Relationships Between Mutations of Brauer Configuration Algebras and Some Diophantine Equations

TL;DR

This paper introduces mutations on Brauer configurations linked with automata to address generalized Chicken McNugget problems and solves new Gelfand-Tsetlin Diophantine equations using algebraic and automata-based methods.

Contribution

It presents novel mutations on Brauer configurations and connects them with automata to solve generalized combinatorial problems and new classes of Diophantine equations.

Findings

Mutations on Brauer configurations can model automata for combinatorial problems.

Gelfand-Tsetlin equations are solved using algebraic and automata techniques.

An algebraic description of AES key schedules via non-deterministic automata is provided.

Abstract

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).