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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| 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. |
| 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. |
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