About the k-binomial equivalence and the associated complexity

In these slides, we present the notions of k-binomial equivalence, and k-binomial complexity. For an arbitrary infinite word w, this function maps every non-negative integer n to the number of length-n factors in w. We then study the values of this function on several well-known infinite words. We finally discuss more deeply the notion of k-binomial equivalence and we rise some interesting open questions.