  A permutation \tau contains another permutation \sigma as a pattern if \tau
has a subsequence whose elements are in the same order with respect to size as
the elements in \sigma. This defines a partial order on the set of all
permutations, and gives a graded poset P. We give a large class of pairs of
permutations whose intervals in P have Mobius function 0. Also, we give a
solution to the problem when \sigma occurs precisely once in \tau, and \sigma
and \tau satisfy certain further conditions, in which case the Mobius function
is shown to be either -1, 0 or 1. We conjecture that for intervals
[\sigma,\tau] consisting of permutations avoiding the pattern 132, the
magnitude of the Mobius function is bounded by the number of occurrences of
\sigma in \tau. We also conjecture that the Mobius function of the interval
[1,\tau] is -1, 0 or 1.
