Polytopes, polyhedra, and the Farkas lemma

TL;DR

This paper presents a proof of the Farkas lemma and uses it to derive a structure theorem for polyhedra, contributing to the theoretical understanding of polyhedral geometry.

Contribution

It provides a new proof of the Farkas lemma and applies it to establish a structure theorem for polyhedra, advancing theoretical insights in polyhedral theory.

Findings

Proof of the Farkas lemma

Structure theorem for polyhedra

Theoretical framework for polyhedral analysis

Abstract

The Farkas lemma is proved and applied to obtain a structure theorem for polyhedra. These notes are based on a talk in the New York Number Theory Seminar on October, 20, 2022.