The number of generalized balanced lines

Details The number of generalized balanced lines The number of generalized balanced lines

2009-04-28

arxiv.org/abs/0904.4429v3

Mathematics

Combinatorics

6 pages, 3 figures, several typos fixed, reference added

Scientific paper

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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