  The notion of \emph{string attractor} has recently been introduced in
[Prezza, 2017] and studied in [Kempa and Prezza, 2018] to provide a unifying
framework for known dictionary-based compressors. A string attractor for a word
$w=w[1]w[2]\cdots w[n]$ is a subset $\Gamma$ of the positions $\{1,\ldots,n\}$,
such that all distinct factors of $w$ have an occurrence crossing at least one
of the elements of $\Gamma$. While finding the smallest string attractor for a
word is a NP-complete problem, it has been proved in [Kempa and Prezza, 2018]
that dictionary compressors can be interpreted as algorithms approximating the
smallest string attractor for a given word.
  In this paper we explore the notion of string attractor from a combinatorial
point of view, by focusing on several families of finite words. The results
presented in the paper suggest that the notion of string attractor can be used
to define new tools to investigate combinatorial properties of the words.
