The Pentagon and Numbers Games - A Dualization of the Mutation Game

Explore the fascinating duality between the Pentagon Game and the Numbers Game in this 23-minute video lecture from the Dynamics on Graphs series. Delve into the mathematical intricacies of these games, which are connected to exceptional structures in mathematics and physics. Learn how the Numbers Game, a generalization of an International Mathematics Olympiad problem, relates to the Mutation Game previously discussed in the series. Discover how this duality applies to arbitrary simple graphs and extends to directed graphs, encompassing special series in Lie theory. Gain insights into the rich combinatorial structures generated by these games and their connections to various areas of mathematics and physics.

Introduction
The Numbers Game
The Graph
The Correspondence
The Relationship