  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.
