On the genericity of Whitehead minimality
Group Theory
2018-04-25 v2 Computational Complexity
Combinatorics
Abstract
We show that a finitely generated subgroup of a free group, chosen uniformly at random, is strictly Whitehead minimal with overwhelming probability. Whitehead minimality is one of the key elements of the solution of the orbit problem in free groups. The proofs strongly rely on combinatorial tools, notably those of analytic combinatorics. The result we prove actually depends implicitly on the choice of a distribution on finitely generated subgroups, and we establish it for the two distributions which appear in the literature on random subgroups.
Keywords
Cite
@article{arxiv.1312.4510,
title = {On the genericity of Whitehead minimality},
author = {Frédérique Bassino and Cyril Nicaud and Pascal Weil},
journal= {arXiv preprint arXiv:1312.4510},
year = {2018}
}