  We give a solution to a problem posed by Corteel and Nadeau concerning
permutation tableaux of length n and the number of occurrences of the dashed
pattern 32--1 in permutations on [n]. We introduce the inversion number of a
permutation tableau. For a permutation tableau T and the permutation $\pi$
obtained from T by the bijection of Corteel and Nadeau, we show that the
inversion number of T equals the number of occurrences of the dashed pattern
32--1 in the reverse complement of $\pi$. We also show that permutation
tableaux without inversions coincide with L-Bell tableaux introduced by Corteel
and Nadeau.
