Semigroups with fixed multiplicity and embedding dimension García García, Juan Ignacio Rosales González, José Carlos Embedding dimension Frobenius number Genus Multiplicity Numerical semigroup Given m E N, a numerical semigroup with multiplicity m is called a packed numerical semigroup if its minimal generating set is included in fm;m + 1,...., 2m - 1g. 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. 2019-12-05T11:52:01Z 2019-12-05T11:52:01Z 2019-11-04 info:eu-repo/semantics/article Garcı́a-Garcı́a, J. I., Marı́n-Aragón, D., Moreno-Frías, M. Á., Rosales, J. C., & Vigneron-Tenorio, A. (2019). Semigroups with fixed multiplicity and embedding dimension. ARS MATHEMATICA CONTEMPORANEA, 17(2), 397-417. http://hdl.handle.net/10481/58215 10.26493/1855-3974.1937.5ea eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España Drustvo Matematikov, Fizikov in Astronomov