  We show that f-vectors of matroid complexes of realisable matroids are
log-concave. This was conjectured by Mason in 1972. Our proof uses the recent
result by Huh and Katz who showed that the coefficients of the characteristic
polynomial of a realisable matroid form a log-concave sequence. We also discuss
the relationship between log-concavity of f-vectors and h-vectors of matroids.
In the last section we explain the connection between zonotopal algebra and
f-vectors and characteristic polynomials of matroids.
