2004/06/10 by Christian Haase, Haase, Christian, Josef Schicho +1 · 1 citation
Computer Science · Mathematics · #11H06 #14M25 #52B20 (secondary) #52C05 (primary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.math/0406224
openalex publication_date 2004/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we classify all triples (a,b,i) such that there is a convex lattice polygon P with area a, and b respectively i lattice points on the boundary respectively in the interior. The crucial lemma for the classification is the necessity of b ≤ 2 i + 7. We sketch three proofs of this fact: the original one by Scott, an elementary one, and one using algebraic geometry. As a refinement, we introduce an onion skin parameter l: how many nested polygons does P contain? and give sharper bounds.