The Covariety of Saturated Numerical Semigroups with Fixed Frobenius Number Rosales González, José Carlos Moreno Frías, María Ángeles Numerical semigroup Covariety Frobenius number 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. 2024-09-19T07:57:30Z 2024-09-19T07:57:30Z 2024-06-03 journal article Rosales, J.C.; Moreno-Frías, M.Á. The Covariety of Saturated Numerical Semigroups with Fixed Frobenius Number. Foundations 2024, 4, 249–262. https://doi.org/10.3390/foundations4020016 https://hdl.handle.net/10481/94699 10.3390/foundations4020016 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional MDPI