The set of Arf numerical semigroups with given Frobenius number

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URI: http://hdl.handle.net/10498/32538

DOI: 10.55730/1300-0098.3436

ISSN: 1303-6149

ISSN: 1300-0098

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Author/s
Moreno Frías, María ÁngelesAuthority UCA; Rosales, José Carlos
Date
2023
Department
Matemáticas
Source
Turkish Journal of Mathematics, Vol. 47, Núm. 5, 2023, pp. 1392-1405
Abstract
A covariety is a nonempty family C of numerical semigroups that satisfies a certain conditions. In this work we will show that if F is a positive integer, then the set of Arf numerical semigroup with Frobenius number F, denoted by Arf(F), is a covatiety. The previous results will be used to give an algorithm which calculates the set Arf(F). Also we will see that if X ⊆ S\Δ(F) for some S ∈ Arf(F), then there is the smallest element of Arf(F) containing X.
Subjects
algorithm; Arf numerical semigroup; Arf-sequence; covariety; Frobenius number; multiplicity; Numerical semigroup
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