TY - GEN
T1 - Regular sets and counting in free groups
AU - Frenkel, Elizaveta
AU - Myasnikov, Alexei G.
AU - Remeslennikov, Vladimir N.
N1 - Publisher Copyright: © 2010 Springer Basel AG.
PY - 2010
Y1 - 2010
N2 - In this paper we study asymptotic behavior of regular subsets in a free group F of finite rank, compare their sizes at infinity, and develop techniques to compute the probabilities of sets relative to distributions on F that come naturally from random walks on the Cayley graph of F. We apply these techniques to study cosets, double cosets, and Schreier representatives of finitely generated subgroups of F with an eye on complexity of algorithmic problems in free products with amalgamation and HNN extensions of groups.
AB - In this paper we study asymptotic behavior of regular subsets in a free group F of finite rank, compare their sizes at infinity, and develop techniques to compute the probabilities of sets relative to distributions on F that come naturally from random walks on the Cayley graph of F. We apply these techniques to study cosets, double cosets, and Schreier representatives of finitely generated subgroups of F with an eye on complexity of algorithmic problems in free products with amalgamation and HNN extensions of groups.
KW - Generic and negligible sets
KW - Geometric group theory
KW - Measures on free groups
KW - Regular set
KW - Schreier transversals
UR - https://www.scopus.com/pages/publications/84975706586
UR - https://www.scopus.com/pages/publications/84975706586#tab=citedBy
U2 - 10.1007/978-3-7643-9911-5_4
DO - 10.1007/978-3-7643-9911-5_4
M3 - Conference contribution
SN - 9783764399108
T3 - Trends in Mathematics
SP - 93
EP - 118
BT - Combinatorial and Geometric Group Theory
A2 - Bogopolski, Oleg
A2 - Bumagin, Inna
A2 - Kharlampovich, Olga
A2 - Ventura, Enric
PB - Springer International Publishing
T2 - International Conference on Combinatorial and Geometric Group Theory with Applications, GAGTA 2007
Y2 - 27 August 2007 through 31 August 2007
ER -