Lattice polygons and the number 2i+7
| dc.creator | Haase, Christian | |
| dc.creator | Schicho, Josef | |
| dc.date | 2004-06-10 | |
| dc.date | 2007-03-05 | |
| dc.date.accessioned | 2026-07-07T07:49:52Z | |
| dc.date.available | 2026-07-07T07:49:52Z | |
| dc.description | 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. | |
| dc.description | 19 pages, 22 figures. To appear in the American Mathematical Monthly | |
| dc.identifier | https://arxiv.org/abs/math/0406224 | |
| dc.identifier | http://arxiv.org/abs/math/0406224 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124977 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 52C05 (primary); 14M25, 11H06, 52B20 (secondary) | |
| dc.title | Lattice polygons and the number 2i+7 | |
| dc.type | text |