On the affine Sylvester problem

In 2006 Lenchner and Brnnimann [14] showed that in the affine plane, given n lines, not all parallel and not all passing through a common point, there have to be at least n6 ordinary points. The present paper improves on this result to show that there must be at least 2n-37 ordinary points, except for a single arrangement of 6 lines with one ordinary point. © 2010 Elsevier B.V. All rights reserved.