… ⧢ v for some word v, the word u is called a shuffled-square. A word u is shuffled-square-free
if it … First, we prove that there exist arbitrarily long shuffled-square-free words in any alphabet …

… For instance, using the above-mentioned three involutions π 1 , π 2 , and π 3 , we can
see that the word 1 is related to two words, 1 and 2, the word 12 is related to four …

… proving avoidance results in combinatorics on words. Namely, we analyze variants of a
simple algorithm that transforms an input word into a word avoiding repetitions of prescribed type…

… We investigate the maximum length of twins in a random word over a k-letter … word of length
n contains twins of length at least 0.34n. Our main result states that in a random ternary word …