On two-generator Fibonacci numerical semigroups with a prescribed genus

Souza, Matheus Bernardini de; Ferreira, Diego Marques; Trojovský, Pavel

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Campo DC	Valor	Lengua/Idioma
dc.contributor.author	Souza, Matheus Bernardini de	-
dc.contributor.author	Ferreira, Diego Marques	-
dc.contributor.author	Trojovský, Pavel	-
dc.date.accessioned	2021-07-14T02:09:40Z	-
dc.date.available	2021-07-14T02:09:40Z	-
dc.date.issued	2021-07	-
dc.identifier.citation	BERNADINI, Matheus; MARQUES, Diego; TROJOVSKÝ, Pavel. On two-generator Fibonacci numerical semigroups with a prescribed genus. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, v. 115, n. 3, 149, jul. 2021. DOI: https://doi.org/10.1007/s13398-021-01091-7.	pt_BR
dc.identifier.uri	https://repositorio.unb.br/handle/10482/41409	-
dc.language.iso	Inglês	pt_BR
dc.publisher	Springer Nature	pt_BR
dc.rights	Acesso Restrito	pt_BR
dc.title	On two-generator Fibonacci numerical semigroups with a prescribed genus	pt_BR
dc.type	Artigo	pt_BR
dc.subject.keyword	Semigrupos numéricos	pt_BR
dc.subject.keyword	Números de Fibonacci	pt_BR
dc.identifier.doi	https://doi.org/10.1007/s13398-021-01091-7	pt_BR
dc.relation.publisherversion	https://link.springer.com/article/10.1007/s13398-021-01091-7	pt_BR
dc.description.abstract1	A numerical semigroup S is a subset of the set of nonnegative integers closed under addition, containing the zero element and with finite complement in N0 (this finite cardinality is named the genus of S). It is well-known that every numerical semigroup S is finitely generated and there are many works concerning the properties of numerical semigroups with a particular type of generators. For instance, Song (Bull Korean Math Soc 57:623–647, 2020) worked on these semigroups whose generators are Thabit numbers of the first, second kind base b and Cunningham numbers. A classical result of Sylvester ensures that if gcd(a,b)=1, then the numerical semigroup ⟨a,b⟩ has genus (a−1)(b−1)2. In this paper, we search for two-generator numerical semigroups whose generators and/or the genus are related to Fibonacci numbers. Our propose is fixing the sets A, B and G and looking for triples (a,b,g)∈A×B×G, where at least one of the sets is related to the Fibonacci numbers.	pt_BR
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