  Savage and Sagan have recently defined a notion of st-Wilf equivalence for
any permutation statistic st and any two sets of permutations $\Pi$ and $\Pi'$.
In this paper we give a thorough investigation of st-Wilf equivalence for the
charge statistic on permutations and use a bijection between the charge
statistic and the major index to prove a conjecture of Dokos, Dwyer, Johnson,
Sagan and Selsor regarding powers of 2 and the major index.
