  Mutations on Brauer configurations are introduced and associated with some
suitable automata in order to solve generalizations of the Chicken McNugget
problem. Besides, based on marked order polytopes a new class of diophantine
equations called Gelfand-Tsetlin equations are also solved. The approach allows
giving an algebraic description of the schedule of an AES key via some suitable
non-deterministic finite automata (NFA).
