Convex lattice polygons with all lattice points visible
Two lattice points are visible to one another if there exist no other lattice points on the line segment connecting them. In this paper we study convex lattice polygons that contain a lattice point such that all other lattice points in the polygon are visible from it. We completely classify such pol...
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| creator | Morrison, Ralph Tewari, Ayush Kumar |
| description | Two lattice points are visible to one another if there exist no other lattice
points on the line segment connecting them. In this paper we study convex
lattice polygons that contain a lattice point such that all other lattice
points in the polygon are visible from it. We completely classify such
polygons, show that there are finitely many of lattice width greater than $2$,
and computationally enumerate them. As an application of this classification,
we prove new obstructions to graphs arising as skeleta of tropical plane
curves. |
| doi_str_mv | 10.48550/arxiv.2005.04180 |
| format | Article |
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points on the line segment connecting them. In this paper we study convex
lattice polygons that contain a lattice point such that all other lattice
points in the polygon are visible from it. We completely classify such
polygons, show that there are finitely many of lattice width greater than $2$,
and computationally enumerate them. As an application of this classification,
we prove new obstructions to graphs arising as skeleta of tropical plane
curves.</description><identifier>DOI: 10.48550/arxiv.2005.04180</identifier><language>eng</language><subject>Mathematics - Algebraic Geometry ; Mathematics - Combinatorics</subject><creationdate>2020-05</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2005.04180$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2005.04180$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Morrison, Ralph</creatorcontrib><creatorcontrib>Tewari, Ayush Kumar</creatorcontrib><title>Convex lattice polygons with all lattice points visible</title><description>Two lattice points are visible to one another if there exist no other lattice
points on the line segment connecting them. In this paper we study convex
lattice polygons that contain a lattice point such that all other lattice
points in the polygon are visible from it. We completely classify such
polygons, show that there are finitely many of lattice width greater than $2$,
and computationally enumerate them. As an application of this classification,
we prove new obstructions to graphs arising as skeleta of tropical plane
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points on the line segment connecting them. In this paper we study convex
lattice polygons that contain a lattice point such that all other lattice
points in the polygon are visible from it. We completely classify such
polygons, show that there are finitely many of lattice width greater than $2$,
and computationally enumerate them. As an application of this classification,
we prove new obstructions to graphs arising as skeleta of tropical plane
curves.</abstract><doi>10.48550/arxiv.2005.04180</doi><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| subjects | Mathematics - Algebraic Geometry Mathematics - Combinatorics |
| title | Convex lattice polygons with all lattice points visible |
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