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 - http://www.scopus.com/inward/record.url?scp=84975706586&partnerID=8YFLogxK
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U2 - 10.1007/978-3-7643-9911-5_4
DO - 10.1007/978-3-7643-9911-5_4
M3 - Conference contribution
AN - SCOPUS:84975706586
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
T2 - International Conference on Combinatorial and Geometric Group Theory with Applications, GAGTA 2007
Y2 - 27 August 2007 through 31 August 2007
ER -