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- W2007454300 abstract "We give an efficient algorithm to randomly generate finitely generated subgroups of a given size, in a finite rank free group. Here, the size of a subgroup is the number of vertices of its representation by a reduced graph such as can be obtained by the method of Stallings foldings. Our algorithm randomly generates a subgroup of a given size n, according to the uniform distribution over size n subgroups. In the process, we give estimates of the number of size n subgroups, of the average rank of size n subgroups, and of the proportion of such subgroups that have finite index. Our algorithm has average case complexity $O(n)$ in the RAM model and $O(n^2log^2n)$ in the bitcost model." @default.
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- W2007454300 date "2007-07-21" @default.
- W2007454300 modified "2023-09-25" @default.
- W2007454300 title "Random generation of finitely generated subgroups of a free group" @default.
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