2 citations · 4 across the 4 of their papers we have counts for
4 papers
On the Bethe-Sommerfeld conjecture for periodic Maxwell operators
Mariya Vorobets
The Bethe-Sommerfeld conjecture states that the spectrum of the stationary Schrodinger operator with a periodic potential in dimensions higher than 1 has only finitely many gaps. A…
Automata over a binary alphabet generating free groups of even rank
Benjamin Steinberg, Mariya Vorobets, Yaroslav Vorobets
We construct automata over a binary alphabet with states, , whose states freely generate a free group of rank . Combined with previous work, this shows that a fre…
On a series of finite automata defining free transformation groups
Mariya Vorobets, Yaroslav Vorobets
We introduce two series of finite automata starting from the so-called Aleshin and Bellaterra automata. We prove that each automaton in the first series defines a free non-Abelian…
On a free group of transformations defined by an automaton
Mariya Vorobets, Yaroslav Vorobets
We prove that three automorphisms of the rooted binary tree defined by a certain 3-state automaton generate a free non-Abelian group of rank 3.