Area bounds for planar convex bodies containing a fixed number of interior integral points

2023/05/19 by Bohnert, Martin
#14M25 (Secondary) #52B20 #52C05 (Primary) 52A38 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2305.11485

Abstract

We prove area bounds for planar convex bodies in terms of their number of interior integral points and their lattice width data. As an application, we obtain sharp area bounds for rational polygons with a fixed number of interior integral points depending on their denominator. For lattice polygons, we also present an equation for the area based on Noether's formula.

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