On the structure of sets with small doubling property on the plane (I)
Volume 83 / 1998
Acta Arithmetica 83 (1998), 127-141
DOI: 10.4064/aa-83-2-127-141
Abstract
Let K be a finite set of lattice points in a plane. We prove that if |K| is sufficiently large and |K+K| < (4 - 2/s)|K| - (2s-1), then there exist s - 1 parallel lines which cover K. We also obtain some more precise structure theorems for the cases s = 3 and s = 4.
