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...
| Main Authors: | Souza, Matheus Bernardini de, Ferreira, Diego Marques, Trojovský, Pavel |
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| Format: | Artigo |
| Language: | Inglês |
| Published: |
Springer Nature
2021
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| Subjects: | |
| Online Access: |
https://repositorio.unb.br/handle/10482/41409 https://doi.org/10.1007/s13398-021-01091-7 |
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| Summary: |
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. |
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