations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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