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arXiv · 0904.4429

The number of generalized balanced lines

David Orden·Pedro Ramos·Gelasio Salazar
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Abstract

Let $S$ be a set of $r$ red points and $b=r+2d$ blue points in general position in the plane, with $d\geq 0$. A line $\ell$ determined by them is said to be balanced if in each open half-plane bounded by $\ell$ the difference between the number of red points and blue points is $d$. We show that every set $S$ as above has at least $r$ balanced lines. The main techniques in the proof are rotations and a generalization, sliding rotations, introduced here.

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David Orden, Pedro Ramos, Gelasio Salazar. 2009-05-22. The number of generalized balanced lines. https://doi.org/10.1007/s00454-010-9253-4

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