Geodesic
Random generation of subgroups of the modular group with a fixed isomorphism type
Frédérique Bassino1 ; Cyril Nicaud2 ; Pascal Weil3
1Universit\'e Sorbonne Paris Nord, LIPN
2LIGM, Univ Gustave Eiffel
3CNRS
The electronic journal of combinatorics, Tome 31 (2024) no. 4
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

We show how to efficiently count and generate uniformly at random finitely generated subgroups of the modular group $\textsf{PSL}(2,\mathbb{Z})$ of a given isomorphism type. The method to achieve these results relies on a natural map of independent interest, which associates with any finitely generated subgroup of $\textsf{PSL}(2,\mathbb{Z})$ a graph which we call its silhouette, and which can be interpreted as a conjugacy class of free finite index subgroups of $\textsf{PSL}(2,\mathbb{Z})$.
DOI : 10.37236/12559
Classification : 05A15, 05A16, 05C30, 20H25, 20-04
Mots-clés : modular group, random generation, algorithms in group theory

Frédérique Bassino  1   ; Cyril Nicaud  2   ; Pascal Weil  3

1 Universit\'e Sorbonne Paris Nord, LIPN
2 LIGM, Univ Gustave Eiffel
3 CNRS 
@article{10_37236_12559,
     author = {Fr\'ed\'erique Bassino and Cyril Nicaud and Pascal Weil},
     title = {Random generation of subgroups of the modular group with a fixed isomorphism type},
     journal = {The electronic journal of combinatorics},
     year = {2024},
     volume = {31},
     number = {4},
     doi = {10.37236/12559},
     zbl = {1552.05016},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/12559/}
}
TY  - JOUR
AU  - Frédérique Bassino
AU  - Cyril Nicaud
AU  - Pascal Weil
TI  - Random generation of subgroups of the modular group with a fixed isomorphism type
JO  - The electronic journal of combinatorics
PY  - 2024
VL  - 31
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.37236/12559/
DO  - 10.37236/12559
ID  - 10_37236_12559
ER  - 
%0 Journal Article
%A Frédérique Bassino
%A Cyril Nicaud
%A Pascal Weil
%T Random generation of subgroups of the modular group with a fixed isomorphism type
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/12559/
%R 10.37236/12559
%F 10_37236_12559
Frédérique Bassino; Cyril Nicaud; Pascal Weil. Random generation of subgroups of the modular group with a fixed isomorphism type. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12559

Cité par Sources :