%0 Journal Article 
%A Moreno Frías, María Ángeles
%A Rosales, José Carlos
%T The covariety of numerical semigroups with fixed Frobenius number
%D 2024
%@ 1572-9192

%U http://hdl.handle.net/10498/35381
%X Denote by m(S) themultiplicity of a numerical semigroup S.A covariety is a nonempty
family C of numerical semigroups that fulfils the following conditions: there is the
minimum of C , the intersection of two elements of C is again an element of C and
S\{m(S)} ∈ C for all S ∈ C such that S  = min(C ). In this work we describe
an algorithmic procedure to compute all the elements of C . We prove that there
exists the smallest element of C containing a set of positive integers. We show that
A (F) = {S | S is a numerical semigroup with Frobenius number F} is a covariety,
and we particularize the previous results in this covariety. Finally, we will see that
there is the smallest covariety containing a finite set of numerical semigroups.
%K Numerical semigroup
%K Covariety
%K Frobenius number
%K Genus
%K Rank
%K Multiplicity
%K Algorithm
%~ Universidad de Cádiz