  Given a permutation w, we look at the range of how often a simple reflection
s_k appears in reduced decompositions of w. We compute the minimum and give a
sharp upper bound on the maximum. That bound is in terms of 321- and
3412-patterns in w, specifically as they relate in value and position to k. We
also characterize when that minimum and maximum are equal, refining a previous
result that braid moves are equivalent to 321-patterns.
