The frobenius problem for generalized repunit numerical semigroups

• Autor(a) principal: Branco, Manuel B.
• Data de Publicação: 2022
• Outros Autores: Colaço, Isabel, Ojeda, Ignacio
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: https://hdl.handle.net/20.500.12207/5968
• topic: Numerical semigroup; Apéry sets; Frobenius problem; Genus; Type; Wilf conjeturee

In this paper, we introduce and study the numerical semigroups generated by {a1, a2, . . .} ⊂ N such that a1 is the repunit number in base b > 1 of length n > 1 and ai − ai−1 = a bi−2, for every i ≥ 2, where a is a positive integer relatively prime with a1. These numerical semigroups generalize the repunit numerical semigroups among many others. We show that they have interesting properties such as being homogeneous and Wilf. Moreover, we solve the Frobenius problem for this family, by giving a closed formula for the Frobenius number in terms of a, b and n, and compute other usual invariants such as the Ap´ery sets, the genus or the type.