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Published online: 2019-06-06
An extremal property of lattice polygonsNikolai Bliznyakov and Stanislav Kondratyev (1) Voronezh State University, Russian Federation
(2) Universidade 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.
Keywords: Integral polygons, lattice-free polygons, broken lines
Bliznyakov Nikolai, Kondratyev Stanislav: An extremal property of lattice polygons. Port. Math. 75 (2018), 205-248. doi: 10.4171/PM/2017