Semigrupos numéricos e o problema do troco de Frobenius

The objective of this work is to present the Frobenius Change problem and the methods used to solve it, illustrating the discussion with problems encountered in everyday life. The problem with Frobênius Change is to find a minimum quota for a sequence of numbers that can be formed through the entire...

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Detalles Bibliográficos
Autor: Ignácio, Pedro Henrique de Oliveira
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2019
País:Brasil
Institución:Universidade Federal do Ceará (UFC)
Repositorio:Repositório Institucional da Universidade Federal do Ceará (UFC)
Idioma:portugués
OAI Identifier:oai:repositorio.ufc.br:riufc/54940
Acceso en línea:http://www.repositorio.ufc.br/handle/riufc/54940
Access Level:acceso abierto
Palabra clave:Eliminação inteira
Número de Frobenius
Equações diofantinas
Semigrupos
Problema do Troco de Frobenius
Entire elimination.
Diophantine equations.
Frobenius number.
Semigroups.
Frobenius Change Problem.
Descripción
Sumario:The objective of this work is to present the Frobenius Change problem and the methods used to solve it, illustrating the discussion with problems encountered in everyday life. The problem with Frobênius Change is to find a minimum quota for a sequence of numbers that can be formed through the entire combination of an initial sequence of integers. This problem is equivalent to finding the solution of a Diophantine equation, for which we can apply the whole elimination method, which is a procedure similar to Gaussian elimination, but applied to linear systems in em. The concepts and techniques related to these problems can be formalized through algebraic structures, especially semigroups. The semigroup theory, when connected with the Frobenius Change problem, provides for it both formal and intuitive tools to seek solutions to it.