Mathematics – Combinatorics
Scientific paper
2011-01-07
Mathematics
Combinatorics
Scientific paper
An important theorem of Beck says that any point set in the Euclidean plane is either ``nearly general position'' or ``nearly collinear'': there is a constant C>0 such that, given n points in the plane with at most r$ of them collinear, the number of lines induced by the points is at least Cr(n-r). Recent work of Gutkin-Rams on billiards orbits requires the following elaboration of Beck's Theorem to bichromatic point sets: there is a constant C>0 such that, given n red points and n blue points in the plane with at most r of them collinear, the number of lines spanning at least one point of each color is at least Cr(2n-r).
Theran Louis
No associations
LandOfFree
Lines induced by bichromatic point sets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Lines induced by bichromatic point sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lines induced by bichromatic point sets will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-484345