The Mutation Game, Coxeter–Dynkin Graphs, and Generalized Root Systems

Abstract

We introduce the mutation game on a directed multigraph, which is dual to Mozes’ numbers game. This new game allows us to create geometric and combinatorial structure that allows generalization of root systems to more general graphs. We interpret Coxeter–Dynkin diagrams in this multigraph context and exhibit new geometric forms for the associated root systems.