Preprint 55/2020

Convex lattice polygons with all lattice points visible

Ralph Morrison and Ayush Kumar Tewari

Contact the author: Please use for correspondence this email.
Submission date: 11. May. 2020
Pages: 24
Bibtex
Download full preprint: PDF (655 kB)
Link to arXiv:See the arXiv entry of this preprint.

Abstract:
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, showing that there are finitely many of lattice width greater than 2 and computationally enumerating them. As an application of this classification, we prove new obstructions to graphs arising as skeleta of tropical plane curves.

10.06.2020, 02:16