2016/06/02 by Bliznyakov, Nikolai, Kondratyev, Stanislav
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1606.00855
In this paper we establish bounds on the number of vertices for a few classes of convex sublattice-free lattice polygons. The bounds are essential for proving the formula for the critical number of vertices of a lattice polygon that ensures the existence of a sublattice point in the polygon. To obtain the bounds, we use relations between the number of edges of lattice broken lines and the coordinates of their endpoints.