Study of some varieties of Frobenius number

• Ano de defesa: 2023
• Autor(a) principal: Traesel, Márcio André
• Orientador(a): González, José Carlos Rosales
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade de Évora (UÉvora); CARAGUATATUBA
• Programa de Pós-Graduação: Instituto de Investigação e Formação Avançada
• Link de acesso: https://repositorio.ifsp.edu.br/handle/123456789/2816
• topic: Numerical semigroups; Frobenius number; Varieties; Pseudo-varieties; Restricted varieties; Semigrupos numéricos; Número de Frobenius; Variedades restritas; Pseudo-variedades

Common behaviors in families of numerical semigroups led to the introduction of Frobenius varieties, pseudo-varieties and restricted varieties concepts. These facts allow us to build, arrange and give algorithms to compute its elements with a given genus, multiplicity and Frobenius number. This thesis is devoted to the study of families of numerical semigroups fitting one of the three above concepts. Families of numerical semigroups covered are modularly equidistant, with concentration two, with fixed multiplicity and concentration, without consecutive small elements, coated with odd elements and with distances no admissible between gaps greater than its multiplicity. Lastly, we study the Frobenius restricted variety of the numerical semigroups contained in a given one where we give formulas for the Frobenius and genus number restricted. Further, we generalize Bras-Amoros and Wilf’s conjecture.