@misc{10498/35414,
year = {2024},
url = {http://hdl.handle.net/10498/35414},
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 fi xed MED(F,m)-rank are.},
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, José Carlos},
}