  In combinatorics of words, a concatenation of $k$ consecutive equal blocks is
called a power of order $k$. In this paper we take a different point of view
and define an anti-power of order $k$ as a concatenation of $k$ consecutive
pairwise distinct blocks of the same length. As a main result, we show that
every infinite word contains powers of any order or anti-powers of any order.
That is, the existence of powers or anti-powers is an unavoidable regularity.
Indeed, we prove a stronger result, which relates the density of anti-powers to
the existence of a factor that occurs with arbitrary exponent. As a
consequence, we show that in every aperiodic uniformly recurrent word,
anti-powers of every order begin at every position. We further show that every
infinite word avoiding anti-powers of order $3$ is ultimately periodic, while
there exist aperiodic words avoiding anti-powers of order $4$. We also show
that there exist aperiodic recurrent words avoiding anti-powers of order $6$.

Discrete Mathematics;Formal Languages and Automata Theory;Combinatorics