Given a permutation w, Stanley defined a symmetric function $F_w$ which encodes information about the reduced words of w, and showed that $F_w$ is a single Schur function exactly when w avoids the pattern 2143. We generalize this statement, showing that the Schur expansion of $F_w$ respects pattern containment in a certain sense, and that the number of Schur function terms is determined by pattern avoidance conditions on w. Along the way, we compute the cohomology of certain subvarieties of Grassmannians, resolving some cases of a conjecture of Liu. This is joint work with Sara Billey.