  In 1977 Stanley conjectured that the $h$-vector of a matroid independence
complex is a pure $O$-sequence. In this paper we use lexicographic shellability
for matroids to motivate a combinatorial strengthening of Stanley's conjecture.
This suggests that a pure $O$-sequence can be constructed from combinatorial
data arising from the shelling. We then prove that our conjecture holds for
matroids of rank at most four, settling the rank four case of Stanley's
conjecture. In general, we prove that if our conjecture holds for all rank $d$
matroids on at most $2d$ elements, then it holds for all matroids.
