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

Relationships Between Mutations of Brauer Configuration Algebras and Some Diophantine Equations