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).
Highlights
Chicken McNuggets are one of the most sold products of the international fast-food restaurant chain McDonald’s
We prove that there exists a solution if the constant term d is the number of Gelfand–Tsetlin patterns of a given type
The Brauer configuration algebra ΛΓ = FQΓ /IΓ induced by the Brauer configuration Γ, where IΓ is an admissible ideal
Summary
Chicken McNuggets are one of the most sold products of the international fast-food restaurant chain McDonald’s. Specializations of some mutations can be used to find out the Frobenius number of variations of some Dion −3 phantine equations called Gelfand–Tsetlin equations of the form ∑ ai xi+2 + an−2 xn = d, i =−1 with suitable positive integers ai , for each −1 ≤ i ≤ n − 2 For these particular equations, we prove that there exists a solution if the constant term d is the number of Gelfand–Tsetlin patterns of a given type. Specializations of mutations and suitable automata are used to solve Diophantine problems of type D(n1 , n2 , Km ), which arise from the research of generalizations of denumerants Such a problem is defined as follows: Find out positive integers λ1 , λ2 , .
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