20 citations · 86 across the 21 of their papers we have counts for
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Constructing Premaximal Binary Cube-free Words of Any Level
Elena A. Petrova, Arseny M. Shur
We study the structure of the language of binary cube-free words. Namely, we are interested in the cube-free words that cannot be infinitely extended preserving cube-freeness. We s…
On Pansiot Words Avoiding 3-Repetitions
Irina A. Gorbunova, Arseny M. Shur
The recently confirmed Dejean's conjecture about the threshold between avoidable and unavoidable powers of words gave rise to interesting and challenging problems on the structure…
Fife's Theorem for (7/3)-Powers
Narad Rampersad, Jeffrey Shallit, Arseny Shur
We prove a Fife-like characterization of the infinite binary (7/3)-power-free words, by giving a finite automaton of 15 states that encodes all such words. As a consequence, we cha…
Almost overlap-free words and the word problem for the free Burnside semigroup satisfying x^2=x^3
A. N. Plyushchenko, A. M. Shur
In this paper we investigate the word problem of the free Burnside semigroup satisfying x^2=x^3 and having two generators. Elements of this semigroup are classes of equivalent word…