Random generation of subgroups of the modular group with a fixed isomorphism type
Résumé
We show how to efficiently count and generate uniformly at random finitely generated subgroups of the modular group PSL 2 (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 PSL 2 (Z) a graph which we call its silhouette, and which can be interpreted as a conjugacy class of free finite index subgroups of PSL 2 (Z).
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