  Super-strong (elsewhere referred to as strong) Wilf equivalence is a type of
Wilf equivalence on words that was introduced by Kitaev et al. in 2009. We
provide a necessary and sufficient condition for two permutations in $n$
letters to be super-strongly Wilf equivalent, using distances between letters
within a permutation. Furthermore, we give a characterization of such
equivalence classes via two-colored binary trees. This allows us to prove, in
the case of super-strong Wilf equivalence, the conjecture stated in (Kitaev et
al., 2009) that the cardinality of each Wilf equivalence class is a power of 2.
