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arXiv · 1606.00855

Bounds on the number of vertices of sublattice-free lattice polygons

Nikolai Bliznyakov·Stanislav Kondratyev
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Abstract

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.

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Nikolai Bliznyakov, Stanislav Kondratyev. 2016-06-02. Bounds on the number of vertices of sublattice-free lattice polygons. https://arxiv.org/abs/1606.00855

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