Counting the Ideals with a Given Genus of a Numerical Semigroup with Multiplicity Two
Moreno Frías, María Ángeles
Rosales González, José Carlos
Numerical semigroup
Almost symmetric numerical semigroup
Ideal
I(S)-semigroup
Genus
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.
2021-05-04T08:53:58Z
2021-05-04T08:53:58Z
2021
info:eu-repo/semantics/article
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
http://hdl.handle.net/10481/68295
10.3390/sym13050794
eng
http://creativecommons.org/licenses/by/3.0/es/
info:eu-repo/semantics/openAccess
Atribución 3.0 España
MDPI