Geodesic
The lattice of ideals of a numerical semigroup and its Frobenius restricted variety associated
Mathematica Bohemica, Tome 149 (2024) no. 3, pp. 439-454
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Let $\Delta $ be a numerical semigroup. In this work we show that $\mathcal {J}(\Delta ) =\{I\cup \nobreak \{0\}\colon I \mbox { is an ideal of } \Delta \}$ is a distributive lattice, which in addition is a Frobenius restricted variety. We give an algorithm which allows us to compute the set $\mathcal {J}_a(\Delta )=\{S\in \mathcal {J}(\Delta )\colon \max (\Delta \backslash S)=a\}$ for a given $a\in \Delta .$ As a consequence, we obtain another algorithm that computes all the elements of $\mathcal {J}(\Delta )$ with a fixed genus.
Let $\Delta $ be a numerical semigroup. In this work we show that $\mathcal {J}(\Delta ) =\{I\cup \nobreak \{0\}\colon I \mbox { is an ideal of } \Delta \}$ is a distributive lattice, which in addition is a Frobenius restricted variety. We give an algorithm which allows us to compute the set $\mathcal {J}_a(\Delta )=\{S\in \mathcal {J}(\Delta )\colon \max (\Delta \backslash S)=a\}$ for a given $a\in \Delta .$ As a consequence, we obtain another algorithm that computes all the elements of $\mathcal {J}(\Delta )$ with a fixed genus.
DOI : 10.21136/MB.2023.0038-23
Classification : 11Y16, 20M14
Keywords: numerical semigroup; ideal; Frobenius restricted variety; embedding dimension; Frobenius number; restricted Frobenius number; genus; multiplicity; Arf numerical semigroup; saturated semigroup 
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Moreno-Frías, Maria Angeles; Rosales, José Carlos. The lattice of ideals of a numerical semigroup and its Frobenius restricted variety associated. Mathematica Bohemica, Tome 149 (2024) no. 3, pp. 439-454. doi: 10.21136/MB.2023.0038-23

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