Uma nova metodologia para a extensão de domínio de operações matemáticas sucessivas, com aplicações na análise combinatória

• Autor(a) principal: Barroso, Marlo Moesia
• Data de Publicação: 2017
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/256
• topic: Teoria dos grupos; Funções recursivas; Group theory; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA

This work stablishes the principles, definitions and properties that allow recursive functions creation using binary operations acting on the elements of sequences. The methodology is developed in the domain of algebraic structures (semigroups, commutative groups and rings), which will demonstrate the potential of these operations to address issues in Elementary Algebra, Number Theory and Abstract Algebra fields. As a consequence of this approach, it is obtained an algebraic structure that allows to create operations similar to the ones that can be conceived through usual products and summations, however, more generic. Thus, it will be possible to address issues involving successive operations with integer domain following a general methodology, where the rules are derived from the basic elements of the presented theory. To highlight the potential of the developed generalization, applications will be shown in the representation of binomial numbers and their possible extensions. Finally, in order to prove the applicability of the new methodology, comparisons were made with results from the literature.