We show that there exists an infinite word over the alphabet {0,1,3,4} containing no three consecutive blocks of the same size and the same sum. This answers an open problem of Pirillo and Varricchio from1994.

We show that there exist binary circular 5/2+ power free words of every length.

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.

The authors introduce the notion of crown-like orders and introduce powerful tools for counting the endomorphisms of orders of this type.

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 ...

There are circular square-free words of length n on three symbols for n≥18. This proves a conjecture of R. J. Simpson.

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

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 ...

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.