@misc{10498/21965,
year = {2019},
url = {http://hdl.handle.net/10498/21965},
abstract = {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.},
publisher = {UP FAMNIT},
keywords = {Embedding dimension},
keywords = {multiplicity},
keywords = {numerical semigroup},
keywords = {Frobenius number},
keywords = {genus},
title = {Semigroups with fixed multiplicity and embedding dimension},
doi = {10.26493/1855-3974.1937.5ea},
author = {García García, Juan Ignacio and Marín Aragón, Daniel and Moreno Frías, María Ángeles and Rosales, José Carlos and Vigneron Tenorio, Alberto},
}