33 citations · 35 across the 6 of their papers we have counts for
6 papers · 1 filter
Measuring cones and other thick subsets in free groups
Elizaveta Frenkel, Vladimir N. Remeslennikov
In this paper we investigate the special automata over finite rank free groups and estimate asymptotic characteristics of sets they accept. We show how one can decompose an arbitra…
Knapsack problems in products of groups
Elizaveta Frenkel, Andrey Nikolaev, Alexander Ushakov
The classic knapsack and related problems have natural generalizations to arbitrary (non-commutative) groups, collectively called knapsack-type problems in groups. We study the eff…
The subgroup membership problem in amalgamated products of finitely generated free groups
Andrew Duncan, Elizaveta Frenkel
Stallings folding theory is modified, using double coset representatives, and to applied to the study of subgroups of amalgamated products of finite rank free groups. As a first ap…
Double cosets in free groups
Elizaveta Frenkel, Vladimir N. Remeslennikov
In this paper we study double cosets of finite rank free groups. We focus our attention on cancellation types in double cosets and their formal language properties.
Commutators cannot be proper powers in metric small-cancellation torsion-free groups
Elizaveta Frenkel, Anton A. Klyachko
A nontrivial commutator cannot be a proper power in a torsion-free group satisfying C'(λ) small cancellation condition with sufficiently small λ.
Regular sets and counting in free groups
Elizaveta Frenkel, Alexei G. Myasnikov, Vladimir N. Remeslennikov
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…