… In this paper we consider instead the existence of infinite cubefree binary words with
many distinct squares. Most known constructions of infinite cubefree words involve the …

… square-free language; the combinatorial part, presented in [19], is much simpler than for the
cube-free … As a byproduct of the search algorithm, we find “building blocks” to construct an …

… observe that infinite squarefree, overlap-free or cube-free words … square is a word uv, such
that v is a permutation of u. It is known that there exist infinite words without abelian squares …

… of the set of finite cube-free words. This set is large (the number of cube-free words of length
n … The factors (elements of the partition) we will call blocks. A partition of an infinite word is …

… letters creates a square (respectively, overlap, cube). We classify the lengths of irreducible
and delicate squarefree, overlap-free, and cubefree words over binary and ternary alphabets. …

… words he proved the existence of an infinite cube-free … a square-free infinite word. On the
other hand, any word over a binary alphabet and with the length at least four contains a square. …

… of binary cube-free words and ternary square-free words. However, many phenomena related
to power-freeness are still not understood. One group of problems about power-free words …

… -free in the sense of Fraenkel and Simpson, or if x is a strongly cube-free binary word such
… on D for strongly cube-free words in a ternary alphabet, nor for cube-free words in a binary …

… -free or cube-free words indeed … square-containing words is cofinite. Another question
concerns transformations that maintain the separation of squarefree and square-containing words …

… for infinitely many square-free ternary words. But how large this function can be for words of
… ]) that there exist infinitely many cube-free words over a 2-letter alphabet. Is the sequence of …