String attractor, a relatively new combinatorial notion, is closely related to measuring the complexity of words and offers a unified approach to the repetitiveness measures induced by dictionary compressors. However, attractors have been only little studied in the context of combinatorics on words, particularly for classes of low complexity, including complementary-symmetric Rote sequences. In this talk, we work with pseudopalindromic closures as a useful way to generate these sequences, and then show the form of minimal attractors of their pseudopalindromic prefixes.[-]

I recently introduced a new proof technique based on a simple counting argument that I applied to many problems from combinatorics. In this talk, I will illustrate this counting argument with a proof that the Thue choice number is at most 4. Suppose we have to construct a square-free word (ie, no non-empty factors is of the form uu) by chosing the letter of each position of the word from an alphabet specific to the position. The Thue choice number is the smallest k such that, if all these alphabets have size at least k, then we can build an infinite square-free word.
I will then present how it can be pushed further in the context of combinatorics on words.[-]