RANDOM GENERATION OF FINITELY GENERATED SUBGROUPS OF A FREE GROUP
2008 ◽
Vol 18
(02)
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pp. 375-405
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Keyword(s):
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 [Formula: see text] in the RAM model and [Formula: see text] in the bitcost model.
1986 ◽
Vol 29
(2)
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pp. 204-207
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Keyword(s):
1992 ◽
Vol 42
(3)
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pp. 145-149
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Keyword(s):
Keyword(s):
1997 ◽
Vol 26
(1)
◽
pp. 1-14
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