An extremal property of lattice polygons
Nikolai BliznyakovVoronezh State University, Russian Federation
Stanislav KondratyevUniversidade de Coimbra, Portugal
We find the critical number of vertices of a convex lattice polygon that guarantees that the polygon contains at least one point of a given square sublattice. As a tool, we prove Diophantine inequalities relating the number of edges of a broken line and the coordinates of its endpoints.
Cite this article
Nikolai Bliznyakov, Stanislav Kondratyev, An extremal property of lattice polygons. Port. Math. 75 (2018), no. 3/4, pp. 205–248DOI 10.4171/PM/2017