Relationships between the chicken McNugget problem, mutations of brauer configuration algebras and the advanced encryption standard

Abstract

Mutations on Brauer configurations are introduced and associated with some suitable automata to solve generalizations of the Chicken McNugget problem. Additionally, based on marked order polytopes, the new Diophantine equations called Gelfand–Tsetlin equations are also solved. The approach allows algebraic descriptions of some properties of the AES key schedule via some Brauer configuration algebras and suitable non-deterministic finite automata (NFA).