# Minimal polygons with fixed lattice width

## TL;DR

This paper classifies minimal polygons with a fixed lattice width up to unimodular equivalence and establishes a sharp upper bound on their lattice points, advancing understanding of lattice polygon structures.

## Contribution

It provides a complete classification of inclusion-minimal polygons with fixed lattice width and derives a precise upper bound on their lattice points.

## Key findings

- Classification of unimodular equivalence classes of minimal polygons
- Sharp upper bound on the number of lattice points
- Insights into the structure of polygons with fixed lattice width

## Abstract

We classify the unimodular equivalence classes of inclusion-minimal polygons with a certain fixed lattice width. As a corollary, we find a sharp upper bound on the number of lattice points of these minimal polygons.