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arXiv · 2310.18923

Random generation of subgroups of the modular group with a fixed isomorphism type

Frédérique Bassino·Cyril Nicaud·Pascal Weil
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Abstract

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 $\textsf{PSL}(2,\mathbb{Z})$.

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Frédérique Bassino, Cyril Nicaud, Pascal Weil. 2023-10-29. Random generation of subgroups of the modular group with a fixed isomorphism type. https://doi.org/10.37236/12559

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