Abelian Anti-Powers in Infinite Words
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An abelian anti-power of order k (or simply an abelian k-anti-power) 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-anti-power, as introduced in [G. Fici et al., Anti-powers in infinite words, J. Comb. Theory, Ser. A, 2018], that is a concatenation of k pairwise distinct words of the same length. We aim to study whether a word contains abelian k-anti-powers for arbitrarily large k. S. Holub proved that all paperfolding words contain abelian powers of every order [Abelian powers in paper-folding words. J. Comb. Theory, Ser. A, 2013]. We show that they also contain abelian anti-powers of every order.
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