@misc{10481/105825,
year = {2024},
month = {9},
url = {https://hdl.handle.net/10481/105825},
abstract = {In this paper we will show that MED(F, m) = {S | S is a numerical semigroup with maximal embedding dimension, Frobenius number F and
multiplicity m} is a ratio-covariety. As a consequence, we present two algorithms: one that computes MED(F, m) and another one that calculates the
elements of MED(F, m) with a given genus.
If X ⊆ S\(⟨m⟩∪{F +1, →}) for some S ∈ MED(F, m), then there exists the
smallest element of MED(F, m) containing X. This element will be denoted by
MED(F, m)[X] and we will say that X one of its MED(F, m)-system of generators. We will prove that every element S of MED(F, m) has a unique minimal
MED(F, m)-system of generators and it will be denoted by MED(F, m)msg(S).
The cardinality of MED(F, m)msg(S), will be called MED(F, m)-rank of S.
We will also see in this work, how all the elements of MED(F, m) with a fixed
MED(F, m)-rank are.},
organization = {Junta de Andalucía (ProyExcel 00868; FQM-298; FQM-343)},
publisher = {International Electronic Journal of Algebra},
keywords = {Numerical semigroup},
keywords = {Ratio-covariety},
keywords = {Frobenius number},
keywords = {Genus},
keywords = {Multiplicity},
keywords = {Algorithm},
title = {The ratio-covariety of numerical semigroups having maximal embedding dimension with fixed multiplicity and Frobenius number},
doi = {10.24330/ieja.1575996},
author = {Moreno Frías, María Ángeles and Rosales González, José Carlos},
}