# A Counterexample to a Conjecture of Gomory and Johnson

## TL;DR

This paper provides a counterexample to Gomory and Johnson's 2003 conjecture, demonstrating that not all facets of the infinite group problem are generated by piecewise linear functions, thus disproving the conjecture.

## Contribution

The paper presents the first known counterexample to the Gomory-Johnson conjecture, challenging the assumption that all facets are piecewise linear.

## Key findings

- Counterexample disproves the conjecture
- Facets of the infinite group problem can be non-piecewise linear
- Challenges previous understanding of the structure of facets

## Abstract

In Mathematical Programming 2003, Gomory and Johnson conjecture that the facets of the infinite group problem are always generated by piecewise linear functions. In this paper we give an example showing that the Gomory-Johnson conjecture is false.