%0 Journal Article 
%A Moreno Frías, María Ángeles
%A Rosales, José Carlos
%T Counting the ideals with given genus of a numerical semigroup
%D 2023
%@ 0219-4988
%U http://hdl.handle.net/10498/35496
%X If S is a numerical semigroup, denote by g(S) the genus of S. A numerical semigroup
T is an I(S)-semigroup if T\{0} is an ideal of S. If k ∈ N, then we denote by i(S, k)
the number of I(S)-semigroups with genus g(S) + k. In this work, we conjecture that
i(S, a) ≤ i(S, b) if a ≤ b, and we show that there is a term from which this sequence
becomes stationary. That is, there exists kS ∈ N such that i(S, kS) = i(S, kS + h)
for all h ∈ N. Moreover, we prove that the conjecture is true for ordinary numerical
semigroups, that is, numerical semigroups which the form {0,m,→} for some positive
integer. Additionally, we calculate the term from which the sequence becomes stationary.
%K Numerical semigroup
%K ideal
%K I(S)-semigroup
%K Frobenius number
%K genus
%K multiplicity
%K genus
%K ordinary semigroup
%~ Universidad de Cádiz