Given m ∈ 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
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivatives 4.0 Internacional