On Ehrhart Polynomials of Lattice Triangles

Johannes Hofscheier, Benjamin Nill, Dennis Öberg


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.


Lattice triangles; Ehrhart polynomials; $h^\ast$-vector; Toric surfaces; Sectional genus; Scott's inequality

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