Stanley's Major Contributions to Ehrhart Theory

TL;DR

This paper highlights Richard Stanley's influential contributions to Ehrhart theory, discussing key results, recent developments, and open problems in the enumeration of integer points in rational polyhedra.

Contribution

It provides an overview of Stanley's foundational work in Ehrhart theory and summarizes recent literature building on his results.

Findings

Summary of Stanley's key results in Ehrhart theory

Discussion of recent literature extending Stanley’s work

Presentation of open problems in the field

Abstract

This expository paper features a few highlights of Richard Stanley's extensive work in Ehrhart theory, the study of integer-point enumeration in rational polyhedra. We include results from the recent literature building on Stanley's work, as well as several open problems.