  It is shown that the h-vectors of Stanley-Reisner rings of three classes of
matroids are pure O-sequences. The classes are (a) matroids that are
truncations of other matroids, or more generally of Cohen-Macaulay complexes,
(b) matroids whose dual is (rank + 2)-partite, and (c) matroids of
Cohen-Macaulay type at most five. Consequences for the computational search for
a counterexample to a conjecture of Stanley are discussed.
