%0 Journal Article 
%A Moreno Frías, María Ángeles
%A Rosales, José Carlos
%T The set of Arf numerical semigroups with given Frobenius number
%D 2023
%@ 1303-6149

%U http://hdl.handle.net/10498/32538
%X 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.
%K algorithm
%K Arf numerical semigroup
%K Arf-sequence
%K covariety
%K Frobenius number
%K multiplicity
%K Numerical semigroup
%~ Universidad de Cádiz