Counting the Ideals with a Given Genus of a Numerical Semigroup with Multiplicity Two
Metadatos
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MDPI
Materia
Numerical semigroup Almost symmetric numerical semigroup Ideal I(S)-semigroup Genus
Fecha
2021Referencia bibliográfica
Moreno-Frías, M.A.; Rosales, J.C. Counting the Ideals with a Given Genus of a Numerical Semigroup with Multiplicity Two. Symmetry 2021, 13, 794. https:// doi.org/10.3390/sym13050794
Patrocinador
FQM-298 and FQM-343 (Junta de Andalucia/Feder); Project MTM2017-84890-PResumen
Let S and T be two numerical semigroups. We say that T is an I(S)-semigroup if T\{0} is
an ideal of S. Given k a positive integer, we denote by ∆(k) the symmetric numerical semigroup
generated by {2, 2k + 1}. In this paper we present a formula which calculates the number of I(S)-
semigroups with genus g(∆(k)) + h for some nonnegative integer h and which we will denote
by i(∆(k), h). As a consequence, we obtain that the sequence {i(∆(k), h)}h∈N is never decreasing.
Besides, it becomes stationary from a certain term.