The Ramsey number as a statistical physics problem

Abstract

In this thesis we are going to study the Ramsey numbers. Our way of doing that differs from the way mathematicians do. Specifically we consider Ramsey numbers as physical systems that interact thermally with an environment. This way we can make use of Statistical Physics in combination with Monte Carlo simulations to answer some of the questions of this project. Using simulations is a different way instead of using analytical methods that are not so effective after all when Ramsey numbers get more complicated. Some of the goals of this thesis are to verify that our methodology works out and thus can be used to improve on the estimation of Ramsey numbers. Last but not least we make a thermodynamic study of the physical system we use to model the search for the Ramsey numbers.