A Dyck tiling of a skew Young diagram is a partition of the
diagram into 'tiles' which resemble Dyck paths. We examine two
particular types of Dyck tilings, and show how the enumeration of these
tilings gives certain change-of-basis coefficients for a permutation
module for the symmetric group. This is motivated by the new graded
representation theory of the symmetric group (and in particular the
homogeneous Garnir relations for graded Specht modules) but I probably
won't have time to explain this.