Semigroups with fixed multiplicity and embedding dimension
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Drustvo Matematikov, Fizikov in Astronomov
Embedding dimensionFrobenius numberGenusMultiplicityNumerical semigroup
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.
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.