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On two-generator Fibonacci numerical semigroups with a prescribed genus

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 wor...

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Main Authors: Souza, Matheus Bernardini de, Ferreira, Diego Marques, Trojovský, Pavel
Format: Artigo
Language: Inglês
Published: Springer Nature 2021
Subjects:
Semigrupos numéricos
Números de Fibonacci
Online Access: https://repositorio.unb.br/handle/10482/41409
https://doi.org/10.1007/s13398-021-01091-7
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spelling ir-10482-414092021-07-14T02:25:19Z On two-generator Fibonacci numerical semigroups with a prescribed genus Souza, Matheus Bernardini de Ferreira, Diego Marques Trojovský, Pavel Semigrupos numéricos Números de Fibonacci 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. 2021-07-14T02:09:40Z 2021-07-14T02:09:40Z 2021-07 Artigo 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. https://repositorio.unb.br/handle/10482/41409 https://doi.org/10.1007/s13398-021-01091-7 Inglês https://link.springer.com/article/10.1007/s13398-021-01091-7 Acesso Restrito Springer Nature
institution REPOSITORIO UNB
collection REPOSITORIO UNB
language Inglês
topic Semigrupos numéricos
Números de Fibonacci
spellingShingle Semigrupos numéricos
Números de Fibonacci
Souza, Matheus Bernardini de
Ferreira, Diego Marques
Trojovský, Pavel
On two-generator Fibonacci numerical semigroups with a prescribed genus
description 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.
format Artigo
author Souza, Matheus Bernardini de
Ferreira, Diego Marques
Trojovský, Pavel
author_sort Souza, Matheus Bernardini de
title On two-generator Fibonacci numerical semigroups with a prescribed genus
title_short On two-generator Fibonacci numerical semigroups with a prescribed genus
title_full On two-generator Fibonacci numerical semigroups with a prescribed genus
title_fullStr On two-generator Fibonacci numerical semigroups with a prescribed genus
title_full_unstemmed On two-generator Fibonacci numerical semigroups with a prescribed genus
title_sort on two-generator fibonacci numerical semigroups with a prescribed genus
publisher Springer Nature
publishDate 2021
url https://repositorio.unb.br/handle/10482/41409
https://doi.org/10.1007/s13398-021-01091-7
_version_ 1710449468128624640
score 13.657419

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