On Ehrhart Polynomials of Lattice Triangles
Keywords: Lattice triangles, Ehrhart polynomials, $h^\ast$-vector, Toric surfaces, Sectional genus, Scott's inequality
AbstractThe 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.