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arXiv · 1609.09526

On Ehrhart polynomials of lattice triangles

Johannes Hofscheier·Benjamin Nill·Dennis Öberg
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Abstract

The Ehrhart polynomial of a lattice polygon P is completely determined by the pair (b(P),i(P)) where b(P) equals the number of lattice points on the boundary and i(P) equals the number of interior lattice points. All possible pairs (b(P),i(P)) are completely described by a theorem due to Scott. In this note, we describe the shape of the set of pairs (b(T),i(T)) for lattice triangles T by finding infinitely many new Scott-type inequalities.

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Johannes Hofscheier, Benjamin Nill, Dennis Öberg. 2016-09-29. On Ehrhart polynomials of lattice triangles. https://doi.org/10.37236/6624

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