PublisherSociety for Industrial and Applied Mathematics
Rights accessRestricted access - publisher's policy
We study and compare two natural distributions of
finitely generated subgroups of free groups. One is
based on the random generation of tuples of reduced
words; that is the one classically used by group theorists.
The other relies on Stallings’ graphical representation
of subgroups and in spite of its naturality, it was
only recently considered. The combinatorial structures
underlying both distributions are studied in this paper
with methods of analytic combinatorics. We use these
methods to point out the differences between these
distributions. It is particularly interesting that certain
important properties of subgroups that are generic in
one distribution, turn out to be negligible in the other.
CitationBassino, F. [et al.]. On two distributions of subgroups of free groups. A: Workshop on Analytic Algorithmics and Combinatorics. "Proceedings of the Seventh Workshop on Analytic Algorithmics and Combinatorics (ANALCO)". Austin, Texas: Society for Industrial and Applied Mathematics, 2010, p. 82-89.
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