%0 Journal Article 
%A García García, Juan Ignacio
%A Marín Aragón, Daniel
%A Moreno Frías, María Ángeles
%A Rosales, José Carlos
%A Vigneron Tenorio, Alberto
%T Semigroups with fixed multiplicity and embedding dimension
%D 2019
%@ 1855-3966

%U http://hdl.handle.net/10498/21965
%X Given m is an element of N, a numerical semigroup with multiplicity m is called a packed numerical semigroup if its minimal generating set is included in {m, m + 1 , ..., 2m - 1}. In this work, packed numerical semigroups are used to build the set of numerical semigroups with a given multiplicity and embedding dimension, and to create a partition of this set. Wilf's conjecture is verified in the tree associated to some packed numerical semigroups. Furthermore, given two positive integers m and e, some algorithms for computing the minimal Frobenius number and minimal genus of the set of numerical semigroups with multiplicity m and embedding dimension e are provided. We also compute the semigroups where these minimal values are achieved.
%K Embedding dimension
%K multiplicity
%K numerical semigroup
%K Frobenius number
%K genus
%~ Universidad de Cádiz