Boundary Lattice-Point Bounds for Pseudointegral Polygons in Ehrhart Theory
A polygon is pseudointegral when its Ehrhart counting function is an actual polynomial even though its vertices are only rational. Students learn that a rational pseudointegral triangle with one interior lattice point has at most 9 boundary lattice points and never exactly 7 (pinning down all such Ehrhart polynomials), and that convex pseudointegral polygons can reach b<=5i+4 boundary points, far beyond Scott's b<=2i+7 bound for genuinely integral polygons.
Boundaries of pseudointegral polygons
We prove that a rational pseudointegral triangle with exactly one lattice point in its interior has at most $9$ lattice points on its boundary, where a polygon $P$ is called pseudointegral if the Ehr…