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The number of generalized balanced lines

David Orden, Pedro Ramos, Gelasio Salazar
Arxiv ID: 0904.4429Last updated: 7/21/2020
Let S be a set of r red points and b=r+2d blue points in general position in the plane, with d≥ 0. A line ℓ determined by them is said to be balanced if in each open half-plane bounded by ℓ 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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