Minimal number of points on a grid forming patterns of blocks

Chai Wah Wu

Published 2016-08-25Version 1

We consider the minimal number of points on a regular grid on the plane that generates n blocks of points of exactly length k and show that this number is upper bounded by kn/3 and approaches kn/4 as $n\rightarrow\infty$ when k+1 is coprime with 6 or when k is large.