%0 Journal Article 
%A Rosales, José Carlos
%A Moreno Frías, María Ángeles
%T The Covariety of Saturated Numerical Semigroups with Fixed Frobenius Number
%D 2024
%U http://hdl.handle.net/10498/35409
%X In this work, we show that if F is a positive integer, then Sat(F) = {S | S is a saturated numerical
semigroup with Frobenius number F} is a covariety. As a consequence, we present two
algorithms: one that computes Sat(F), and another which computes all the elements of Sat(F) with
a fixed genus. If X ⊆ S\Δ(F) for some S ∈ Sat(F), then we see that there exists the least element
of Sat(F) containing X. This element is denoted by Sat(F)[X]. If S ∈ Sat(F), then we define the
Sat(F)-rank of S as the minimum of {cardinality(X) | S = Sat(F)[X]}. In this paper, we present an
algorithm to compute all the elements of Sat(F) with a given Sat(F)-rank.
%K Numerical semigroup
%K covariety
%K Frobenius number
%K genus
%K saturated numerical semigroup
%K algorithm
%~ Universidad de Cádiz