A Brief Survey on Lattice Zonotopes

TL;DR

This paper surveys classical and recent results on lattice zonotopes, highlighting their connections to combinatorics, enumeration, and structures like graphs and permutations, providing a comprehensive overview of the field.

Contribution

It offers a concise survey of lattice zonotopes, emphasizing their combinatorial and enumerative aspects, and synthesizes recent developments in the area.

Findings

Connections between lattice zonotopes and Ehrhart theory

Enumeration results related to lattice zonotopes

Links between zonotopes and combinatorial structures like graphs and permutations

Abstract

Zonotopes are a rich and fascinating family of polytopes, with connections to many areas of mathematics. In this article we provide a brief survey of classical and recent results related to lattice zonotopes. Our emphasis is on connections to combinatorics, both in the sense of enumeration (e.g. Ehrhart theory) and combinatorial structures (e.g. graphs and permutations).