On rich lines in grids

Mathematics – Combinatorics

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

21 pages

Scientific paper

In this paper we show that if one has a grid A x B, where A and B are sets of n real numbers, then there can be only very few ``rich'' lines in certain quite small families. Indeed, we show that if the family has lines taking on n^epsilon distinct slopes, and where each line is parallel to n^epsilon others (so, at least n^(2 epsilon) lines in total), then at least one of these lines must fail to be ``rich''. This result immediately implies non-trivial sum-product inequalities; though, our proof makes use of the Szemeredi-Trotter inequality, which Elekes used in his argument for lower bounds on |C+C| + |C.C|.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

On rich lines in grids 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 On rich lines in grids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On rich lines in grids will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-596510

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.