  In this paper we study a mapping from permutations to Dyck paths. A Dyck path
gives rise to a (Young) diagram and we give relationships between statistics on
permutations and statistics on their corresponding diagrams. The distribution
of the size of this diagram is discussed and a generalisation given of a parity
result due to Simion and Schmidt. We propose a filling of the diagram which
determines the permutation uniquely. Diagram containment on a restricted class
of permutations is shown to be related to the strong Bruhat poset.
