Random generation of subgroups of the modular group with a fixed isomorphism type
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915053854261248 |
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| author | Bassino, Frédérique Nicaud, Cyril Weil, Pascal |
| author_facet | Bassino, Frédérique Nicaud, Cyril Weil, Pascal |
| contents | 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 $\textsf{PSL}(2,\mathbb{Z})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18923 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Random generation of subgroups of the modular group with a fixed isomorphism type Bassino, Frédérique Nicaud, Cyril Weil, Pascal Group Theory Combinatorics 20E07, 20F69, 05A15, 05E16, 05C30 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 $\textsf{PSL}(2,\mathbb{Z})$. |
| title | Random generation of subgroups of the modular group with a fixed isomorphism type |
| topic | Group Theory Combinatorics 20E07, 20F69, 05A15, 05E16, 05C30 |
| url | https://arxiv.org/abs/2310.18923 |