@misc{10481/94699,
year = {2024},
month = {6},
url = {https://hdl.handle.net/10481/94699},
abstract = {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.},
organization = {Proyecto de Excelencia de la Junta de Andalucía
Grant Number ProyExcel_00868},
organization = {Junta de Andalucía
Grant Number FQM-343},
organization = {Junta de Andalucía Grant
Number FQM-298},
organization = {Proyecto de investigación del Plan Propio—UCA 2022-2023 (PR2022-004)},
publisher = {MDPI},
keywords = {Numerical semigroup},
keywords = {Covariety},
keywords = {Frobenius number},
title = {The Covariety of Saturated Numerical Semigroups with Fixed Frobenius Number},
doi = {10.3390/foundations4020016},
author = {Rosales González, José Carlos and Moreno Frías, María Ángeles},
}