Name
Abstract | ||
|---|---|---|
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 \le 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. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.4169/193009709X469913 | AMERICAN MATHEMATICAL MONTHLY |
Keywords | Field | DocType |
algebraic geometry,lattice points | Toric variety,Discrete mathematics,Combinatorics,Polygon,Algebraic number,Graph paper,Lattice (order),Algebra,Mathematical analysis,Invariant (mathematics),Integer lattice,Mathematics | Journal |
Volume | Issue | ISSN |
116 | 2 | 0002-9890 |
Citations | PageRank | References |
7 | 0.97 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Christian Haase | 1 | 29 | 3.41 |
| Josef Schicho | 2 | 121 | 21.43 |