Integer Area Dissections of Lattice Polygons via a Non-Abelian Sperner's Lemma

TL;DR

This paper characterizes convex lattice polygons that can be subdivided into lattice triangles with integer areas, utilizing a novel version of Sperner's Lemma to provide a comprehensive description.

Contribution

It introduces a new Sperner's Lemma variant and applies it to classify lattice polygons dissectible into integer-area triangles.

Findings

Complete characterization of dissectible convex lattice polygons

Introduction of a non-abelian Sperner's Lemma

Simplified description of polygon dissections

Abstract

We give a simple and complete description of those convex lattice polygons in the plane that can be dissected into lattice triangles of integer area. A new version of Sperner's Lemma plays a central role.