Oscillations and their applications in partition calculus

TL;DR

This paper surveys the use of oscillations as a technique in partition calculus, demonstrating their effectiveness in constructing colorings that witness negative partition relations and exploring various applications.

Contribution

It provides a comprehensive overview of oscillation techniques in partition calculus and introduces new applications of these methods.

Findings

Oscillations effectively construct colorings for negative partition relations.

Survey of multiple results illustrating oscillation applications.

New applications of oscillation techniques in partition calculus.

Abstract

Oscillations are a powerful tool for building examples of colorings witnessing negative partition relations. We survey several results illustrating the general technique and present a number of applications.