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 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 
@article{10_21136_MB_2023_0038_23,
     author = {Moreno-Fr{\'\i}as, Maria Angeles and Rosales, Jos\'e Carlos},
     title = {The lattice of ideals of a numerical semigroup and its {Frobenius} restricted variety associated},
     journal = {Mathematica Bohemica},
     pages = {439--454},
     year = {2024},
     volume = {149},
     number = {3},
     doi = {10.21136/MB.2023.0038-23},
     mrnumber = {4801112},
     zbl = {07953713},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2023.0038-23/}
}
TY  - JOUR
AU  - Moreno-Frías, Maria Angeles
AU  - Rosales, José Carlos
TI  - The lattice of ideals of a numerical semigroup and its Frobenius restricted variety associated
JO  - Mathematica Bohemica
PY  - 2024
SP  - 439
EP  - 454
VL  - 149
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2023.0038-23/
DO  - 10.21136/MB.2023.0038-23
LA  - en
ID  - 10_21136_MB_2023_0038_23
ER  - 
%0 Journal Article
%A Moreno-Frías, Maria Angeles
%A Rosales, José Carlos
%T The lattice of ideals of a numerical semigroup and its Frobenius restricted variety associated
%J Mathematica Bohemica
%D 2024
%P 439-454
%V 149
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2023.0038-23/
%R 10.21136/MB.2023.0038-23
%G en
%F 10_21136_MB_2023_0038_23
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

Cité par Sources :