%0 Journal Article 
%A Moreno Frías, María Ángeles
%A Rosales, José Carlos
%T Counting the Ideals with a Given Genus of a Numerical Semigroup with Multiplicity Two
%D 2021
%@ 2073-8994
%U http://hdl.handle.net/10498/25138
%X 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 Delta(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(Delta(k))+h for some nonnegative integer h and which we will denote by i(Delta(k),h). As a consequence, we obtain that the sequence {i(Delta(k),h)}(h is an element of N) is never decreasing. Besides, it becomes stationary from a certain term.
%K numerical semigroup
%K symmetric numerical semigroup
%K ideal
%K I(S)-semigroup
%K genus
%~ Universidad de Cádiz