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.
Highlights
A lattice polygon P ⊆ R2 is the two-dimensional convex hull of finitely many lattice points, i.e., points in Z2
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
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
Summary
A lattice polygon P ⊆ R2 is the two-dimensional convex hull of finitely many lattice points, i.e., points in Z2. 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.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
