We answer a question of Harju: For every n ≥ 3 there is a square-free ternary word of length n with a square-free self-shuffle.

We study the combinatorics of vtm, a variant of the Thue-Morse word generated by the non-uniform morphism 0 ↦ 012, 1 ↦ 02, 2 ↦ 1 starting with 0. This infinite ternary sequence appears a lot in the literature and finds ...

We present an infinite family of formulas with reversal whose avoidability index is bounded between 4 and 5, and we show that several members of the family have avoidability index 5. This family is particularly interesting ...

For every pattern p over the alphabet {x,x^R,y,y^R}, we specify the least k such that p is k-avoidable.

Given an infinite word x over an alphabet A, a letter b occurring in x, and a total order \sigma on A, we call the smallest word with respect to \sigma starting with b in the shift orbit closure of x an extremal word of ...

In previous work, Currie and Rampersad showed that the growth of the number of binary words avoiding the pattern xxxR was intermediate between polynomial and exponential. We now show that the same result holds for the ...

Strings (aka sequences or words) form the most basic and natural data structure. They occur whenever information is electronically transmitted (as bit streams), when natural language text is spoken or written down (as words ...

We characterize exactly the lengths of binary circular words containing no squares other than 00, 11, and 0101.

While a characterization of unavoidable formulas (without reversal) is well-known, little is known about the avoidability of formulas with reversal in general. In this article, we characterize the unavoidable formulas ...

We construct infinite cubefree binary words containing exponentially many distinct squares of length n . We also show that for every positive integer n , there is a cubefree binary square of length 2n.