Abelian antipowers in infinite words

An abelian antipower of order k (or simply an abelian k-antipower) is a concatenation of k consecutive words of the same length having pairwise distinct Parikh vectors. This definition generalizes to the abelian setting the notion of a k-antipower, as introduced in Fici et al. (2018) [7], that is a concatenation of k pairwise distinct words of the same length. We aim to study whether a word contains abelian k-antipowers for arbitrarily large k. Š. Holub proved that all paperfolding words contain abelian powers of every order (Holub, 2013 [8]). We show that they also contain abelian antipowers of every order.