JournalspmVol. 75, No. 3/4pp. 205–248

An extremal property of lattice polygons

  • Nikolai Bliznyakov

    Voronezh State University, Russian Federation

  • Stanislav Kondratyev

    Universidade de Coimbra, Portugal
An extremal property of lattice polygons cover
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Abstract

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. 205–248

DOI 10.4171/PM/2017