9 citations · 25 across the 14 of their papers we have counts for
5 papers · 2 filters
Implicit function theorem over free groups
O. Kharlampovich, A. Miasnikov
We introduce the notion of a regular quadratic equation and a regular NTQ system over a free group. We prove the results that can be described as Implicit function theorems for alg…
Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture
Alexei D. Miasnikov, Alexei G. Myasnikov
The Andrews-Curtis conjecture states that every balanced presentation of the trivial group can be reduced to the standard one by a sequence of the elementary Nielsen transformation…
Whitehead method and Genetic Algorithms
Alexei D. Miasnikov, Alexei G. Myasnikov
In this paper we discuss a genetic version (GWA) of the Whitehead's algorithm, which is one of the basic algorithms in combinatorial group theory. It turns out that GWA is surprisi…
On the Andrews-Curtis equivalence
Alexei D. Myasnikov, Alexei G. Myasnikov, Vladimir Shpilrain
The Andrews-Curtis conjecture claims that every balanced presentation of the trivial group can be reduced to the standard one by a sequence of ``elementary transformations" which a…
Foldings, graphs of groups and the membership problem
Ilya Kapovich, Richard Weidmann, Alexei Myasnikov
We introduce a combinatorial version of Stallings-Bestvina-Feighn-Dunwoody folding sequences. We then show how they are useful in analyzing the solvability of the uniform subgroup…