  In 2000, Babson and Steingr\'imsson introduced the notion of what is now
known as a permutation vincular pattern, and based on it they re-defined known
Mahonian statistics and introduced new ones, proving or conjecturing their
Mahonity. These conjectures were proved by Foata and Zeilberger in 2001, and by
Foata and Randrianarivony in 2006.
  In 2010, Burstein refined some of these results by giving a bijection between
permutations with a fixed value for the major index and those with the same
value for STAT, where STAT is one of the statistics defined and proved to be
Mahonian in the 2000 Babson and Steingr\'imsson's paper. Several other
statistics are preserved as well by Burstein's bijection.
  At the Formal Power Series and Algebraic Combinatorics Conference (FPSAC) in
2010, Burstein asked whether his bijection has other interesting properties. In
this paper, we not only show that Burstein's bijection preserves the Eulerian
statistic ides, but also use this fact, along with the bijection itself, to
prove Mahonity of the statistic STAT on words we introduce in this paper. The
words statistic STAT introduced by us here addresses a natural question on
existence of a Mahonian words analogue of STAT on permutations. While proving
Mahonity of our STAT on words, we prove a more general joint equidistribution
result involving two six-tuples of statistics on (dense) words, where
Burstein's bijection plays an important role.
