Geodesic
Semigroups with fixed multiplicity and embedding dimension
Ars Mathematica Contemporanea, Tome 17 (2019) no. 2, pp. 397-417.

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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.
DOI : 10.26493/1855-3974.1937.5ea
Keywords: Embedding dimension, Frobenius number, genus, multiplicity, numerical semigroup 
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Juan Ignacio Garcı́a-Garcı́a; Daniel Marı́n-Aragón; María Ángeles Moreno-Frías; José Carlos Rosales; Alberto Vigneron-Tenorio. Semigroups with fixed multiplicity and embedding dimension. Ars Mathematica Contemporanea, Tome 17 (2019) no. 2, pp. 397-417. doi : 10.26493/1855-3974.1937.5ea. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1937.5ea/

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